The Early Generations of Rotating Massive Stars and the Origin of   Carbon-Enhanced Metal-Poor Stars

Arthur Choplin

arXiv:1901.10708·astro-ph.SR·January 31, 2019

The Early Generations of Rotating Massive Stars and the Origin of Carbon-Enhanced Metal-Poor Stars

Arthur Choplin

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TL;DR

This paper investigates the role of early rotating massive stars in the universe's chemical evolution by modeling their evolution and nucleosynthesis, and comparing results with observations of ancient, metal-poor stars.

Contribution

It combines stellar evolution models with nucleosynthesis and observational data to explore the origins of CEMP stars and the physics of early massive stars.

Findings

01

Rotating massive star models can reproduce observed CEMP star abundances.

02

Rotation significantly influences nucleosynthesis yields in early massive stars.

03

The results support a link between early massive stars and the formation of CEMP stars.

Abstract

The study of the long-dead early generations of massive stars is crucial in order to obtain a complete picture of the chemical evolution of the Universe, hence the origin of the elements. The nature of these stars can be inferred indirectly by investigating the origin of low-mass metal-poor stars observed in our Galaxy, some of which are almost as old as the Universe. The peculiar extremely iron-poor Carbon-Enhanced Metal-Poor (CEMP) stars, whose precise origin is still debated, are thought to have formed with the material ejected by only one or very few previous massive stars. The main aim of this thesis is to explore the physics and the nucleosynthesis of the early generations of massive stars. It is achieved by combining stellar evolution modeling including rotation and full nucleosynthesis with observations of CEMP stars.

Tables9

Table 1. Table 2.1: Nomenclature for stars of different metallicites, as defined in Beers & Christlieb ( 2005 ) . The last column is the number of Milky Way stars observed below the given [Fe/H] ratio (numbers are from the SAGA database). For the MMP class, the recently discovered star J0023+0307, with [Fe/H] < − 6.6 absent 6.6 <-6.6 ( Aguado et al. 2018 ) , was added since not in SAGA yet.

[Fe/H]	Term	Acronym	N
$< - 1$	Metal-poor	MP	$> 500$
$< - 2$	Very Metal-poor	VMP	$> 500$
$< - 3$	Extremely Metal-poor	EMP	499
$< - 4$	Ultra Metal-poor	UMP	29
$< - 5$	Hyper Metal-poor	HMP	5
$< - 6$	Mega Metal-poor	MMP	2

Table 2. Table 2.2: Classification of CEMP stars, as defined in Beers & Christlieb ( 2005 ) .

Term	Conditions
CEMP	[C/Fe] $> 1.0$
CEMP-r	[C/Fe] $> 1.0$ [Eu/Fe] $> 1.0$
CEMP-s	[C/Fe] $> 1.0$ [Ba/Fe] $> 1.0$ [Ba/Eu] $> 0.5$
CEMP-r/s	[C/Fe] $> 1.0$ $0.0 <$ [Ba/Eu] $< 0.5$
CEMP-no	[C/Fe] $> 1.0$ [Ba/Fe] $< 0$

Table 3. Table 4.1: Effect of diluting the source star ejecta with two different kinds of ISM: metal-poor and metal-free. Different kinds of abundance ratios are considered. X refers to metals.

	[X/H]	[X/Fe]	isotopic ratios
Metal-poor ISM	towards ISM value	towards ISM value	towards ISM value
Metal-free ISM	towards ISM value	unchanged	unchanged

Table 4. Table 4.2: Stars with [Fe/H] < − 3 absent 3 <-3 and [C/Fe] > 1 absent 1 >1 . [C/Fe] is corrected from Δ Δ \Delta [C/Fe] (also reported in the table), that accounts for the effect of the first dredge-up ( Placco et al. 2014c ) . Recognized CEMP-s, -r/s and -r stars are excluded. Abundance data is from the SAGA database ( Suda et al. 2008 ) . When multiple abundances exist for a star, the abundance from the most recent literature source is selected.

Star	$T_{eff}$	$\log g$	[Fe/H]	A(Li)	[C/Fe]	[N/Fe]	[O/Fe]	[Na/Fe]	[Mg/Fe]	[Al/Fe]	[Si/Fe]	¹²C/¹³C	$Δ$ [C/Fe]	Ref
BD+44_493	5430	3.4	-3.8	0.64	1.23	$<$ 2.2	1.54	0.3	0.89	-0.44	0.48	$>$ 15.0	0.0	1,2,3
CS22877-001	4790	1.45	-3.24	0.66	1.54	-0.08	1.22	-	0.38	-0.73	-	35.0	0.44	2
CS22891-200	4490	0.5	-3.88	$<$ 0.13	1.26	1.38	$<$ 1.67	0.29	0.82	-0.37	1.05	$>$ 6.0	0.73	2,4
CS22897-008	4550	0.7	-3.73	0.77	1.05	0.05	$<$ 1.86	-0.05	0.6	-0.77	0.46	$>$ 20.0	0.45	5,6,7
CS22949-037	4630	0.95	-4.2	$<$ 0.13	1.9	2.67	$<$ 2.39	1.89	1.56	0.26	1.52	$>$ 4.0	0.74	5,8,2
CS22950-046	4380	0.5	-3.64	$<$ -0.05	1.13	1.13	$<$ 2.39	-0.18	0.58	-0.63	1.08	-	0.52	5,4
CS22953-037	6150	3.7	-3.05	1.97	1.0	$<$ 2.18	$<$ 0.5	-	0.55	-0.56	0.21	-	0.0	5
CS22957-027	5220	2.65	-3.0	$<$ 0.86	2.63	1.69	$<$ 1.2	0.98	0.08	-0.12	-	6.0	0.02	2
CS22960-053	4860	1.65	-3.33	$<$ 0.55	1.42	3.41	-	-	0.77	0.51	-	-	0.02	5
CS29498-043	4440	0.5	-3.85	$<$ -0.05	3.06	1.74	2.37	1.03	1.78	0.75	1.08	8.0	0.31	2
CS29502-092	4820	1.5	-3.2	$<$ 0.45	1.45	1.1	1.13	-0.02	0.5	-0.6	-	12.0	0.39	2
CS29527-015	6240	4.0	-3.55	2.091	1.29	-	-	-0.19	0.41	0.07	0.18	-	0.0	9,10,11,12,13,14
CS29528-041	6170	4.0	-3.06	1.71	1.57	3.04	$<$ 1.38	0.67	0.38	-0.38	-0.16	-	0.0	12,15
G77-61	4000	5.1	-4.0	$<$ 3.31	3.21	2.2	1.82	0.77	0.56	-	-	5.0	0.0	16,17
HE0015+0048	4600	0.9	-3.07	$<$ 0.92	1.29	-	-	-	0.66	-0.37	0.5	-	0.67	18
HE0017-4346	6198	3.8	-3.07	-	3.11	-	-	1.51	0.87	0.03	-	-	0.0	8
HE0102-0633	6012	3.7	-3.1	-	1.08	-	-	$<$ 1.06	0.44	-0.27	0.32	-	0.0	8
HE0107-5240	5100	2.2	-5.4	$<$ 1.12	3.88	2.54	2.54	1.06	0.25	$<$ -0.08	$<$ 0.48	$>$ 50.0	0.06	19,20
HE0134-1519	5500	3.2	-4.0	1.27	1.0	$<$ 1.0	$<$ 2.9	-0.24	0.25	-0.38	0.05	$>$ 4.0	0.0	21,22
HE0146-1548	4636	1.7	-3.46	-	1.57	-	-	1.16	0.87	0.14	0.5	-	0.73	23,24
HE0233-0343	6100	3.4	-4.7	1.77	3.48	$<$ 2.8	$<$ 4.0	$<$ 0.5	0.59	$<$ 0.03	0.05	$>$ 5.0	0.0	21
HE0251-3216	5750	3.7	-3.15	-	2.53	-	-	0.97	0.61	0.05	-0.6	-	0.0	8
HE0450-4902	6300	4.5	-3.1	$<$ 1.98	2.03	2.0	$<$ 3.5	0.23	0.53	-0.78	0.0	-	-	21
HE0557-4840	4900	2.2	-4.8	$<$ 0.7	1.77	$<$ 0.96	2.3	-0.25	0.16	-0.71	-	-	0.01	25,26
HE1005-1439	5000	1.9	-3.2	-	2.51	1.79	-	1.17	0.59	-	-	-	0.02	27
HE1012-1540	5230	2.65	-3.76	$<$ 0.75	2.4	1.15	$<$ 2.18	1.65	1.81	0.69	0.65	$>$ 30.0	0.0	2,8
HE1029-0546	6650	4.3	-3.3	$<$ 2.0	2.64	2.9	$<$ 3.7	-	-0.03	$<$ -0.42	-0.03	9.0	-	21
HE1150-0428	5200	2.5	-3.21	-	2.51	2.62	-	1.44	0.35	-	-	-	0.02	8
HE1201-1512	5725	4.2	-3.89	-	1.14	$<$ 1.23	-	-0.35	0.2	-0.73	-	-	0.0	23,24
HE1249-3121	5373	3.4	-3.23	-	1.91	-	-	-	0.24	-0.79	-	-	0.0	28,29
HE1300+0157	5550	3.3	-3.49	1.06	1.34	$<$ 0.8	1.78	-0.13	0.33	-0.15	0.57	-	0.0	8,30
HE1300-0641	5308	2.96	-3.14	-	1.25	-	-	-	0.02	-1.19	-	-	0.01	28,29
HE1305-0331	6081	4.22	-3.26	-	1.09	-	-	-	-	-0.7	-	-	0.0	31,28
HE1310-0536	5000	1.9	-4.2	$<$ 0.8	2.44	3.2	$<$ 2.8	0.19	0.42	-0.39	0.8	3.0	0.08	21
HE1327-2326	6180	3.7	-5.66	$<$ 0.7	4.18	4.67	3.86	2.46	1.65	1.16	-	$>$ 5.0	0.0	32,33
HE1338-0052	5856	3.7	-3.0	-	1.53	-	-	-	0.44	-0.16	0.39	-	0.0	8
HE1351-1049	5204	2.85	-3.46	-	1.74	-	-	-	0.28	-0.75	-	-	0.01	28,29
HE1410-0004	5605	3.5	-3.02	$<$ 1.32	2.24	-	1.28	0.61	0.53	-	-	-	0.04	8,34
HE1413-1954	6302	3.8	-3.5	2.035	1.67	-	-	-	-	-	-	-	0.0	10,29
HE1456+0230	5664	2.2	-3.32	-	2.37	3.03	-	0.3	0.29	-0.09	0.54	-	0.02	8
HE1506-0113	5016	2.4	-3.54	-	1.49	0.61	-	1.65	0.89	-0.53	0.5	-	0.02	23,24
HE2123-0329	4725	1.15	-3.22	$<$ 0.58	1.06	-	-	-	0.58	-0.57	0.56	-	0.66	18
HE2139-5432	5416	2.2	-4.02	-	2.61	2.09	-	2.15	1.61	0.36	1.0	-	0.01	23,24
HE2318-1621	4846	1.4	-3.67	-	1.04	1.24	-	0.71	0.2	-0.58	-	-	0.5	35
HE2331-7155	4900	1.5	-3.7	$<$ 0.37	1.34	2.57	$<$ 1.7	0.46	1.2	-0.38	$<$ 0.25	5.0	-	21
LAMOSTJ125346.09	6030	3.65	-4.02	1.8	1.59	-	-	-0.2	0.24	-	-	-	-	36
LAMOSTJ131331.18	4750	1.6	-4.12	$<$ 0.68	1.83	-	-	-0.06	0.34	-	0.45	-	-	36
LAMOSTJ1626+1721	5930	3.6	-3.2	-	1.07	-	-	-0.02	0.5	-0.33	0.46	-	-	37
LAMOSTJ1709+1616	5780	3.5	-3.71	-	1.58	-	-	-	0.28	-	0.18	-	-	37
SDSSJ0002+2928	6150	4.0	-3.26	-	2.63	-	-	0.99	0.36	-	-	-	-	38
SDSSJ0126+0607	6900	4.0	-3.01	$<$ 2.2	3.08	-	-	0.86	0.66	-	-	-	-	38,39
SDSSJ0212+0137	6333	4.0	-3.59	2.04	2.28	$<$ 2.66	1.6	-	0.52	-0.55	0.23	-	-	40
SDSSJ0351+1026	5450	3.6	-3.18	-	1.55	-	-	-0.15	0.71	-	-	-	-	38
SDSSJ0723+3637	5150	2.2	-3.32	-	1.79	-	-	-0.1	0.23	-	-	-	-	38
SDSSJ1035+0641	6262	4.0	$<$ -5.07	$<$ 1.1	3.54	-	-	-	$<$ -0.06	-	-	-	-	40
SDSSJ1114+1828	6200	4.0	-3.35	-	3.3	2.2	-	-	-	-	-	$>$ 60.0	-	41
SDSSJ1143+2020	6240	4.0	-3.15	-	2.8	2.48	-	-	-	-	-	20.0	-	41
SDSSJ1245-0738	6110	2.5	-3.21	-	3.45	-	-	1.29	0.68	-0.12	0.02	-	-	40
SDSSJ131326.89	5200	2.6	-5.0	$<$ 0.8	2.96	3.46	-	0.37	0.44	-0.11	$<$ 0.21	-	-	42
SDSSJ1349-0229	6200	4.0	-3.24	-	3.01	-	-	1.87	0.73	-	-	$>$ 30.0	-	38,43
SDSSJ1422+0031	5200	2.2	-3.03	-	1.7	-	-	0.36	0.77	-	-	-	-	38
SDSSJ1613+5309	5350	2.1	-3.33	-	2.09	-	-	0.76	0.92	-	-	-	-	38
SDSSJ161956+170539	6191	4.0	-3.57	-	2.34	-	-	-	0.02	-	-0.27	-	-	44
SDSSJ1646+2824	6100	4.0	-3.05	-	2.52	-	-	-	0.71	-	-	-	-	38
SDSSJ1742+2531	6345	4.0	-4.8	-	3.63	-	$<$ 3.03	$<$ 0.7	$<$ 0.27	-	$<$ 0.34	-	-	40
SDSSJ1746+2455	5350	2.6	-3.17	-	1.24	-	-	0.48	0.69	-	-	-	-	38
SDSSJ2209-0028	6440	4.0	-3.96	-	2.61	-	-	-	-	-	-	-	-	41
SMSSJ005953.98	5413	2.95	-3.94	2.0	1.2	-	-	1.99	0.61	-0.25	0.73	-	-	45
SMSSJ031300.36	5125	2.3	$<$ -7.3	0.7	4.9	$<$ 3.8	$<$ 5.0	$<$ 1.8	3.0	$<$ 1.1	$<$ 3.0	-	-	46

Table 5. Table 4.3: Initial and final (after the first dredge-up) surface log \log ( 12 C/ 13 C) and [C/N] ratios for the ten 0.8 M ⊙ subscript 𝑀 direct-product M_{\odot} models computed.

$\log$ (¹²C/¹³C)_ini	$0.85$	$0.85$	$0.85$	$0.95$	$0.95$	$0.95$	$1.08$	$1.08$	$1.08$	2
$\log$ (¹²C/¹³C)_1DUP	$0.81$	$0.81$	$0.81$	$0.91$	$0.91$	$0.91$	$1.01$	$1.01$	$1.01$	$1.17$
$[$ C/N]_ini	$- 1$	$- 0.1$	1	$- 1$	$- 0.1$	1	$- 1$	$- 0.1$	1	$1.8$
$[$ C/N]_1DUP	$- 1.02$	$- 0.16$	$- 0.69$	$- 1.02$	$- 0.15$	$0.71$	$- 1.02$	$- 0.15$	$0.70$	$1.62$

Table 6. Table 4.4: Properties of the source star models: model label (column 1) initial mass (column 2), υ ini / υ crit subscript 𝜐 ini subscript 𝜐 crit \upsilon_{\rm ini}/\upsilon_{\rm crit} (column 3), initial equatorial velocity (column 4), total lifetime (column 5), duration of the main sequence, helium, carbon, neon, oxygen, and silicon-burning phases (column 6 − 11 6 11 6-11 ), mass of the model at the end of the evolution (column 12 12 12 ), remnant mass according to the relation of Maeder ( 1992 , column 13 13 13 ) .

Model	$M_{ini}$	$υ_{ini} / υ_{crit}$	$υ_{ini}$	$τ_{life}$	$τ_{MS}$	$τ_{He}$	$τ_{C}$	$τ_{Ne}$	$τ_{O}$	$τ_{Si}$	$M_{final}$	$M_{rem}$
	[ $M_{⊙}$ ]		[km/s]	[Myr]	[Myr]	[Myr]	[yr]	[day]	[day]	[day]	[ $M_{⊙}$ ]	[ $M_{⊙}$ ]
No rotation
20s0	20	0	0	8.93	8.02	0.79	978	168	318	3.1	19.98	1.88
32s0	32	0	0	5.78	5.24	0.48	124	22	47	0.6	31.94	2.98
60s0	60	0	0	3.81	3.44	0.33	15	7	7	0.5	59.80	6.35
Rotation
20s7	20	0.7	610	11.0	10.1	0.76	400	277	128	1.4	19.50	2.20
32s7	32	0.7	680	7.14	6.61	0.47	45	7	15	0.6	30.71	3.69
60s7	60	0.7	770	4.69	4.33	0.32	5	1	3	0.2	47.65	8.88
No rotation, late mix
20s0mix	20	0	0	8.93	8.02	0.79	993	-	-	-	19.98	1.88
32s0mix	32	0	0	5.78	5.24	0.48	157	-	-	-	31.94	2.98
60s0mix	60	0	0	3.81	3.44	0.33	18	-	-	-	59.80	6.35
Rotation, late mix
20s7mix	20	0.7	610	11.0	10.1	0.76	412	-	-	-	19.50	2.20
32s7mix	32	0.7	680	7.14	6.61	0.47	51	-	-	-	30.70	3.69
60s7mix	60	0.7	770	4.69	4.33	0.32	5	-	-	-	47.64	8.73

Table 7. Table 4.5: Parameters of the best source star models (column 2) for the considered CEMP-no stars (column 1). f H subscript 𝑓 H f_{\rm H} , f He subscript 𝑓 He f_{\rm He} and f CO subscript 𝑓 CO f_{\rm CO} correspond to the ejected fraction of the H-envelope (above M α subscript 𝑀 𝛼 M_{\alpha} ), He-shell (between M α subscript 𝑀 𝛼 M_{\alpha} and M CO subscript 𝑀 CO M_{\rm CO} ) and CO-core (below M CO subscript 𝑀 CO M_{\rm CO} ), respectively. D 𝐷 D is the dilution factor, X 𝑋 X (He) is the mass fraction of helium predicted for the CEMP-no star, ξ 𝜉 \xi the error on the fit and N 𝑁 N the number of abundances used to make the fit.

Star	Best model	$M_{cut}$ [ $M_{⊙}$ ]	$f_{H}$	$f_{He}$	$f_{CO}$	$D$	$X$ (He)	$ξ$	$N$
BD+44_493	60s7mix	29.88	1	0.72	0	1000	0.25	0.46	4
CS22877-001	20s7mix	5.07	1	0.97	0	1000	0.25	1.32	5
CS22891-200	20s7mix	8.5	0.92	0	0	10	0.26	0.62	4
CS22897-008	60s0	22.7	1	0.47	0	1000	0.25	0.31	4
CS22949-037	20s7mix	8.54	0.92	0	0	0	0.38	1.38	4
CS22950-046	20s7mix	8.53	0.92	0	0	10	0.26	0.21	4
CS22957-027	20s7mix	7.4	1	0.03	0	10	0.26	1.03	5
CS22960-053	20s7	7.97	1	0.02	0	0	0.39	1.11	3
CS29502-092	20s7mix	7.32	1	0.07	0	100	0.25	1.19	6
CS29527-015	60s7mix	28.04	1	1	0	1000	0.25	0.1	3
CS29528-041	32s7mix	19.05	0.75	0	0	0	0.42	0.99	4
G77-61	20s0mix	12.78	0.5	0	0	0	0.27	1.28	6
HE0017-4346	20s7mix	7.77	0.98	0	0	0	0.4	0.28	3
HE0134-1519	60s0mix	24.21	1	0.1	0	10	0.27	0.71	3
HE0146-1548	20s7mix	8.51	0.92	0	0	0	0.38	1.05	3
HE0251-3216	20s7mix	7.09	1	0.16	0	10	0.26	0.34	3
HE0450-4902	20s7mix	8.43	0.92	0	0	0	0.38	0.94	4
HE1005-1439	20s7mix	6.86	1	0.25	0	10	0.27	0.66	4
HE1029-0546	20s0mix	11.58	0.58	0	0	0	0.31	0.55	4
HE1150-0428	20s7mix	8.31	0.93	0	0	0	0.38	0.45	4
HE1201-1512	60s0	24.29	1	0.13	0	10	0.27	0.63	3
HE1300+0157	60s7	28.22	1	1	0.01	1000	0.25	0.27	4
HE1310-0536	32s0mix	14.99	0.79	0	0	10	0.27	0.89	5
HE1327-2326	60s7	33.51	1	0.21	0	0	0.62	1.08	5
HE1410-0004	20s7mix	8.43	0.92	0	0	0	0.38	1.04	4
HE1456+0230	20s7	7.86	1	0.06	0	0	0.4	0.96	4
HE2318-1621	20s0mix	13.63	0.44	0	0	0	0.25	0.73	4
HE2331-7155	20s7	7.99	1	0.02	0	0	0.39	1.14	5
LAMOSTJ125346.09	60s0mix	24.22	1	0.1	0	0	0.53	0.5	3
LAMOSTJ131331.18	60s0	24.33	1	0.12	0	0	0.53	0.42	3
LAMOSTJ1626+1721	20s0	5.8	1	0.16	0	0	0.38	0.7	3
SDSSJ0002+2928	20s7mix	7.18	1	0.12	0	10	0.26	0.16	3
SDSSJ0126+0607	32s7mix	10.73	1	1	0.03	10	0.27	0.18	3
SDSSJ0212+0137	20s7	7.89	1	0.05	0	0	0.4	0.21	3
SDSSJ0351+1026	60s7mix	8.84	1	1	0.68	1000	0.25	0.51	3
SDSSJ0723+3637	20s0	5.78	1	0.16	0	0	0.38	0.23	3
SDSSJ1143+2020	20s7mix	6.48	1	0.41	0	10	0.27	0.51	3
SDSSJ1245-0738	20s7	3.72	1	1	0.26	10	0.26	0.23	3
SDSSJ1349-0229	20s7mix	5.78	1	0.69	0	10	0.27	0.48	3
SDSSJ1422+0031	20s7mix	3.03	1	1	0.4	100	0.25	0.67	3
SDSSJ1613+5309	20s7mix	3.3	1	1	0.34	100	0.25	0.68	3
SDSSJ1746+2455	20s7mix	8.51	0.92	0	0	0	0.38	0.79	3
SMSSJ005953.98	20s7mix	8.55	0.92	0	0	0	0.38	1.13	3

Table 8. Table 5.1: Apparently single CEMP-s stars (abundances taken from the SAGA database, Suda et al. 2008 ) .

Star	HE 0206-1916	HE 1045+0226	HE 2330-0555	CS 30301-015
$[$ Fe/H]	-2.09	-2.20	-2.78	-2.64
$T_{eff}$	5200	5077 (100)	4900	4750
$\log g$	2.7	2.2 (0.25)	1.7	0.8
$[$ C/Fe]	2.11 (0.19)	1.18	2.09 (0.19)	1.72 (0.28)
$[$ N/Fe]	1.61 (0.33)	-	0.99 (0.42)	1.84
$[$ Na/Fe]	0.72 (0.14)	0.96 (0.05)	0.95 (0.12)	-
$[$ Mg/Fe]	0.50 (0.15)	0.27 (0.09)	0.64 (0.17)	0.84 (0.22)
$[$ Al/Fe]	-	-	-	0.17
$[$ Si/Fe]	-	0.45 (0.17)	-	-
$[$ K/Fe]	-	0.51	-	-
$[$ Ca/Fe]	0.13 (0.13)	0.22 (0.16)	0.44 (0.19)	0.79 (0.16)
$[$ Sc/Fe]	-	0.09 (0.05)	0.20 (0.08)	-
$[$ Ti I/Fe]	0.41 (0.14)	0.34 (0.1)	0.31 (0.11)	0.30 (0.13)
$[$ Ti II/Fe]	0.59 (0.19)	0.43 (0.13)	0.38 (0.23)	0.45 (0.24)
$[$ Cr/Fe]	0.05 (0.13)	-0.05 (0.01)	-0.05 (0.10)	-
$[$ Mn/Fe]	-	-0.23 (0.28)	-	-
$[$ Ni/Fe]	-	0.17 (0.16)	-	-
$[$ Zn/Fe]	-	-	-	0.37
$[$ Sr/Fe]	-	-	-	0.37 (0.23)
$[$ Y/Fe]	-	1.29 (0.25)	-	0.31 (0.20)
$[$ Zr/Fe]	-	1.52	-	-
$[$ Ba/Fe]	2.01 (0.16)	1.24 (0.1)	1.25 (0.25)	1.49 (0.16)
$[$ La/Fe]	-	0.92 (0.17)	-	0.96 (0.25)
$[$ Ce/Fe]	-	-	-	1.21 (0.15)
$[$ Pr/Fe]	-	1.14	-	-
$[$ Nd/Fe]	-	0.85 (0.32)	-	0.80 (0.17)
$[$ Sm/Fe]	-	-	-	0.87 (0.20)
$[$ Eu/Fe]	-	0.27	-	0.22 (0.18)
$[$ Dy/Fe]	-	-	-	0.64 (0.20)
$[$ Pb/Fe]	-	-	-	1.70 (0.24)
Source	1	2	1	3, 4

Table 9. Table A.1: s-process parameters at the end of the core helium burning phase for the models in Choplin et al. ( 2018 ) : model label (column 1), central neutron exposure (column 2, Eq. A.24 ), neutron exposure averaged over He-core (column 3, Eq. A.25 ), number of neutron capture per seed (Eq. A.27 ) averaged over the He-core mass (column 4), maximum of the central neutron density (column 5), 22 Ne burnt (column 6) and left (column 7).

Model	$τ_{c}$	$⟨ τ ⟩$	$n_{c}$	$n_{n, c, m a x}$	$Δ X$ (²²Ne)	$X_{r}$ (²²Ne)
	[mb^-1]	[ $10^{- 1}$ mb^-1]		[cm $- 3$ ]
10s0	0.23	0.13	0.13	8.01(5)	6.73( $- 5$ )	1.09( $- 3$ )
10s4	0.68	0.38	0.61	2.44(6)	1.69( $- 4$ )	1.32( $- 3$ )
15s0	0.93	0.45	0.62	5.07(6)	2.14( $- 4$ )	9.46( $- 4$ )
15s4	3.53	1.82	3.36	1.43(7)	7.66( $- 4$ )	1.45( $- 3$ )
20s0	2.10	0.88	1.45	1.15(7)	4.15( $- 4$ )	7.58( $- 4$ )
20s4	8.51	3.72	9.18	2.66(7)	2.08( $- 3$ )	1.56( $- 3$ )
25s0	3.29	1.29	2.32	1.71(7)	5.98( $- 4$ )	5.93( $- 4)$
25s4	12.47	4.92	14.42	3.16(7)	3.32( $- 3$ )	1.17( $- 3)$
25s7	16.56	6.52	22.54	7.11(7)	5.43( $- 3$ )	1.87( $- 3)$
25s7B^a	21.54	8.57	33.19	4.21(7)	5.08( $- 3$ )	1.83( $- 3)$
40s0	6.16	2.14	4.47	2.23(7)	9.81( $- 4$ )	2.64( $- 4$ )
40s4	14.8	5.11	15.38	2.89(7)	3.37( $- 3$ )	2.12( $- 4$ )
60s0	8.57	2.70	6.26	2.04(7)	1.24( $- 3$ )	6.75( $- 5)$
60s4	11.06	3.43	8.56	2.15(7)	1.68( $- 3$ )	2.19( $- 5$ )
85s0	10.05	2.98	7.27	1.99(7)	1.33( $- 3$ )	1.53( $- 5)$
85s4	11.12	3.28	8.08	1.96(7)	1.44( $- 3$ )	3.30( $- 6)$
120s0	11.08	3.19	8.08	1.94(7)	1.36( $- 3$ )	2.99( $- 6)$
120s0B^a	14.20	4.23	12.49	2.30(7)	1.30( $- 3$ )	2.33( $- 6)$
120s4	11.87	3.37	8.52	2.66(8)	1.39( $- 3$ )	4.09( $- 7)$
150s0	11.95	3.38	8.66	1.99(7)	1.37( $- 3$ )	4.49( $- 7)$
150s4	12.68	3.52	9.04	1.94(8)	1.37( $- 3$ )	7.07( $- 8)$

Equations106

τ_{⋆} ≃ 10 [\frac{M}{M _{⊙}}] . [\frac{L _{⊙}}{L}] ≃ 10 [\frac{M}{M _{⊙}}]^{1 - a} Gyr

τ_{⋆} ≃ 10 [\frac{M}{M _{⊙}}] . [\frac{L _{⊙}}{L}] ≃ 10 [\frac{M}{M _{⊙}}]^{1 - a} Gyr

[X/Y] = lo g_{10} (N_{X} / N_{Y})_{⋆} - lo g_{10} (N_{X} / N_{Y})_{⊙}

[X/Y] = lo g_{10} (N_{X} / N_{Y})_{⋆} - lo g_{10} (N_{X} / N_{Y})_{⊙}

\frac{d P}{d M _{P}} = - \frac{G M _{P}}{4 π r _{P}^{4}} f_{P}

\frac{d P}{d M _{P}} = - \frac{G M _{P}}{4 π r _{P}^{4}} f_{P}

\frac{d r _{P}}{d M _{P}} = \frac{1}{4 π r _{P}^{2} ρ ˉ}

\frac{d r _{P}}{d M _{P}} = \frac{1}{4 π r _{P}^{2} ρ ˉ}

\frac{d L _{P}}{d M _{P}} = ϵ_{nucl} - ϵ_{ν} + ϵ_{grav}

\frac{d L _{P}}{d M _{P}} = ϵ_{nucl} - ϵ_{ν} + ϵ_{grav}

\frac{d ln T}{d M _{P}} = - \frac{G M _{P}}{4 π r _{P}^{4}} f_{P} min [\nabla_{ad}, \nabla_{rad} \frac{f _{T}}{f _{P}}]

\frac{d ln T}{d M _{P}} = - \frac{G M _{P}}{4 π r _{P}^{4}} f_{P} min [\nabla_{ad}, \nabla_{rad} \frac{f _{T}}{f _{P}}]

⟨ X ⟩ = \frac{1}{S _{P}} \oint_{isobar} X (r, θ) d σ

⟨ X ⟩ = \frac{1}{S _{P}} \oint_{isobar} X (r, θ) d σ

ρ \frac{d}{d t} (r^{2} \overset{ˉ}{Ω})_{M_{r}} = advection \frac{1}{5 r ^{2}} \frac{\partial}{\partial r} (ρ r^{2} U (r) \overset{ˉ}{Ω}) + diffusion \frac{1}{r ^{2}} \frac{\partial}{\partial r} (ρ r^{4} D \frac{\partial Ω ˉ}{\partial r})

ρ \frac{d}{d t} (r^{2} \overset{ˉ}{Ω})_{M_{r}} = advection \frac{1}{5 r ^{2}} \frac{\partial}{\partial r} (ρ r^{2} U (r) \overset{ˉ}{Ω}) + diffusion \frac{1}{r ^{2}} \frac{\partial}{\partial r} (ρ r^{4} D \frac{\partial Ω ˉ}{\partial r})

E_{Ω} ≃ \frac{8}{3} [1 - \frac{Ω ^{2}}{2 π G ρ ˉ}] (\frac{Ω ^{2} r ^{3}}{G M _{r}}) .

E_{Ω} ≃ \frac{8}{3} [1 - \frac{Ω ^{2}}{2 π G ρ ˉ}] (\frac{Ω ^{2} r ^{3}}{G M _{r}}) .

D_{eff} = \frac{1}{30} \frac{\textbar r U ( r ) \textbar ^{2}}{D _{h}}

D_{eff} = \frac{1}{30} \frac{\textbar r U ( r ) \textbar ^{2}}{D _{h}}

ρ \frac{d X _{i}}{d t} = \frac{1}{r ^{2}} \frac{\partial}{\partial r} [ρ r^{2} (D + D_{eff}) \frac{\partial X _{i}}{\partial r}] + (\frac{d X _{i}}{d t})_{nucl} .

ρ \frac{d X _{i}}{d t} = \frac{1}{r ^{2}} \frac{\partial}{\partial r} [ρ r^{2} (D + D_{eff}) \frac{\partial X _{i}}{\partial r}] + (\frac{d X _{i}}{d t})_{nucl} .

D_{shear}^{TZ97} = f_{energ} \frac{H _{p}}{g δ} \frac{K + D _{h}}{( \nabla _{a d} - \nabla ) + \frac{φ}{δ} \nabla _{μ} ( \frac{K}{D _{h}} + 1 )} (\frac{9 π}{32} Ω \frac{d ln Ω}{d ln r})^{2}

D_{shear}^{TZ97} = f_{energ} \frac{H _{p}}{g δ} \frac{K + D _{h}}{( \nabla _{a d} - \nabla ) + \frac{φ}{δ} \nabla _{μ} ( \frac{K}{D _{h}} + 1 )} (\frac{9 π}{32} Ω \frac{d ln Ω}{d ln r})^{2}

(\frac{d X _{i}}{d t})_{nucl} = 1-body reactions A_{i} j \sum N_{j}^{i} λ_{j} \frac{X _{j}}{A _{j}} + 2-body reactions A_{i} j, k \sum \frac{1}{1 + δ _{j k}} N_{j, k}^{i} ρ N_{A} ⟨ σ v ⟩_{j; k} f_{j; k} \frac{X _{j} X _{k}}{A _{j} A _{k}} + 3-body reactions A_{i} j, k, l \sum \frac{1}{1 + Δ _{ij k}} N_{j, k, l}^{i} ρ^{2} N_{A}^{2} ⟨ σ v ⟩_{j; k; l} f_{j; k; l} \frac{X _{j} X _{k} X _{l}}{A _{j} A _{k} A _{l}}

(\frac{d X _{i}}{d t})_{nucl} = 1-body reactions A_{i} j \sum N_{j}^{i} λ_{j} \frac{X _{j}}{A _{j}} + 2-body reactions A_{i} j, k \sum \frac{1}{1 + δ _{j k}} N_{j, k}^{i} ρ N_{A} ⟨ σ v ⟩_{j; k} f_{j; k} \frac{X _{j} X _{k}}{A _{j} A _{k}} + 3-body reactions A_{i} j, k, l \sum \frac{1}{1 + Δ _{ij k}} N_{j, k, l}^{i} ρ^{2} N_{A}^{2} ⟨ σ v ⟩_{j; k; l} f_{j; k; l} \frac{X _{j} X _{k} X _{l}}{A _{j} A _{k} A _{l}}

X_{i, ⊙} = 1 0^{l o g ϵ_{e, ⊙} - 12} f_{i} A_{i} X_{H, ⊙}

X_{i, ⊙} = 1 0^{l o g ϵ_{e, ⊙} - 12} f_{i} A_{i} X_{H, ⊙}

X_{i, α} = X_{i, ⊙} \frac{X _{Fe}}{X _{Fe, ⊙}} 1 0^{B_{α}} f_{i} A_{i}

X_{i, α} = X_{i, ⊙} \frac{X _{Fe}}{X _{Fe, ⊙}} 1 0^{B_{α}} f_{i} A_{i}

\dot{M} (Z) = (\frac{Z}{Z _{⊙}})^{a} \dot{M} (Z_{⊙})

\dot{M} (Z) = (\frac{Z}{Z _{⊙}})^{a} \dot{M} (Z_{⊙})

m_{i}^{ej} = wind contribution \int_{0}^{τ} \dot{M} (t) X_{i, s} (t) d t + supernova contribution \int_{M_{cut}}^{M_{fin}} X_{i} (M_{r}) d M_{r},

m_{i}^{ej} = wind contribution \int_{0}^{τ} \dot{M} (t) X_{i, s} (t) d t + supernova contribution \int_{M_{cut}}^{M_{fin}} X_{i} (M_{r}) d M_{r},

m_{i} = wind contribution \int_{0}^{τ} \dot{M} (t) (X_{i, s} (t) - X_{i, 0}) d t + supernova contribution \int_{M_{cut}}^{M_{fin}} (X_{i} (M_{r}) - X_{i, 0}) d M_{r},

m_{i} = wind contribution \int_{0}^{τ} \dot{M} (t) (X_{i, s} (t) - X_{i, 0}) d t + supernova contribution \int_{M_{cut}}^{M_{fin}} (X_{i} (M_{r}) - X_{i, 0}) d M_{r},

f_{i} = \frac{M _{ej}}{M _{ini}} \frac{X _{i, ej}}{X _{i, 0}},

f_{i} = \frac{M _{ej}}{M _{ini}} \frac{X _{i, ej}}{X _{i, 0}},

M_{^{14} N}^{prim} = (\int_{0}^{M} X_{^{14} N} (M_{r}) d M_{r})_{Y_{c} = 0} - M (X_{C, ini} + X_{N, ini} + X_{O, ini})

M_{^{14} N}^{prim} = (\int_{0}^{M} X_{^{14} N} (M_{r}) d M_{r})_{Y_{c} = 0} - M (X_{C, ini} + X_{N, ini} + X_{O, ini})

R_{^{12} C +^{16} O} = \frac{M _{^{14} N}^{prim}}{τ _{HeB}}

R_{^{12} C +^{16} O} = \frac{M _{^{14} N}^{prim}}{τ _{HeB}}

D = \frac{M _{ISM}}{M _{ej}}

D = \frac{M _{ISM}}{M _{ej}}

X (Li)_{CEMP} = \frac{M _{ej} X ( Li ) _{ej} + M _{ISM} X ( Li ) _{ISM}}{M _{ej} + M _{ISM}} = \frac{M _{ISM} X ( Li ) _{ISM}}{M _{ej} + M _{ISM}}

X (Li)_{CEMP} = \frac{M _{ej} X ( Li ) _{ej} + M _{ISM} X ( Li ) _{ISM}}{M _{ej} + M _{ISM}} = \frac{M _{ISM} X ( Li ) _{ISM}}{M _{ej} + M _{ISM}}

D = \frac{M _{ISM}}{M _{ej}} = \frac{X ( Li ) _{CEMP}}{X ( Li ) _{ISM} - X ( Li ) _{CEMP}} .

D = \frac{M _{ISM}}{M _{ej}} = \frac{X ( Li ) _{CEMP}}{X ( Li ) _{ISM} - X ( Li ) _{CEMP}} .

ξ = i \sum ∣ A_{i}^{obs} - A_{i}^{mod} ∣ .

ξ = i \sum ∣ A_{i}^{obs} - A_{i}^{mod} ∣ .

⟨ σ v ⟩ N_{A} = k = 1 \sum n e^{[a_{0} (k) + a_{1} (k) T_{9}^{- 1} + a_{2} (k) T_{9}^{- 1/3} + a_{3} (k) T_{9}^{1/3} + a_{4} (k) T_{9} + a_{5} (k) T_{9}^{5/3} + a_{6} (k) l o g (T_{9})]}

⟨ σ v ⟩ N_{A} = k = 1 \sum n e^{[a_{0} (k) + a_{1} (k) T_{9}^{- 1} + a_{2} (k) T_{9}^{- 1/3} + a_{3} (k) T_{9}^{1/3} + a_{4} (k) T_{9} + a_{5} (k) T_{9}^{5/3} + a_{6} (k) l o g (T_{9})]}

ϵ_{ax} = K g_{10}^{2} T_{8}^{7} ρ_{3}^{- 1} Z (ξ^{2}) C

ϵ_{ax} = K g_{10}^{2} T_{8}^{7} ρ_{3}^{- 1} Z (ξ^{2}) C

A (ξ^{2}) = \frac{1.037 ξ ^{2}}{1.01 + ξ ^{2} /5.4} + \frac{1.037 ξ ^{2}}{44 + 0.628 ξ ^{2}} and B (ξ^{2}) = 3.85 + \frac{3.99}{ξ ^{2}}

A (ξ^{2}) = \frac{1.037 ξ ^{2}}{1.01 + ξ ^{2} /5.4} + \frac{1.037 ξ ^{2}}{44 + 0.628 ξ ^{2}} and B (ξ^{2}) = 3.85 + \frac{3.99}{ξ ^{2}}

ξ \equiv \frac{ℏ c k _{S}}{2 k _{B} T} .

ξ \equiv \frac{ℏ c k _{S}}{2 k _{B} T} .

k_{S}^{2} \equiv 4 π α (\frac{ℏ c}{k _{B} T}) i = e, ions \sum n_{i} Z_{i}^{2}

k_{S}^{2} \equiv 4 π α (\frac{ℏ c}{k _{B} T}) i = e, ions \sum n_{i} Z_{i}^{2}

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TopicsStellar, planetary, and galactic studies · Astronomy and Astrophysical Research

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**Université de Genève Faculté des Sciences

Département d’astronomie Professeur Georges Meynet

The Early Generations of Rotating Massive Stars

and the Origin of

Carbon-Enhanced Metal-Poor Stars

Thèse

**

**présentée à la Faculté des sciences de l’Université de Genève

pour obtenir le grade de Docteur ès sciences,

mention Astronomie et Astrophysique

**

**par

Arthur Choplin

de

Gex (France)

**

**Thèse No 5269

Genève

Observatoire de Genève

2018

**

Abstract

The study of the long-dead early generations of massive stars is crucial in order to obtain a complete picture of the chemical evolution of the Universe, hence the origin of the elements. The nature of these stars can be inferred indirectly by investigating the origin of low-mass metal-poor stars observed in our Galaxy, some of which are almost as old as the Universe. The peculiar extremely iron-poor Carbon-Enhanced Metal-Poor (CEMP) stars, whose precise origin is still debated, are thought to have formed with the material ejected by only one or very few previous massive stars, hereafter called the source stars. In this context, the source stars belong to the very first generations of massive stars.

The main aim of this thesis is to explore the physics and the nucleosynthesis of the early generations of massive stars. It is achieved by combining stellar evolution modeling including rotation and full nucleosynthesis with observations of CEMP stars. By fitting the abundances of CEMP stars with the ejecta of new massive source star models, characteristics of the massive source stars can be deduced.

The efficient rotational mixing operating in rotating source stars triggers exchanges of material between the helium burning core and the hydrogen burning shell, and leads to a very rich and varied nucleosynthesis. This interplay between rotation and nucleosynthesis in massive source stars is able to cover the abundance scatter of light elements (carbon to silicon) of the CEMP stars with [Fe/H] $<-3$ . Some remaining discrepancies between models and observations can be alleviated if a late mixing process is included in the source star. It operates about 200 years before the end of the source star evolution, between the hydrogen burning shell and the helium burning shell. A detailed investigation of the abundances of light elements of 69 CEMP stars with [Fe/H] $<-3$ suggests that the best source stars are preferentially fast rotating 20 $M_{\odot}$ stars which experienced the late mixing process and an ejection of only their outer layers.

The rotation-induced mixing also boosts the weak s-process in source stars, provided the initial metallicity is not strictly zero. The s-elements up to barium are strongly overproduced, especially if the initial rotation rate is high. The s-process boost induced by rotation was found to be significant for stars with initial masses below 60 $M_{\odot}$ . Above this threshold, the interplay between rotation and nucleosynthesis is weaker so that rotating and non-rotating models give similar results. The signature of the rotation-induced s-process boost in $20-25$ $M_{\odot}$ source stars was found to be consistent with the abundance pattern of several CEMP stars enriched in s-elements.

The examination of the origin of CEMP stars in light of new massive source star models suggests that rotation was a dominant effect in the early generations of massive stars. Strong mixing events between burning shells are also expected to be a common feature in these early massive stars. Finally, early massive stars should have lost only their envelope and experienced rather strong fallback.

Résumé

Les premières générations d’étoiles massives en rotation

et l’origine des étoiles CEMP

Contexte

Les premières générations d’étoiles massives111Au moins 8 $M_{\odot}$ , i.e. 8 fois la masse du Soleil. sont des acteurs essentiels dans l’histoire de l’Univers. À la fin de leur évolution, ces étoiles à courte durée de vie ont explosé en supernovae $-$ un évènement dont la luminosité peut atteindre 10 milliards de fois celle du Soleil $-$ et ont, pour la première fois, enrichi l’Univers en métaux222Éléments plus lourds que l’hélium (par exemple l’oxygène)., dont nous-mêmes et notre Terre sommes constitués. La compréhension, encore méconnue aujourd’hui, de l’évolution de ces étoiles, est primordiale afin d’acquérir une connaissance globale de l’évolution de l’Univers, en particulier de son évolution chimique.

Bien qu’autour de nous, ces étoiles ne peuvent plus être observées, leur nature peut être étudiée indirectement grâce à l’observation, dans notre Galaxie, d’étoiles de faible masse et très pauvres en métaux. Certaines de ces étoiles $-$ Carbon-Enhanced Metal-Poor ou CEMP $-$ se sont probablement formées très tôt dans l’Univers, avec la matière éjectée d’une ou de quelques-unes des premières étoiles massives, appelées ci-après étoiles sources. La composition chimique particulière des étoiles CEMP, déterminée par spectroscopie, donne de précieuses informations sur la nucléosynthèse, et donc sur la nature de leur(s) étoile(s) source(s). Les étoiles CEMP pourraient être comparées à des “Pierre de Rosette”: leur déchiffrement permet d’étudier une civilisation ancienne, aujourd’hui disparue.

Objectifs et méthodes

Le but principal de ce travail de thèse est d’obtenir de nouveaux indices sur la physique des premières générations d’étoiles massives en utilisant les contraintes liées à l’observation des étoiles CEMP. Une telle étude est possible en combinant des modèles numériques d’étoiles sources avec les observations d’étoiles CEMP disponibles dans la littérature. Le code d’évolution stellaire de Genève, principal outil utilisé durant cette thèse, permet de modéliser l’évolution des étoiles sources. Une des spécificités de ce code est d’inclure une modélisation sophistiquée de la rotation différentielle. En outre, ce code permet le calcul de la nucléosynthèse complète, y compris le processus s (capture lente de neutron par des noyaux atomiques, permettant la production d’éléments lourds). Ce processus, intervenant dans les étoiles de masse intermédiaire $-$ entre 1 et 8 $M_{\odot}$ $-$ et massives, est supposé être à l’origine d’environ 50 % des éléments plus lourds que le fer, tels que le strontium, baryum, tungstène ou plomb par exemple.

Résultats

Le mélange induit par la rotation dans l’étoile source déclenche des échanges successifs de matière entre la zone de combustion d’hélium et celle d’hydrogène. Il en résulte une nucléosynthèse riche et variée, permettant la création, en grande quantité, de carbone, azote, oxygène, fluor, néon, sodium, magnésium et aluminium. La composition chimique de cette matière, enrichie en éléments divers, et finalement éjectée par les vents stellaires et/ou lors de la supernova des modèles d’étoiles sources, est en accord global avec la composition chimique des étoiles CEMP les plus pauvres en fer.

Une comparaison plus détaillée entre ces étoiles CEMP et les modèles d’étoiles sources a mis en évidence certains écarts entre les modèles et les observations. Un mélange additionnel, survenant dans une zone spécifique de l’étoile source, quelques centaines d’années avant son explosion, permet de pallier ces désaccords. Une procédure automatique, déterminant, parmi environ 35000 possibilités, le meilleur modèle d’étoile source pour une étoile CEMP donnée, a été appliquée à un échantillon de 69 étoiles CEMP. Les résultats suggèrent que les étoiles sources sont préférentiellement des étoiles en rotation rapide, d’environ 20 $M_{\odot}$ , qui ont subi le mélange additionnel et qui n’ont éjecté que leurs couches externes.

Le mélange rotationnel affecte également la synthèse d’éléments s dans l’étoile source, et ce, d’autant plus que la vitesse de rotation initiale est élevée. La modélisation d’une nouvelle grille d’étoiles massives $-$ $10<M_{\rm ini}<150$ $M_{\odot}$ $-$ , incluant rotation et processus s montre que l’effet de la rotation sur le processus s intervient de manière significative uniquement si la masse initiale de l’étoile est inférieure à 60 $M_{\odot}$ . Au-delà de ce seuil, l’interaction entre le mélange rotationnel et la nucléosynthèse est moindre. Par conséquent, les modèles d’étoiles sources en rotation donnent des résultats similaires aux modèles sans rotation. La signature chimique induite par la rotation sur la production d’éléments s dans des étoiles sources de $20-25$ $M_{\odot}$ a été identifiée dans plusieurs étoiles CEMP enrichies en éléments s.

Conclusion

L’étude de l’origine des étoiles CEMP à la lumière de nouveaux modèles d’étoiles sources vient corroborer l’idée selon laquelle la rotation a joué un rôle prépondérant dans l’Univers jeune. Par ailleurs, ce travail suggère que (1) les premières générations d’étoiles massives pourraient, pour la plupart, avoir une masse d’environ 20 $M_{\odot}$ (2) de puissantes interactions entre différentes coquilles de combustion étaient à l’œuvre dans ces étoiles et (3) ces étoiles ont probablement éjecté uniquement leur enveloppe, tandis que les régions plus internes sont tombées sur l’objet compact central.

Remerciements

Tout d’abord, un immense merci à Georges. C’est une grande chance d’avoir eu un directeur si enthousiaste et compétent, doté d’une curiosité sans bornes, captivant en cours, conférence ou lors d’une fondue bien arrosée. Merci de m’avoir laissé si libre et autonome, tout en restant toujours immédiatement disponible pour discuter, pour me conseiller, me rassurer ou me remettre sur les rails quand je m’égarais un peu. Un grand merci à Sylvia, en particulier pour son aide précieuse dans les premiers mois. Il en va de même pour André, ses conseils avisés et encouragements furent très appréciés. Merci à Cyril, toujours disponible et prêt à m’aider quand je l’ai sollicité. Merci à Corinne pour m’avoir chaleureusement accueilli et pour sa bienveillance. Je tiens à souligner que ce fut un vrai régal de travailler au sein d’une telle équipe, accueillante, dynamique, drôle. Bref, l’ambiance est bonne. Un merci tout spécial à Patrick, pour sa bonne humeur et son indéfectible humour.

En dehors de Genève, je remercie Raphael, avec qui c’est un vrai plaisir de collaborer. Merci pour m’avoir initié au processus s, au golf et pour m’avoir gracieusement permis de stocker quelques téraoctets sur tes disques… Je remercie Cristina pour ses précieux conseils scientifiques et encouragements. Merci à Alain Coc, Keith A. Olive, Jean-Philippe Uzan et Elisabeth Vangioni, sans lesquels une partie de cette thèse n’aurait pas pu exister. Merci à Alison Laird pour sa contribution et son interêt pour certains des travaux de cette thèse. Merci à Maria Lugaro pour ses commentaires bienveillants et constructifs sur mon travail. Merci à Tim Beers, aux organisateurs de Gala of GALAH et à Jinmi Yoon pour l’interêt qu’ils ont porté à mon travail et pour la confiance qu’ils m’ont accordée. Une pensée aussi à mes anciens maîtres de stage de Grenoble, Jérôme, Véronique et Jean-Charles avec qui j’ai fait mes premiers pas dans le monde de la recherche.

De retour à Genève, je dis grazie à Giovanni pour m’avoir épaulé au démarrage, et aussi pour ses merveilleuses lasagnes. Merci à Mads pour nos premières soirées sans limites à Gex, Sauverny ou Genthod. Merci à Lionel pour son introduction musclée au marxisme-léninisme. Merci à Thibaut, un compagnon fort sympathique et enjoué pour cette fin de thèse. Merci à ceux qui excellent dans l’art d’égayer les pauses cafés, les parties de pétanque ou de ping-pong: Patrick bien sûr mais aussi Stéphane et Thierry. Merci à Song, qu’il me suffisait de croiser dans le couloir pour passer une bonne journée, tant sa joie et son affection sont grandes et communicatives. Merci à Koh et Yu, mes collègues éphémères, curieux de tout, au travail comme en dehors. Merci à Carlo pour sa visite à Genève et nos discussions sur ces beaux objets que sont les CEMP. Merci à Jose et Aline pour leur gentillesse et leur accueil bien amical au sein du groupe. Ce fut un vrai plaisir de les retrouver à Dublin pour un petit projet scientifique. Ce séjour irlandais n’aurait pu être aussi fructueux sans l’attention et la patience de Jose. En passant, merci aux collègues dublinois, en particulier Laura, Ioana et Eoin. Assez rapidement, on se sent bien parmi eux, au bureau comme au pub. Au risque d’en faire un peu trop, j’ai envie de remercier l’Observatoire en général, car l’atmosphère y est bien agréable… je pense à l’administration, la cafet’, la mécanique (Robin pour la réparation du piano…), les footeux du vendredi, les (not so) lazy runners et les grimpeurs. Un grand merci au groupe de musique de l’Obs. C’était une superbe parenthèse hebdomadaire que de jouer avec vous dans ce bunker antiatomique. Je pense aussi à la belle fête de Noël 2016 de l’Obs organisée avec vous, inoubliable! Toujours dans la musique, merci à Lorenzo et Iris pour m’avoir fait connaitre puis permis de jouer le jeudi soir dans ce chouette endroit qu’est c’est ici l’endroit où. Musique encore: merci à la team du Cully Jazz Festival, spécialement Barbara et l’incroyable Job (je te suis reconnaissant d’avoir gardé ton sang froid à la fourrière). Enfin, merci à Uriel pour m’avoir fait découvrir les joies du studio.

J’ai aussi des pensées affectueuses et non sans émotion pour tous ceux que j’ai rencontré voire rerencontré lors de mes escapades, parfois dans le cadre professionnel, parfois en dehors. Je pense déjà à Taygun, Panos, Matt, Sanjana, Jacqueline, Brent et tout ce chouette petit monde croisé à Niigata. Je pense à Taygun encore, Melisa, Mehmet et son chat à Istanbul. Je pense aussi à Gen, Tilman, Rick, Tim, Camilla et Marc-Antoine à Melbourne, à Rana à Notre-Dame. Je pense à ceux du Chili, où j’ai vécu une magnifique experience d’observation sur Euler. Soyez salués sur l’heure Justyn, Simona, Chiara (membres du LSVB ou La Silla VolleyBall), James, Vincent, Sophie, Amélie, Max, Mikaela et Lila! Je pense aussi aux chamoniards et au refuge. Je pense à Solène, Klimt et Bill Viola. Je pense à Nicolas, Guillaume, Marco et autres très joyeux drilles de l’EJC 2016. Je pense à Simon, Damien et aux Genevois à Saas-Fee. Je pense enfin à Michael, Eric et les amis de l’Observatoire François-Xavier Bagnoud pour avoir partagé avec moi cette conférence, raclette et belle soirée à Saint-Luc.

Pendant cette thèse, si j’ai pu garder (je crois) les pieds sur Terre, c’est déjà en partie grâce aux volleyeurs de Prévessin, avec qui j’allais me défouler, boire des canettes et manger des ’zia’ chez da Ettore. C’est surement aussi grâce à la sophrologie (quelle belle découverte…) chez Philippe et Dominique. C’est certainement aussi grâce à mes très chers amis Gessiens, Chenevessiens et Divonnais. Je vous salue chaleureusement Louis, Florian, Tim, Olja, William, Nico, Remy, Aline, Baptiste…! Allez… quelques doux mots-clés, au hasard de mes pensées: lingot, chess championship à l’huile de foie de morue, bière-pizza (Charly’s), Salève, parcours de santé (10 tours), lactaire délicieux (1), bobsleigh, Krazy House… Une franche accolade à Louis, présent (mais disparaissant parfois après quelques pintes) aussi bien dans les moments un peu difficiles que moins difficiles. Si j’ai gardé la raison, c’est aussi grâce à Fanny, qui a compté, et à tous les chouettes moments passés avec la bande, à Grenoble, Gex, Paris ou au fin fond de l’Ardèche. C’est sans nul doute aussi grâce à mes tous proches et leur bienveillance, mes parents et grand-parents, ma sœurette, Nathalie, Uli, Julia. Je remercie au passage les relecteurs pour vos corrections et suggestions en général fort pertinentes (mention spéciale à Laurent et Jacqueline). Avec certitude, si je n’ai pas débloqué, c’est aussi grâce à ma chère petite Perru***, arrivée sur le tard mais bien arrivée. Que dire? Comment dire? Merci pour ta pétillance, bonne humeur permanente, légèreté, humour, joie de vivre si communicative, pour avoir eu des paroles réconfortantes quand mon moral dégringolait. Merci surtout de m’avoir initié aux plantes vertes, à Dalida, aux Colocs, à la brasse coulée et j’en passe. En passant, justement, merci au reste de la famille Lap’ pour votre accueil simple et chaleureux. Pour terminer, si je n’ai pas trop ondulé de la toiture pendant ces années, c’est peut être aussi grâce à mes amis de longue et très longue date. Je pense à Nathan, notre récent chavirement et notre future régate, à Rémi, au frelon disparu et aux micro trous noirs, à Bidou et au thème entêtant de Taxi Driver, à Dri, mutique ou chantant John Legend, à Verrier ainsi qu’à son lit à mémoire de forme, à Dupin, aux ménisques bien faits et aux GBF bien réglés, à Robin et Jeff Thirion, à Jouty et à nos frasques à la Machine du Moulin Rouge, à Fercot et au Rachais, à Antoine motocross et au robot de table, à Félix et au fameux jeu, à Manu et à l’inondation du 3ème étage, à Gorjup enfin, avec sa clochette et son poil soyeux.

Abstract
Résumé
Remerciements
1 Introduction
1.1 From the Big Bang to the first stars
1.1.1 Big Bang nucleosynthesis
1.1.2 The formation of the first stars
1.2 Origin of the elements
1.3 Stellar rotation
1.4 Observable signatures of the early generations of massive stars
1.5 Overview of this thesis
2 CEMP stars: observations and origins
2.1 Generalities on metal-poor stars
2.2 Observation and abundances of metal-poor stars
2.2.1 The observational steps
2.2.2 Abundances and uncertainties
2.3 CEMP stars as peculiar metal-poor stars
2.4 Internal mixing processes in CEMP stars
2.5 The origin of CEMP stars: external sources
2.5.1 CEMP-s stars
2.5.2 CEMP-r, -r+s, -r/s, -i stars
2.5.3 CEMP-no stars
2.6 Summary
3 Massive source stars: nucleosynthesis and models with rotation
3.1 Nucleosynthesis processes in massive stars
3.1.1 Stellar fusion
3.1.2 The weak s-process
3.1.3 Explosive nucleosynthesis
3.2 The s-process in AGB stars
3.3 Massive stellar models including rotation
3.3.1 Transport induced by rotation
3.3.2 Convection
3.3.3 Nuclear network
3.3.4 Initial composition and opacity tables
3.3.5 Mass loss
3.3.6 Chemical composition of the ejecta
3.4 Axions and their impact on Pop III stars
3.5 Summary
4 Mixing in CEMP-no source stars
4.1 The back-and-forth mixing process
4.2 Nucleosynthesis in a box
4.3 Massive source stars with rotation
4.3.1 Physical ingredients
4.3.2 Evolution with rotation
4.3.3 Composition of the ejecta
4.4 Comparison with CEMP-no stars
4.4.1 A global comparison
4.4.2 The C/N $-$ 12C/13C puzzle
4.5 The late mixing process in the source star
4.5.1 General idea
4.5.2 Implementation in source star models
4.5.3 Comparison with CEMP-no stars
4.5.4 Physical origin
4.6 A systematic study of the CEMP-no source star population
4.7 Are CEMP-no stars helium-rich?
4.8 Other CEMP-no source star models
4.8.1 An energetic H-ingestion event in the source star
4.8.2 Other source star models in the C/N $-$ 12C/13C diagram
4.9 Summary
5 The s-process in CEMP source stars
5.1 The weak s-process in a box
5.2 A new grid of massive stars with rotation and s-process
5.2.1 Nuclear network and reaction rates
5.2.2 The $\mu$ and $\Omega$ profiles
5.3 The origin of the single CEMP-s stars
5.3.1 Massive source stars
5.3.2 The AGB scenario
5.4 The weak s-process at lower metallicities
5.4.1 A rotating 25 $M_{\odot}$ model with various initial metallicities
5.4.2 The origin of HE 1327-2326
5.5 Summary
6 Conclusions and perspectives
6.1 Conclusions
6.2 Perspectives
6.2.1 Linking the old and local with the old and distant Universe
A Numerical aspects
A.1 Axion cooling
A.2 Secular shear mixing
A.3 Mass loss recipes
A.4 Locally weighted scatterplot smoothing
A.5 S-process parameters
B Abundance fits
C Publications

List of Figures

1.1 Big Bang nucleosynthesis
1.2 Mass range of the first stars
1.3 Schematic view of the pre supernovae structure of a massive star
1.4 Neutron capture processes
1.5 Probability density of the rotation velocities for 496 observed OB stars
1.6 Schematic view of the chemical evolution of the Universe
2.1 Spectrum of stars with different metallicities
2.2 Schematic view of the architecture of the Galaxy
2.3 Spectrum of a metal-poor star: from low to high resolution
2.4 X/Fe ratios of the most iron-poor stars
2.5 Evolutionary tracks of 0.85 $M_{\odot}$ models at $Z=0.0001$ without thermohaline and without rotation (top panels), with thermohaline and with rotation (bottom panels, models from Lagarde et al. 2012). The color shows the surface 12C/13C (left panels) and [C/N] ratios (right panels). Symbols show CEMP stars with [C/Fe] $>1$ and [Fe/H] $<-3$ (recognized CEMP-s, -r and -r/s are not plotted). The triangle shows HE 1029-0546 with 12C/13C $=9$ and [C/N] $=-0.26$ . The square shows CS 29528-041 with [C/N] $=-1.47$ (12C/13C is unknown).
2.6 Schematic view of the binary scenario for CEMP-s stars
2.7 Schematic view of a possible formation channel for CEMP-no stars
2.8 Inner abundances of a Pop III 25 $M_{\odot}$ after explosive nucleosynthesis
2.9 Schematic view of the mixing and fallback model
2.10 Post-supernova yields of a non rotating Pop III 40 $M_{\odot}$ model
3.1 The CNO cycle
3.2 The Ne-Na and Mg-Al chains
3.3 Schematic view of the interior of a star during the AGB phase
3.4 Internal $U(r)$ profile in rotating 20 $M_{\odot}$ models with various metallicities
3.5 HR diagram of rotating 20 $M_{\odot}$ computed with different $D_{\rm shear}$ coefficients
3.6 Visualization of the large network used in the present work
3.7 Some important effects of rotation at low metallicity
4.1 Schematic view of the back-and-forth mixing process
4.2 Abundances profile of a 20 $M_{\odot}$ with $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.7$ at $Z=10^{-5}$
4.3 A possible classification of CEMP-no stars
4.4 Nucleosynthesis in a one-zone model while injecting 12C, 16O, 22Ne and 26Mg
4.5 Masses of the cores as a function of initial velocity for 20 $M_{\odot}$ model with $Z=10^{-5}$
4.6 Internal abundance profiles of 20 $M_{\odot}$ models at $Z=10^{-5}$ with various initial rotations
4.7 Same as Fig. 4.6 for other isotopes
4.8 Wind composition of 20 $M_{\odot}$ models at $Z=10^{-5}$ with various initial rotations
4.9 Same as Fig. 4.8 but for the composition of all the H-rich material
4.10 Same as Fig. 4.9 but for the composition of all the H-rich + He-rich material
4.11 Abundances of the 20 $M_{\odot}$ at $Z=10^{-5}$ and $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.4$ (pre-SN)
4.12 Ejecta composition of a 20 $M_{\odot}$ model with $Z=10^{-5}$ and $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.4$ for various mass cuts
4.13 Impact of the dilution in the ejecta composition for a fast rotating 20 $M_{\odot}$
4.14 Effect of varying the efficiency of rotational mixing ( $f_{\rm energ}$ ) on the yields
4.15 Ejecta composition of $Z=10^{-5}$ , $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.4$ models with different initial masses
4.16 Ejecta composition of 20 $M_{\odot}$ , $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.4$ models with different metallicities
4.17 C/N vs. 12C/13C: CEMP-no stars and source star models
4.18 CNO equilibrium timescales as a function of the temperature
4.19 Schematic view of the late mixing process at work in the source star
4.20 Abundances of the 20 $M_{\odot}$ with $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.7$ with/without late mixing
4.21 C/N vs. 12C/13C: CEMP-no stars and source star models including late mixing
4.22 Convective boundary regions of the C-burning shell of a 15 $M_{\odot}$ model
4.23 Best fits of G77-61 and HE 1005-1439 with the source star models of Table 4.4
4.24 Characteristics of the best source star models
4.25 Occurrence of the four categories of the best source star models
4.26 Distribution of $f_{\rm H}+f_{\rm He}+f_{\rm CO}$ for the best source star models
4.27 Same as Fig. 4.23 but for CS 29498-043
4.28 Distribution of the helium mass fraction in the ejecta of the best source star models
4.29 $\log g$ vs. $\log(T_{\rm eff})$ for CEMP-no star models with various initial helium content
4.30 Ejecta composition of massive and AGB star models from various authors
4.31 Same as Fig. 4.30 but in the region where observations lie
5.1 Composition of a one-zone model with various 22Ne content
5.2 Composition of a one-zone model with various 16O content
5.3 Rate of the 17O( $\alpha,\gamma$ )21Ne reaction
5.4 $D_{\rm shear}$ , 14N and 22Ne profiles in 25 $M_{\odot}$ models
5.5 Composition of the ejecta of models computed with low and high resolution
5.6 Composition of AGB models and apparently single CEMP-s stars
5.7 Ejected mass of 4 isotopes as a function of metallicity for rotating 25 $M_{\odot}$ models
5.8 Production factors of 25 $M_{\odot}$ models with various initial rotation rates
5.9 Composition of HE 1327-2326 and of a 25 $M_{\odot}$ source star models with s-process
6.1 Link between the old and local Universe with the old and distant Universe
6.2 Emergent spectra of massive non-rotating models
A.1 Locally weighted scatterplot smoothing
A.2 $\nabla\mu$ in a rotating 25 $\rm M_{\odot}$ model: the impact of smoothing
B.1 Best fits of 69 CEMP stars with $20-60$ source star models
B.2 Fig. B.1, continued
B.3 Fig. B.1, continued
B.4 Fig. B.1, continued
B.5 Fig. B.1, continued

List of Tables

2.1 Nomenclature of iron-deficient stars.
2.2 Classification of CEMP stars.
4.1 Effect of dilution on the source star ejecta composition
4.2 Stars with [Fe/H] $<-3$ and [C/Fe] $>1$ (recognized CEMP-s, -r/s and -r excluded)
4.3 Initial and final surface $\log$ (12C/13C) and [C/N] ratios for 0.8 $M_{\odot}$ models
4.4 Properties of the source star models
4.5 Parameters of the best source star models
5.1 Apparently single CEMP-s stars
A.1 s-process parameters at the end of the core helium burning phase for the models in Choplin et al. (2018): model label (column 1), central neutron exposure (column 2, Eq. A.24), neutron exposure averaged over He-core (column 3, Eq. A.25), number of neutron capture per seed (Eq. A.27) averaged over the He-core mass (column 4), maximum of the central neutron density (column 5), 22Ne burnt (column 6) and left (column 7).

Chapter 1 Introduction

Stars are cosmic engines catching interstellar material, processing it and giving it back during their lives or when they die. Almost all the content in metal111Metals are elements heavier than helium. in the Universe was synthesized in stars. Especially, the first metals in the Universe were synthesized by the first stars, that were predominantly massive222Stars are considered as massive when they go through all hydrostatic burning stages, ultimately leading to an iron-core. The lower mass limit is around 10 $M_{\odot}$ . and that are long-dead now. The comprehension of the entire chemical evolution of the Universe requires to understand its chemical evolution at all the different epochs, from the first stars era to the present day Universe. The onset of the chemical evolution, triggered by the early generation of massive stars, is a crucial and still largely missing piece of the puzzle.

1.1 From the Big Bang to the first stars

1.1.1 Big Bang nucleosynthesis

During the first minutes following the Big Bang, as the temperature decreased from $\sim 10^{32}$ K to about $10^{8}$ K, the first nucleosynthetic event in the Universe took place. The Big Bang nucleosynthesis (BBN) finished about 15 minutes after the Big Bang, when the density and temperature became too low for further nucleosynthesis to occur. At this time, for 100 g of Universe, about 24.8 g was in the form of 4He and almost all the rest in the form of protons (Cyburt et al. 2003). As shown in the left panel of Fig. 1.1, a bit of 2H, 3H, 3He and other light elements is also found. Metals up to oxygen could also be synthesized but in negligible amounts (generally below $10^{-15}$ in mass fraction, see Fig. 1.1, right panel, also Iocco et al. 2007; Coc et al. 2012, 2014).

380000 years after the BBN, the Universe became cool enough (about 3100 K), allowing protons and electrons to recombine and form neutral hydrogen atoms. From this point, the Universe entered the dark ages. It is transparent but no light-producing structures such as stars exist yet.

1.1.2 The formation of the first stars

The first stars (Population III or Pop III stars) formed $\sim 200$ Myr later, with almost exactly 25 % of Helium and 75 % of Hydrogen in mass. For a star to form, a gas cloud has to cool until its Jeans mass333The Jeans mass is the minimum mass of a gas cloud required in order the gravitational force to overcome the gas pressure. When $M_{J}$ is reached, the cloud becomes unstable and collapses. $M_{J}\propto T^{3/2}\rho^{-1/2}$ reaches the mass scale of individual stars. In metal-rich environments, the cooling of the molecular cloud is mainly controlled by heavy elements such as carbon or oxygen. On the other side, it was found by Saslaw & Zipoy (1967) that the cooling in a low-temperature and metal-free environment is achieved by molecular hydrogen H2. The cooling efficiency of H2 being low, the primordial gas is able to cool down to about $200$ K only (Abel et al. 2002; Bromm et al. 2002), against $\sim 10-20$ K at solar metallicity444The metallicity is the sum of the mass fraction of elements heavier than helium. The solar metallicity is $Z_{\odot}=0.0134$ (Asplund et al. 2009).. The higher temperature in primordial gas clouds implies a higher $M_{J}$ and makes the collapse and fragmentation of these clouds more difficult. The fragments are consequently larger, suggesting that the first stars were more massive.

Various multidimensional cosmological simulations have shown that the first stars were predominantly massive (generally $\gtrsim 30$ $M_{\odot}$ , e.g. Abel et al. 2002; Bromm et al. 2002). Some authors have refined this picture by suggesting the existence of two distinct star formation modes for Pop III, leading to two classes of Pop III stars: Pop III.1 and Pop III.2 (e.g. Johnson & Bromm 2006). Pop III.1 stars formed from metal-free $\sim 10^{6}$ $M_{\odot}$ dark matter minihalos. Pop III.2 stars formed from a metal-free gas cloud but which was significantly ionized by photons from already existing Pop III.1 stars. Such an ionization favors the creation of HD molecules in the star forming cloud, which increases the cooling efficiency and leads to lower initial stellar masses. The mass distribution of Pop III.2 stars, possibly peaking at $\sim 10$ $M_{\odot}$ (Hirano et al. 2014), is shifted towards lower values compared to Pop III.1 stars. However, if important turbulent motions were present in primordial gas clouds, the picture is reversed: Pop III.2 stars are on average more massive than Pop III.1 stars (Clark et al. 2011). Indeed, Clark et al. (2011) have shown that turbulence may be more vigorous in Pop III.1 clouds than in Pop III.2 clouds, hence facilitating the fragmentation of Pop III.1 clouds, and ultimately leading to less massive stars on average. The Pop III initial mass range predicted by the most recent simulations still varies a lot from a study to another (cf. Fig. 1.2). For instance, Stacy et al. (2016) predicts masses between 0.05 and 20 $M_{\odot}$ while Hosokawa et al. (2016) between 15 and 600 $M_{\odot}$ . This could be due to differences in the adopted resolution, number of minihaloes followed during the simulation, time of the simulation or types of feedback implemented in the simulation (see Table 1 of Stacy et al. 2016, for an overview of the characteristics of some simulations of first star formation).

1.2 Origin of the elements

If gravity were the only force in stars, they would collapse in less than one hour (the free-fall timescale is about 30 minutes for the Sun). Stars have to produce energy to counteracts their own gravity. The Kelvin-Helmholtz timescale $\tau_{\rm KH}$ gives an estimate of how long a star would shine with its current luminosity if the only power source were the conversion of gravitational potential to heat. For the Sun, $\tau_{\rm KH}=GM_{\odot}^{2}/(R_{\odot}L_{\odot})\simeq 30$ Myr. A lifetime of 30 Myr for the Sun is however too short in regards to geological and biological evidences that the Earth is billions of years old. Nuclear fusion provides another source of energy that sustains stars for a much longer time. Stars gain energy by fusion only up to iron because it is the most bound nucleus. Beyond iron, no fusion can occur. Massive stars with initial masses $M_{\rm ini}>8~{}M_{\odot}$ undergo successive shorter and shorter core burning stages, lasting from millions of years to fractions of days, and ultimately leading to the onion-like structure shown in Fig. 1.3. At the end of each core burning phase, the burning continues in a shell. As evolution proceeds, more and more burning regions are present in the massive star (Fig. 1.3). Nucleosynthesis in massive stars is discussed in more details in Sect. 3.1.

As mentioned, stellar fusion can synthesize elements up to iron. The main processes building elements beyond iron are neutron capture processes (Burbidge et al. 1957). Neutrons are captured by nuclei that can experience a $\beta-$ decay reaction (a neutron is transformed into a proton) if they are unstable. Neutron capture processes are generally separated into two categories: slow and rapid (s- and r-processes), that are both expected to contribute to synthesize about 50 % of the nuclei beyond iron. For the r-process, neutron captures operate on much smaller timescales than for the s-process, giving the possibility to reach very neutron rich (unstable) isotopes that finally decay to the valley of stability (i.e. to stable isotopes, see Fig. 1.4). For the s-process, the neutron capture timescales $\tau_{n}$ are larger than the $\beta-$ decay timescales $\tau_{\beta}$ of unstable isotopes. It means that unstable isotopes $\beta-$ decay before another neutron is captured (with the exception of the branching points where $\tau_{n}\sim\tau_{\beta}$ ). Starting from Fe, the s-process runs mainly along the s-process path which stays close to the valley of stability (black path in Fig. 1.4). The small neutron cross sections of the magic nuclei around A=88, 140, and 208 are bottlenecks for the flow and create distinct peaks in the typical s-process abundance pattern. These peaks can be seen in the abundance pattern of the Sun (top left panel of Fig. 1.4). The s-process ends at 208Pb, the last stable nucleus.

Some isotopes are called s-only (marked as s in Fig. 1.4) because they cannot be synthesized with the r-process. An example is 82Kr. The very neutron-rich isotopes that $\beta-$ decays to the valley of stability (following a diagonal in the (N, Z) plane) after r-process nucleosynthesis cannot reach 82Kr. This isotope is shielded by the stable isotope 82Se. Clayton et al. (1961) have shown that abundances of s-only isotopes in the Sun cannot be reproduced by a single neutron irradiation of an iron seed. In fact, the abundances of elements between $90<$ A $<204$ can be reproduced by a main s-process component while for the elements below $A=90$ , a weak s-process component is required (Kappeler et al. 1989). The main component is associated to Thermally Pulsing (TP) Asymptotic Giant Branch (AGB) stars with $1\lesssim M_{\rm ini}\lesssim 8$ $M_{\odot}$ . The weak component is associated to massive stars with $M_{\rm ini}\gtrsim$ 8 $M_{\odot}$ . These two s-process components are discussed in Sect. 3.1 and 3.2.

1.3 Stellar rotation

During the star formation process, the initial molecular cloud shrinks by $\gtrsim 5$ orders of magnitudes. The local conservation of angular momentum ( $\Omega r^{2}=$ constant) tells us that even if the initial gas cloud rotates very slowly, the newly formed star will rotate fast. A simple conservation of the angular momentum during star formation will however produce only very fast rotator. Since all stars are not very fast rotators, some processes able to dissipate angular momentum during the star formation process have to be invoked.

There are many observational evidences that stars rotate. Huang & Gies (2006) have reported the equatorial velocity distribution of 496 OB stars, whose velocity distribution peaks at 200 km s*-1* (Fig. 1.5). Because of the centrifugal force exerted by rotation, fast rotating stars have an ellipsoid-like shape with a bigger equatorial than polar radius. Thanks to interferometric observations, Domiciano de Souza et al. (2003) have reconstructed the shape of the fast rotating massive star Achernar (about 10 $M_{\odot}$ ). They reported an equatorial radius 1.56 $\pm 0.05$ larger than the polar radius.

Rotation is expected to affect the stellar luminosity, stellar lifetimes, mass loss or the chemical composition of the stellar surface for instance (e.g. Meynet & Maeder 2000; Heger & Langer 2000). Especially, massive stellar models predict surface nitrogen enhancements because of the combined effect of the CNO cycle operating in the stellar interior and rotational mixing. Martins et al. (2015) reported the CNO surface abundances of 74 observed O-type stars with masses between about 20 and 50 $M_{\odot}$ . 80 % of their sample can be explained by single stellar models including rotation.

Rotation at low and zero metallicity

Low metallicity stars have less metals so that they are less opaques and more compact. As a consequence, for the same angular momentum content, low-metallicity stars rotate faster than solar metallicity stars. Low metallicity stars generally lose little mass through winds meaning that they keep more angular momentum than their solar counterpart. This also favors a faster rotation. Faster rotation at low metallicity is supported by different observations: Hunter et al. (2008) have shown that stars in the Small Magellanic Cloud rotate on average faster than Galactic stars (the latter having higher metallicities in general). Maeder et al. (1999) and Martayan et al. (2007) have shown that the fraction of Be-type stars, whose existence is possibly linked to fast rotation, increases with decreasing metallicity.

For Pop III stars, Stacy et al. (2011) estimated their rotation speed thanks to smoothed particle hydrodynamic simulations. They have recorded the angular momentum of the sink particles falling into the growing protostar. The large amount of angular momentum suggests initial velocities of $1000$ km s*-1* or higher for stars with $M_{\rm ini}\geq 30$ $M_{\odot}$ . A caveat in this study is that they estimated the total angular momentum accreted within a radius of 50 UA from the center of the star, meaning that they do not resolve stellar scales. This prevents to see whether some angular momentum removal processes (e.g. stellar winds, disk-locking or magnetic torques) occur in the inner region.

Recently, by studying the angular momentum transfer in primordial discs including magnetic fields, Hirano & Bromm (2018) suggested that the final rotational state of Pop III protostars should exhibit a net bimodality: either the protostar do not rotate at all, or it is a fast rotator, close to breakup speed. As mentioned in their paper, this study does not properly include MHD effects, which are likely required to self-consistently assess this possible bimodality.

Rotation and its effect in low metallicity massive stars is discussed in more details in the next chapters (especially in Sect. 2.5.3 and 3.3).

1.4 Observable signatures of the early generations of massive stars

We have many images of the Universe when it was older than a billion year. With the Cosmic Microwave Background, we also have a picture of the Universe when it was only 380000 years old. One big challenge today is to obtain pictures in between these two periods, when the primordial Universe started to evolve into the incredibly rich zoo of objects we see today. To cite Loeb (2010): “ the situation is similar to having a photo album of a person that begins with the first ultrasound image of him or her as an unborn baby and then skip to some additional photos of his or her years as teenager and adult ”.

The first generations of massive stars in the Universe have specific signatures that one can look for to reveal their nature. The present work focuses on one of these signatures (the metal-poor stars) but the list below includes also other observables, for completeness.

Integrated light of high redshift galaxies

Thousands of very distant galaxies with redshift $z>5$ have been observed (e.g. Bouwens et al. 2007, 2009; Oesch et al. 2010; McLure et al. 2010). The most distant object observed today is a galaxy, GN-z11, with $z=11.1_{+0.08}^{-0.12}$ , possibly formed $\sim 400$ Myr after the Big Bang (Oesch et al. 2016). In the future, the James Webb Space Telescope (JWST) might be able to detect up to a thousand star-bursting galaxies with $z>10$ (Pawlik et al. 2011). Their colors and spectra could be compared with predictions of the integrated light coming from such objects in order to interpret these observations in terms of stellar populations (e.g. Schaerer 2002; Salvaterra et al. 2011).

Abundance determination of high-z objects is challenging. Past and current observations managed to evaluate the abundances of a few elements (generally C, N, O, Si) of $z\lesssim 4$ objects. These objects are mostly damped Lyman $\alpha$ (DLA) systems with $2<z<3$ (e.g. Lehner et al. 2016). In general, the metallicity of such objects is estimated from considerations on the nebular emission lines formed in ionized gas at the sites of star formation (e.g. Pettini & Pagel 2004; Pettini 2008). To date, the most metal-poor DLA system is at $z=3.076$ and has [C/H] $=-3.43\pm 0.06$ , [O/H] $=-3.05\pm 0.05$ , [Si/H] $=-3.21\pm 0.05$ and [Fe/H] $\leq-2.81$ (Cooke et al. 2017).

One difficulty regarding high- $z$ objects is that most of the metal lines are redshifted to the infrared range (by a factor of $1+z$ ), a regime where the sky background is high. In space, although the current telescopes cannot reach the far infrared region (the Hubble Space Telescope, HST, goes up to $\lambda=2.5$ $\mu$ m), JWST should reach $\lambda=28$ $\mu$ m, which may allow to detect the metal lines of very high- $z$ objects.

Reionization

As the first stars formed and radiated energy, the Universe reverted from being neutral, to being ionized once again. At the epoch of reionization and before significant expansion had occurred, the free electron density in the Universe was high enough for Cosmic Microwave Background (CMB) photons to undergo significant Thomson scattering. This let a detectable imprint on the CMB anisotropy map. Inspection of the tiny fluctuations in the CMB polarization by the Wilkinson Microwave Anisotropy Probe (WMAP) first suggested that reionization occured between $11<z<30$ (Kogut et al. 2003). Nine years of observations by WMAP have revised this result and suggested a reionization at $z\sim 10.4$ (Hinshaw et al. 2013). More recently, Planck Collaboration et al. (2016) found that the average redshift at which reionization occured lies between $z=7.8$ and $8.8$ .

Photons from reionization also altered the excitation state of the 21-cm hyperfine line of neutral hydrogen (e.g. the reviews of Morales & Wyithe 2010; Pritchard & Loeb 2012). Models predict that the 21 cm cosmic hydrogen signal will show an absorption feature at $z\simeq 20$ , coming from the Lyman- $\alpha$ radiation of the earliest stars. The 21-cm transition is forbidden but since hydrogen amounts to $\sim 75$ % of the gas mass present in the intergalactic medium, the line intensity is enough to be detected. The line frequency is $\nu=\nu_{0}/(1+z)$ MHz with $\nu_{0}$ the rest-frame frequency of 1420 MHz. For redshifts $6<z<50$ the corresponding frequencies are $30<\nu<200$ MHz. It corresponds to the radio frequency domain, making this line is a prime target for present and future radio interferometers like the Murchison Widefield Array, the Low Frequency Array or the Experiment to Detect the Global Epoch of Reionization Signature (EDGES). Recently, Bowman et al. (2018) reported the detection (with EDGES) of such an absorption feature peaking at 78 MHz consistent with expectations for the 21-cm signal induced by stars having existed by 180 million years ( $z\simeq 20$ ) after the Big Bang. Some discrepancies between this observation and models further suggest that an unknown interaction between dark matter and baryons occurred at early times (Barkana 2018). It may provide new clues on the nature of dark matter.

Supernovae and Gamma-Ray Bursts in distant galaxies

Until now, the Swift Gamma-Ray Burst555Gamma-Ray Bursts are sudden and powerful gamma-ray flashes observed in the Universe, lasting from 0.001 seconds to about 15 minutes. mission (Gehrels et al. 2004) has detected 8 Gamma-Ray Bursts (GRB) at $z>6$ (reported in Table 1 of Salvaterra 2015). The [S/H] ratio of the host system of GRB 050904 ( $z=6.3$ , Kawai et al. 2006) has been inferred to be [S/H] $=-1.6\pm 0.3$ (Thöne et al. 2013), suggesting a sub-solar metallicity for this object. It remains nevertheless still far from the zero or extremely low metallicity Universe. The fact that the metallicity is likely already rather high at $z=6$ somewhat supports the idea of a rapid enrichment in metals. The next generation of space and ground telescopes, such as JWST, the European Extremely-Large Telescope (E-ELT) or the Giant Magellan Telescope (GMT) may not be able to directly see individual first stars (Pawlik et al. 2011). Even if such stars are gravitationally lensed, their detection will remain extremely challenging (Rydberg et al. 2013). The explosion of the first massive stars, on the other hand, should be observable with the next generation of telescopes (Tanaka et al. 2013; Whalen et al. 2013a, b, c).

Gravitational waves

The first stars were likely top-heavy and retained a significant part of their mass because of weaker stellar winds. As a consequence, they could have produced massive black holes (BH) that released gravitational waves (GW) if two of them merged. Recent results suggested that the GW background coming from Pop III binary black holes mergers might be detectable by Advanced LIGO/VIRGO detectors (Kinugawa et al. 2014; Inayoshi et al. 2016).

GW150914 was the first direct detection of gravitational waves. The signal came from the coalescence of a binary BH merger whose components had masses of $36^{+5}_{-4}$ and $29^{+4}_{-4}$ $M_{\odot}$ (Abbott et al. 2016). Cosmological simulations of Hartwig et al. (2016) show that there is a probability of $\gtrsim 1$ % that GW150914 is of primordial origin. These simulations also suggest that Advanced LIGO could detect $\sim 1$ primordial BH-BH merger per year. The GW background from the explosion of the first massive stars might also be detectable but with the next-generation space GW detectors, like the Decihertz Interferometer Gravitational wave Observatory (DECIGO) and the Big Bang Observer (BBO, Sandick et al. 2006; Suwa et al. 2007; Marassi et al. 2009).

Pockets of primordial material

Pockets of primordial gas might be observable in the very distant Universe, but possibly also in the relatively local Universe if such pockets escaped metal pollution. Fumagalli et al. (2011) have observed two gas clouds at $z\sim 3$ with no discernible elements heavier than hydrogen. The derived upper limit for the metallicity is $Z<10^{-4}$ $Z_{\odot}$ . Simcoe et al. (2012) have reported the discovery of another similar cloud at $z=7$ . Such gas clouds might be used as laboratories to probe the formation of metal-free stars. However, in such clouds, the stellar formation process may be different from the formation process of true Pop III stars, formed at the beginning of the Universe: in the early Universe, it is the mass of the cloud that triggers the collapse and the star formation process. In the more mature Universe, a cloud is believed to collapse because of one of several events (e.g. nearby supernovae, collision of molecular clouds…) that compress the cloud and initiate its gravitational collapse. The way the star formation process is triggered may change the initial stellar characteristics (e.g. initial mass).

Nucleosynthetic imprints in low-mass metal-poor stars

As discussed in Sect. 1.1.1, Big Bang nucleosynthesis formed almost only H and He. The first metals were created and released by the first stars. As time proceeded, successive generations of stars formed, evolved and exploded as supernovae, releasing more and more metals in the Universe (see Fig. 1.6 for a schematic view). A consequence is that the global metallicity in the Universe increases with time. It also implies that the metallicity of a star can be used as a proxy for its age. From this consideration follows the assumption that the most metal-poor stars are the oldest stars and then the best candidates to probe the beginning of the stellar era666This assumption is however challenged by recent works suggesting that more metal-rich stars (in the Galactic bulge) are better candidates (see the next point).. While massive metal-poor stars have short lifetimes and are then long dead, low-mass metal-poor stars that formed very early may still be alive around us, and hence observable. These low-mass and very metal-poor stars likely formed with the material ejected by the first short-lived massive stars. On the opposite, the Sun, which was born about 9 Gyr after the Big Bang, formed with a more metal rich material, processed by different generations of stars.

The quest for the most metal-deficient stars in our neighborhood, called stellar archaeology, has started with the HK-survey (Beers et al. 1985, 1992) and the Hambourg/ESO survey (Wisotzki et al. 1996). These surveys discovered a population of metal-poor stars in the Galactic halo. A significant fraction of these stars, especially the most iron-poor, are enriched in carbon (they are called Carbon-Enhanced Metal-Poor or CEMP stars, Beers & Christlieb 2005, see also Chapter 2). Nowadays, several thousands of metal-poor stars are known, some of them possibly having an age close to the age of the Universe (e.g. Sneden et al. 1996, 2008). This opened a new window on the first stars: the chemical composition of the most metal-poor stars delivers valuable clues on the first nucleosynthetic events that took place in the Universe, hence on the nature of early massive stars. Chapter 2 discusses metal-poor stars in more detail.

Nucleosynthetic imprints in the metal-poor stars of the Galactic bulge

The star formation rate is likely more intense in the bulge than in the other parts of the Milky Way. It implies that the metal content increased more rapidly so that there is a different metallicity-age relation in the bulge compared to the Galactic halo. A given metallicity likely corresponds to an earlier age in the bulge than in the halo. Using a chemodynamical model that mimics the formation of the Milky Way, Tumlinson (2010) suggested that of all the stars with very little metals (less than 1/1000 of the solar metallicity), those found in the central regions of the Galaxy were more likely to have formed earlier. It is however very challenging to find metal-poor stars in the bulge since this is the place in the Galaxy where the average metallicity is the highest (the most metal-rich stars known are in the bulge). Another difficulty is that the bulge is a crowded region with high extinction due to dust, making observations more difficult. Finally, the large distance to the bulge (around 8.5 kpc) precludes the observation of too faint stars, unless they are gravitationally microlensed (Bensby et al. 2013).

The globular cluster (GC) NGC 6522 (first observed by Baade 1946), is an interesting metal-poor object located in the bulge. The low metal content derived from the spectra of 8 stars in this GC (about 1 tenth of the solar metallicity, Barbuy et al. 2009) suggests that this GC is old. Images from HST were obtained for this cluster and compared to isochrones (Kerber et al. 2018). The derived age is $\sim 12.5\pm 0.5$ Gyr. High abundances of s-element (Y and Sr) were also detected, possibly pointing towards a signature of massive rotating stars, that enriched the original gas from which the GC formed (Chiappini et al. 2011).

1.5 Overview of this thesis

The aim of the present work is to get clues on the nature of the early generations of massive stars. Informations on these short-lived hence long-dead massive stars are obtained by combining predictions from stellar evolution models including rotation with the observation of metal-poor low-mass stars observed in the halo of the Milky Way.

Chapter 2 reviews the observational steps to get abundances from metal-poor stars as well as the scenarios for the origin of the peculiar Carbon-Enhanced Metal-Poor (CEMP) stars. The mixing & fallback and spinstar scenarios are discussed in detail.

Chapter 3 discusses the theoretical and modeling aspects of massive stellar evolution that are relevant for this work. The specificities of low metallicity models are stressed. The physical ingredients used and/or implemented in the stellar evolution code are presented. A study on the effect of axions on Pop III stars is also included.

Chapter 4 and 5 are the main results of this thesis. The origin of the CEMP (mainly CEMP-no and CEMP-s) stars is investigated using predictions from new massive stellar models I have computed. Chapter 4 investigates the origin of the most iron-poor CEMP stars, generally not significantly enriched in s- and/or r-elements. A simplified nucleosynthesis model is first used and compared to observations. Then, massive source star models are computed, their physics (especially nucleosynthesis) is discussed before comparing the chemical composition of their ejecta to observations. Chapter 5 extends the investigation by following the s-process in massive source star models. New confrontations between source star models including extended nucleosynthesis and observations of CEMP stars enriched in s-elements are presented.

Chapter 6 summarizes the main results of this work, goes to the conclusions and considers the perspectives.

Chapter 2 CEMP stars: observations and origins

This chapter reviews observational aspects and existing scenarios for the origin of CEMP stars. Metal-poor stars are first discussed before going into the special case of CEMP stars. What are the observational and modeling steps to obtain their abundances? What are the specificities of CEMP stars? Can these chemically peculiar stars be explained by internal mixing processes? If no, what kind of external sources should be invoked?

2.1 Generalities on metal-poor stars

Observing the oldest stars is a crucial task to better understand the early Universe. As a first step, it seems natural to wonder whether some stars born very early could live for long enough to be still alive today and around us. At first order, the lifetime of a star $\tau_{\star}$ is equal to the mass of fuel available divided by the stellar luminosity. It yields

[TABLE]

where the mass-luminosity (ML) relationship $L\sim M^{a}$ is used. Setting a standard value of $a=3.5$ leads to lifetimes of 17.5 and 13 Gyr for 0.8 and 0.9 $M_{\odot}$ stars, respectively. It means that nowadays, stars with mass $\lesssim 0.9$ $M_{\odot}$ that formed early in the Universe are still alive, hence possibly observable.

As discussed in Sect. 1.4, the metallicity of a star can be used as a proxy for its age. As a consequence, the oldest stars may be searched among the most metal-poor stars. However, determining the metallicity Z at the surface of a star would require to determine the abundance of all elements heavier than helium, which is not possible. Iron is often taken as an indicator of the metallicity of a star since it is one of the most abundant and easily measurable element in a stellar spectrum. It can be obtained from every observed star. The iron content at the surface of a star is given with the [Fe/H] ratio. For two elements X and Y one has

[TABLE]

with $N_{\rm X}$ and $N_{\rm Y}$ the number density111In the Sun, $N_{\rm H}/N_{\rm Fe}\simeq 32000$ (Asplund et al. 2009) meaning that for each iron atom there are 32000 hydrogen atoms. of elements X and Y. For instance, [Fe/H] $=-4.0$ corresponds to an iron abundance of 1/10000 that of the Sun. This notation requires the abundances of the observed star and the ones of the Sun, taken as a reference. Chamberlain & Aller (1951) first reported a deficiency in iron for 2 stars: HD19445 and HD140283. They derived values of [Fe/H] $=-0.8$ and $-1.0$ . Nowadays, several hundreds of stars with [Fe/H] $<-3$ are known. Eight stars with [Fe/H] $<-4.5$ were observed (listed in the Table 1 of Frebel & Norris 2015). The spectra of the Sun and 3 stars with decreasing [Fe/H] ratios are shown in Fig. 2.1. We clearly see the decreasing line strength with decreasing metallicity. We also see that at very low metallicity, the iron line is the (or among the) strongest lines.

Beers & Christlieb (2005) first established a classification of metal-poor stars based on the [Fe/H] ratio (Table 2.1). According to this terminology, iron-poor stars are classified as metal-poor stars. Rigorously, this association is correct as long as all the abundances (compared to the Sun) of a given iron-poor star scale down like iron, i.e. if a star having [Fe/H] $=-4$ has also [X/H] $=-4$ (where X are all metals). For instance, an iron-poor star with [Fe/H] $=-4$ and [X/H] $=1$ (where X are all metals except iron) is iron-poor but not metal-poor. It will have a super-solar metallicity. However, observations of iron-poor stars show that, in general, other metals roughly scale down in proportion to iron. Notable exceptions, which are the object of this thesis, nevertheless exist: some iron-poor stars are strongly enhanced in other metals and then their chemical pattern is highly non-solar (cf. Sect. 2.3). But even in such extreme cases, the star very likely stays metal-poor. As an illustrative example, a star with [X/H] $=-4$ (X are all metals) has a total metallicity $Z=Z_{\odot}/10^{4}\simeq 1.4~{}10^{-6}$ . Taking the same star but with [C/H] $=0$ (equivalent to [C/Fe] $=+4$ ) gives $Z=2.2~{}10^{-3}$ , which is $\sim 6$ times lower than $Z_{\odot}$ . It shows that even if some metals are strongly enhanced in iron-poor stars, one can securely guess that the total metal content of an iron-poor star stays low (except in very rare cases222Taking the same star as before but this time with [C/H] $=1$ (equivalent to [C/Fe] $=+5$ ) will have $Z>Z_{\odot}$ . Such kind of stars with very little iron but with $Z>Z_{\odot}$ are extremely rare. HE 1045-1434 (Beers et al. 2007) and SDSS J1245-0738 (Bonifacio et al. 2015), with respectively [Fe/H] $=2.55$ and [C/Fe] $=3.2$ , and [Fe/H] $=-3.21$ and [C/Fe] $=3.45$ , may belong to this rare class of stars.). This said, it is important to keep in mind that the most iron-poor stars are not necessarily the most metal-poor stars.

As a final remark, let us mention that the direct association of the lack of metals with the stellar age is not straightforward. For instance, some metal-poor stars could have formed later in isolated pockets of interstellar material that remained metal-poor. Also, some more metal-rich stars could have form early if the star formation rate (hence steepness of age-metallicity relation) was very high. Nevertheless, it is worth noting that the age of some very metal-poor stars was determined owing to the detection of radioactive elements like Th and U at their surface. 238U and 232Th have half lives of about 4.5 and 14 Gyr respectively. Assuming that Th and U were synthesized before the birth of the metal-poor star and supposing that the initial abundances of Th and U are known, one can compare the initial abundances of Th and U to the observed abundances to estimate the age of the star. Ages of about $13-14$ Gyr were derived for several metal-poor stars with [Fe/H] $\sim-3$ (Hill et al. 2002; Sneden et al. 2003; Frebel et al. 2007a). It gives some support to the fundamental hypothesis of stellar archaeology stating that very metal-poor stars are very old stars. The uncertainties related to this dating method are however large (several Gyr). It is mainly because our understanding of the nuclear processes responsible for the formation of Th is still incomplete (especially the uncertainties in the nuclear data and unknown thermodynamic conditions in which the nuclear processes, able to form Th, take place, Goriely & Clerbaux 1999).

2.2 Observation and abundances of metal-poor stars

Metal-poor stars are very rare objects: in the solar neighborhood, only $\sim 1/10^{5}$ field star would have [Fe/H] $<-3.5$ (Frebel & Norris 2015, see also Table 2.1). How and where to find them in the Milky Way which contains billion of stars? As schematically shown in Fig. 2.2, our Galaxy contains four main components: a thick disk, a thin disk, a bulge and a spheroidal halo. The disk is about 30 kpc. Carollo et al. (2007) have shown that the halo can be divided into two broadly overlapping structural components: the inner (radius $\lesssim 15$ kpc) and outer halo (radius $\gtrsim 15$ kpc). These two components have different spatial density profiles, stellar orbits and stellar metallicities. The metallicity of the inner and outer halo peaks at [Fe/H] $\simeq-1.6$ and $-2.2$ , respectively. Surveys carried out over the past decades have shown that the most metal-poor stars are found in the halo of the Milky Way. It is reviewed below the observational steps required to efficiently spot the good metal-poor candidates among the field stars.

2.2.1 The observational steps

The process of getting the surface chemical composition of metal-poor stars is long. As discussed in the review of Beers & Christlieb (2005), there are 3 main observational steps to obtain accurate abundances of metal-poor stars:

•

Step 1 : a wide-angle survey in order to select the metal-poor candidates.

•

Step 2 : a moderate-resolution spectroscopic follow-up of the candidates to validate their lack of metals.

•

Step 3 : a high-resolution spectroscopy of the most interesting candidates to accurately determine the abundances.

Typical spectra obtained from each of these three steps are shown in Fig. 2.3. The star is HE 1327-2326 (Frebel et al. 2005a, b, 2006a, 2006b, 2008; Aoki et al. 2006), having [Fe/H] $=-5.6$ . From step 1 to 3, the resolution $R=\lambda/\Delta\lambda$ increases from 400 to 60000. The high resolution spectroscopy (step 3) was performed with the High Dispersion Spectrograph (Noguchi et al. 2002) on the 8.2-meter optical-infrared SUBARU telescope in Hawaii. Below I give some details on these three observational steps.

Step 1 : wide-angle surveys

The first step, finding metal-poor candidates, can be achieved in different ways.

Proper-motion surveys

A significant fraction of halo stars has high proper motion333The proper-motion of a star corresponds to its apparent angular motion across the sky with respect to more distant stars. compared to Galactic disk stars. It arises because halo stars have elliptical orbits that are not in the Galactic plane (i.e. very different orbits than disk stars like the Sun) and because halo stars have typically larger space velocities than disk stars. This last point implies that a halo star will likely have a higher proper motion than a disc star at the same distance. Schwarzschild & Schwarzschild (1950) and Roman (1950) first suggested a possible correlation between the space velocity of stars and the weakness of their lines (attributed to the lack of metals in their atmosphere). These pioneering works motivated further studies that confirmed the connection between the kinematics of stars and their abundances: metal-poor stars are preferentially found among the stars with a high space velocity. For instance, the first star having [Fe/H] $<-3.0$ (G64-12) was discovered by Carney & Peterson (1981) as the result of its high space velocity. Ryan & Norris (1991) carried out a large spectroscopic follow-up of a sample of stars with high proper-motion. About 10 % of the sample was found to have [Fe/H] $<-2.0$ .

Among the first surveys measuring proper motion, which were based on photographic plates, one finds the Lick Northern Proper Motion survey (Klemola et al. 1987), the Southern Proper Motion survey (Girard et al. 1998) or the SuperCOSMOS Sky Survey (Hambly et al. 2001). More recent surveys are the Sloan Digital Sky Survey (SDSS, York et al. 2000, both photometry and spectroscopy) or the Gaia mission (e.g Perryman et al. 2001).

Colorimetric surveys

The metals (particularly Fe) in the atmospheres of stars absorb preferentially the blue light so that metal-rich stars appear redder while metal-poor stars appear bluer. The color of a star and more specifically the ultraviolet excess $\delta(U-B)$ can be used as a metallicity indicator (e.g. the early works of Wallerstein & Carlson 1960; Wildey et al. 1962).

The SkyMapper Southern Sky Survey (SMSS, Keller et al. 2007) is a photometric program of the Southern Hemisphere started in 2008 and giving accurate estimates of atmospheric parameters of metal-poor stars (effective temperature, surface gravity and stellar metallicity). This survey led to the discovery of the most metal-poor star currently known: SM 0313-6708 with [Fe/H] $<-7.3$ (Keller et al. 2014).

The Pristine survey (Starkenburg et al. 2017) is a photometric survey using a narrow filter with a width of $\sim 100$ Å that covers the wavelengths of the Ca doublet lines (at 3968.5 and 3933.7 Å). A spectroscopic follow-up of promising metal-poor candidates selected by the Pristine survey has led to the discovery of numerous metal-poor stars with [Fe/H] $<-3$ (Youakim et al. 2017).

Objective-prism surveys

Such surveys are wide-angle spectroscopic surveys with low-resolution ( $R\simeq$ 400). The idea is generally to examine the strength of the CaII K line so as to obtain a first estimate of the metal content of the star. Bond (1970) and Bidelman & MacConnell (1973) first carried out such surveys, aiming at identifying metal-poor stars based on spectroscopy only. The HK survey (Beers et al. 1985, 1992) and the Hamburg/ESO (HES) survey (Wisotzki et al. 1996) are other surveys of this type, that were prolific sources of metal-poor stars.

After a spectroscopic follow-up of metal-poor candidates selected from the HK survey, it appeared that 11 % of the candidates had [Fe/H] $<-2.0$ (Beers & Christlieb 2005). A drawback regarding the HK survey is that metal-deficient cool stars would likely be missed. Indeed, such stars have enhanced strengths of their Ca II K lines because of the lower temperature and therefore are considered as metal-rich stars. The HK-II survey (Rhee 2001) aimed at identifying the metal-poor red giant cool stars that may have been missed in the original analysis due to the temperature bias against cool stars. It allowed to raise the efficiency of the HK survey to detect metal-poor stars from 11 to 32 %.

The HES survey can observe fainter objects than the HK survey (about 2 magnitude deeper). Because of the broad wavelength range covered ( $3200<\lambda<5200$ against $3875<\lambda<4025$ for the HK survey), the $U-V$ color of stars can be directly obtained from the spectra and combined to the spectroscopy to select metal-poor candidates with more security. A spectrum obtained from the HES survey is shown on the upper panel of Fig. 2.3. Spectroscopic follow-up of metal-poor candidates selected from the HES survey have shown that $50-60$ % of the candidates have [Fe/H] $<-2.0$ .

Step 2 : moderate-resolution spectroscopy

After step 1, a moderate-resolution spectroscopic follow-up of the candidates is required to validate the metal-poor stars among the sample. It also exists surveys targeting hundredth thousands of stars with a moderate-resolution and thus allowing to skip the step 1.

The SDSS survey do both photometry and medium resolution spectroscopy ( $R\sim 2000$ ). SDSS has gone through 3 stages: SDSS-I (from 2000 to 2005), SDSS-II (from 2005 to 2008) and SDSS-III (from 2008 to 2014, Eisenstein et al. 2011). SDSS includes several individual surveys, among them the Sloan Extension for Galactic Understanding and Exploration (SEGUE) survey (Yanny et al. 2009). The two phases of SEGUE, SEGUE-1 and -2, obtained spectra for 240000 and 118151 stars, respectively, with typical errors in $T_{\rm eff}$ , [Fe/H] and $\log g$ of 117 K, 0.22 and 0.26 dex, respectively. SDSS/SEGUE surveys were prolific sources of metal-poor stars (e.g. Fukugita et al. 1996; Adelman-McCarthy et al. 2008; Abazajian et al. 2009) and motivated numerous high-resolution observations (e.g. Aoki et al. 2013, where 137 metal-poor SDSS candidates were observed with the high dispersion spectrograph of the Subaru telescope.).

The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) survey (Deng et al. 2012) started in 2008. It should provide spectra for 2.5 million stars. The resolution is about $R=$ 1800. This survey also triggered high-resolution observations. Li et al. (2015) reported $R=$ 36000 spectra for two stars with [Fe/H] $\sim-4$ , selected in the LAMOST database.

From 2003 to 2013, the RAdial Velocity Experiment (RAVE, Steinmetz 2003) targeted bright stars ( $8<m<12$ , it represents stellar distances up to $\sim$ 3 kpc from the Sun). This survey delivered spectra for about 480000 stars with a resolution $R=7000$ . In a RAVE database of approximately 200000 stars belonging to the Galactic disk or halo, Fulbright et al. (2010) identified 631 stars with [Fe/H] $<-2$ ( $\sim$ 0.3 %). In the Galactic bulge, the ARGOS survey (Abundances and Radial velocity Galactic Origins Survey) revealed 16 stars with [Fe/H] $<-2$ within a sample of 14150 stars ( $\sim$ 0.1 %, Ness et al. 2013). In the frame of the EMBLA (Extremely Metal-poor BuLge stars with AAOmega) survey, Howes et al. (2014, 2015, 2016) reported the discovery of about 30 other bulge stars with [Fe/H] $<-2$ (among them a star with [Fe/H] $=-3.94\pm 0.16$ ). No star with [Fe/H] $<-4$ was found in the bulge.

Step 3 : high-resolution spectroscopy

Once the promising candidates are identified, the next step consists in obtaining high-resolution (R $\geq$ 30000), high S/N (signal-to-noise) spectra.

Numerous studies conducted high-resolution spectroscopic observations on metal-poor star candidates, originally selected from the HE, HK, SDSS or SEGUE surveys (e.g. McWilliam et al. 1995; Carretta et al. 2002; Cohen et al. 2004, 2008, 2013; Barklem et al. 2005; Aoki et al. 2007, 2013; Hollek et al. 2011; Caffau et al. 2011; Bonifacio et al. 2012; Norris et al. 2013; Yong et al. 2013; Roederer et al. 2014b; Hansen et al. 2014). There are at least three public database, grouping the abundances of metal-poor stars derived from high-resolution spectra:

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The SAGA database444http://sagadatabase.jp. (Suda et al. 2008).

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The Frebel (2010) database555http://www.metalpoorstars.com..

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The JINAbase666http://jinabase.pythonanywhere.com. (Abohalima & Frebel 2017).

Among the future high resolution surveys one finds 4MOST (e.g. Feltzing et al. 2017), WEAVE, a spectrograph that will offer two possible resolutions: 5000 and 20000 or GALAH (Galactic Archaeology with the HERMES spectrograph Martell 2016) which aims at collecting R $\sim$ 28000 spectra for one million stars in the Milky Way.

2.2.2 Abundances and uncertainties

Once a high-resolution spectrum is acquired from a star, the abundances in term of numbers have to be determined (e.g. [X/Fe] ratios). This is a highly nontrivial task that required a realistic stellar atmosphere model. Stellar abundances are therefore not observed but deduced by modeling the spectral lines. The stellar abundances are generally determined by inspection of the equivalent width of spectral absorption lines. The observational uncertainty varies as $\sqrt{\rm FWHM}$ / (S/N) where FWHM is the full width at half maximum of the line. A spectrograph with a high resolving power and a high S/N minimizes the uncertainties, allowing the detection of weaker features, which is primordial when observing stars with little metals, hence with weak lines.

A perfect atmosphere model would be a 3D model taking into account departures from local thermodynamic equilibrium (LTE) and where all the atomic and molecular physics (determining the absorption lines) is included. Such a model does not exist. Often, abundances are derived using a 1D LTE model.

Frebel et al. (2008), have estimated by how much the abundances are affected when deriving the abundances with either a 1D or a 3D model. They investigated the star HE 1327-2326 ([Fe/H] $=-5.7$ ). They found a 3D-1D correction for C, N and O of about $-0.7$ dex.

Ezzeddine et al. (2017) studied anew the stellar parameters of 20 stars with [Fe/H] $<-4$ using a 1D NLTE (non LTE) atmosphere model instead of a 1D LTE model. They derived [Fe/H] corrections up to 1 dex compared to the 1D LTE case. These corrections are larger at lower [Fe/H]: at [Fe/H] $=-4$ and $-7$ , the corrections are about 0.5 and 1 dex respectively. Lind et al. (2012) reported a similar trend: they derived NTLE corrections of $\lesssim 0.1$ and $\lesssim 0.5$ dex at solar and low metallicity, respectively. Also, these corrections apply only for the derivation of Fe abundances from neutral lines (Fe I). The corrections are mostly insignificant if using Fe II lines. Determining the Fe abundance with accuracy is important since it is generally a prerequisite for the determination of the abundance of other elements.

2.3 CEMP stars as peculiar metal-poor stars

This section aims at describing the characteristics of CEMP stars. Their possible origin is discussed in the next section.

A natural guess could be that in metal-poor stars, all metals are scaled down compared to the Sun by roughly the same factor. However, observations progressively revealed that metal-poor stars generally have non-solar-like abundance patterns. In particular, the carbon to iron ratio is super-solar in many metal-poor stars. The first carbon stars were observed about 150 years ago by Angelo Secchi (Secchi 1868). At that time, he only reported a peculiar banding in the stellar spectra. These stars were later identified by Rufus (1916) as stars enriched in carbon. Since, many carbon-rich stars were discovered, particularly among the most iron-poor stars. Stars enriched in carbon and depleted in iron were called Carbon-Enhanced Metal-Poor (CEMP, Beers & Christlieb 2005). This name might seem somewhat contradictory since carbon is a metal. However, CEMP stars likely stay metal-poor compared to the Sun, even if they show overabundances in carbon or other metals (cf. discussion in Sect. 2.1). Beers & Christlieb (2005) proposed two criteria defining a CEMP star: [Fe/H] $<-1.0$ and [C/Fe] $>1.0$ . The criterium of [C/Fe] $>0.7$ is also often used in the literature (first proposed by Aoki et al. 2007). For what follows, depending on the criterium used by the considered author, I use the names

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CEMP1.0 if the condition is [C/Fe] $>1.0$ .

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CEMP0.7 if the condition is [C/Fe] $>0.7$ .

Are CEMP stars enriched in other elements?

CEMP stars have various lithium abundances, from777A(X) = $\log\epsilon(\rm X)$ = $\log(N_{\rm X}/N_{\rm H})+12$ , where X represents a given element. A(Li) $\simeq 2$ (i.e. close to the Spite plateau of $2.05\pm 0.16$ , Spite & Spite 1982) to A(Li) $<0.62$ for HE 1327-2326 with [Fe/H] $=-5.7$ (Frebel et al. 2008). Some observational works have suggested a melt-down of the Spite plateau below [Fe/H] $\simeq-3$ (Aoki et al. 2009; Sbordone et al. 2010; Bonifacio et al. 2012). The melt-down has nevertheless to be further confirmed since some iron-poor stars could have experienced severe surface Li depletion episodes (especially those who are giants). Korn et al. (2009) have computed models of the star HE 1327-2326 including the effects of atomic diffusion. They predict a maximal Li depletion of 1.2 dex from the birth of the star to the present day. It gives a maximal initial Li abundance of about 1.8, which is much closer to the Spite plateau. Other scenarios in the same work predict a milder Li depletion, of the order of 0.2 dex, which would give an initial Li well below the Spite plateau. In any case, these initial Li abundances are not compatible with the WMAP-based primordial Li abundance of 2.63 predicted from primordial nucleosynthesis (Spergel et al. 2007).

Many CEMP stars have high N/Fe, O/Fe, Na/Fe or Mg/Fe ratios. For stars with [Fe/H] $<-$ 3, the scatter of the [X/Fe] ratios globally decreases from X $=$ C to Ca (Frebel & Norris 2015). For instance, the [C/Fe], [O/Fe], [Na/Fe], [Mg/Fe] and [Ca/Fe] ratios span about 5, 4, 2.5, 1.5 and 0.5 dex, respectively (see Fig. 2.4).

A significant amount of CEMP stars are also enriched in elements heavier than iron. These elements are thought to be mostly synthesized through the slow and rapid neutron capture processes (also the intermediate process or i-process, see Sect. 2.5). Aoki et al. (2000) and Van Eck et al. (2001) discovered the first VMP stars enriched in Pb. Many other CEMP stars enriched in s- and/or r-elements were discovered, down to [Fe/H] $\sim-3$ (Burris et al. 2000; Simmerer et al. 2004; Sivarani et al. 2004; Lai et al. 2007; Placco et al. 2013). Below this threshold, enhancements in s- and r- elements are generally very modest (see Fig. LABEL:12ab).

Beers & Christlieb (2005) established a classification of CEMP stars based on their heavy element abundances (see Table 2.2). One finds CEMP stars enriched in s-elements (CEMP-s), r-elements (CEMP-r), both r- and s-elements (CEMP-r/s) and without significant enhancement in s-/r-elements (CEMP-no). As they note, this classification should be viewed as a first approximation and used as a guideline for the future. Indeed, the location of the class boundaries are somewhat arbitrary and in some cases, it may exist a continuity between the classes rather that very distinct groups. Eu and Ba were chosen to define such classes because (1) they are generally readily measurable in a stellar spectrum and (2) they are expected to be produced in a different amount by the s- and r-process (Eu: mainly r-process, Ba: mainly s-process). It has been shown (especially Yoon et al. 2016) that CEMP-no stars are generally found on the low carbon band with A(C) $\leq$ 7.1 and CEMP-s/rs on the high carbon band with A(C) $>$ 7.1. It might be linked to the different formation channel for CEMP-no and CEMP-s/rs stars (Sect. 2.5). Interestingly, this separation into 2 bands, allows (with some level of confidence) to classify CEMP stars only based on their C abundance rather on e.g. Ba, whose abundance determination requires much higher resolution spectra. Fig. LABEL:12ab shows that CEMP-s stars mainly lie at [Fe/H] $>-3$ (green symbols). CEMP-no stars (blue symbols) are generally found at lower [Fe/H]. Some CEMP stars (magenta symbols) are still unclassified, according to the criteria of Table 2.2.

Are CEMP stars frequent?

Carbon et al. (1987) and Norris et al. (1997) first emitted the possibility of a higher frequency of C-rich stars with decreasing [Fe/H]. Marsteller et al. (2005) reported a possibly high fraction of about 50 % of CEMP1.0 stars888I remind here that CEMP1.0 means that the author used the condition [C/Fe] $>1$ for a star to be CEMP. CEMP0.7 means that the author used the condition [C/Fe] $>0.7$ . among [Fe/H] $<-2$ stars selected in the HES survey. However, Cohen et al. (2005) showed that the [Fe/H] ratio of some stars in the HES survey was overestimated by $\sim 0.5$ dex. Consequently, they derived a CEMP1.0 fraction of $14\pm$ 4 % (instead of 50 %) among the stars with [Fe/H] $<-2$ . In 240 stars with [Fe/H] $\leq-2$ , Lucatello et al. (2006) found a CEMP1.0 fraction of 21 $\pm 2$ %. Lee et al. (2013) considered a sample from SDSS/SEGUE of about 247000 stars and found that 12 % of [Fe/H] $<-2$ stars are CEMP0.7.

One of the possible bias to these frequencies is that in giant stars, the first dredge-up has occurred. Amongst other, it changes the surface carbon abundance (cf. Sect. 2.4). For a sample of 505 stars with [Fe/H] $<-2$ , Placco et al. (2014c) have estimated the effect of the first dredge-up on the surface carbon abundance. The recognized CEMP stars enriched in s- and/or r-elements were excluded from their analysis999Note that this does not mean that all stars they consider are CEMP-no. Some CEMP stars in the sample without a determined Ba abundance might appear to be CEMP-s, -r/s or -r in the future.. The stellar models they used predict that the correction on the [C/Fe] ratio induced by the first dredge-up is generally about 0.5 dex for the evolved stars. They recovered the initial [C/Fe] ratio of the 505 stars of their sample (the initial ratio is higher in case the star has experienced the first dredge-up). They finally found that 20, 43 and 81 % of stars with [Fe/H] $<-2$ , $<-3$ and $-4$ are CEMP0.7, respectively. The first dredge-up effect corrected, it likely gives the fraction of stars which were born as CEMP0.7.

There is also a spatial variation of the CEMP frequency: Carollo et al. (2012) have shown that the CEMP0.7 frequency is increasing with the distance to the Galactic plane. Almost all CEMP0.7 stars belong to the halo and the fraction is higher in the outer than in the inner halo. Considering the most distant stars (more than 9 kpc from the Galactic plane, i.e. mainly in the outer halo), they derived a CEMP0.7 frequency of 20 %. Carollo et al. (2014) reported a fraction of CEMP-no stars of 43 and 70 % in the inner and outer halo respectively. For the CEMP-s stars, they found 57 and 30 % in the inner and outer halo respectively. It suggests that the dominant source of CEMP stars in the two halo components were different. A recent study suggested that the CEMP fraction (among the [Fe/H] $<-3$ stars and after excluding the likely CEMP-s and -r/s stars) in the Sculptor dwarf galaxy is $\sim 36\pm 8~{}\%$ (Chiti et al. 2018), i.e. similar to the $\sim 43~{}\%$ of the Galactic halo (Placco et al. 2014c).

Are CEMP stars in binary systems?

Lucatello et al. (2005) and Starkenburg et al. (2014) showed that the whole sample of CEMP-s stars is consistent with the hypothesis of them all existing in binary systems. A careful monitoring of the radial velocity of 22 CEMP-s stars over several years has revealed a clear orbital motion for 18 stars ( $\sim 82~{}\%$ ) while 4 stars appeared to be single (Hansen et al. 2016b). The probability of finding one face-on system in their sample is about $0.01~{}\%$ , meaning that it is extremely unlikely that all the four apparently single CEMP-s stars are in fact binary systems that were seen face-on. Apparently single stars might nevertheless have a companion with a long orbital period (about $10^{3}-10^{4}$ days at minimum), which would prevent to detect radial motions of the CEMP-s stars. A similar study was carried out for CEMP-r and CEMP-no stars. The binary frequency was found to be $18\pm 6~{}\%$ for CEMP-r (Hansen et al. 2015b) and $17\pm 9~{}\%$ for CEMP-no stars (Hansen et al. 2016a), i.e. much lower than for CEMP-s stars. It suggests that the CEMP-r and CEMP-no stars are likely disconnected from a binary origin.

2.4 Internal mixing processes in CEMP stars

CEMP stars formed with the material ejected by previous stars (at least some of it). One may see the nucleosynthetic signature from these previous stellar generations in the CEMP star surface chemical composition. However, the CEMP star surface composition can be altered during the life of the CEMP star itself. If this alteration is important enough, it could erase the chemical imprint let by the previous star(s). Two different categories of processes can affect the surface abundances of CEMP stars: external and internal processes.

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External processes can be accretion of interstellar material or accretion of material from a binary companion. While accretion of interstellar material was found to not have a significant effect on metal-poor stars (Frebel et al. 2009; Johnson & Khochfar 2011), the accretion of material ejected by a companion is certainly an important process, especially for CEMP-s stars (cf. Sect. 2.5.1).

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Internal processes happen in the CEMP star itself. There are for instance the first dredge-up or thermohaline mixing.

Below it is discussed the main (known) internal mixing processes that can happen in CEMP stars and possibly alter their surface composition. A sample of CEMP stars is considered and compared with low-mass stellar models. The sample comprises the CEMP stars with [C/Fe] $>1$ and [Fe/H] $<-3$ . The CEMP stars enriched in s- and/or r-elements are excluded101010This likely excludes most of the CEMP stars whose surface abundances were modified because of the accretion of material from a companion (especially the CEMP-s stars, see Sect. 2.5.1)..

The first dredge-up.

Stellar models predict that as a low-mass star runs out of hydrogen, its envelope expands, the surface temperature decreases, making the star evolving to the red giant branch (RGB). During that stage, the outer convective envelope expands inward and penetrates hotter regions, where the CN-cycle is active. Some CN-processed material is consequently brought to the surface and alters the star’s surface light element abundances. This mixing episode is called the first dredge-up (Iben 1964). Since the CN-cycle mainly transforms 12C into 14N and to a lesser extent into 13C, the effect of the first dredge-up is to decrease the surface C/N and 12C/13C ratios. Charbonnel (1994) has shown that if starting with 12C/13C $\simeq 65$ and 12C/14N $\simeq 3.7$ (equivalent to [C/N $=0$ ]) in a 1 $M_{\odot}$ model at $Z=10^{-3}$ , the first dredge-up decreases 12C/13C and 12C/14N to about 25 and 2 (equivalent to [C/N] $\sim-0.3$ ) respectively. In the top panels of Fig. 2.5 the surface 12C/13C and [C/N] ratios along the evolution of a standard low metallicity 0.85 $M_{\odot}$ model are shown. The first dredge-up occurs at $\log(T_{\rm eff})\sim 3.7$ and $\log g\sim 3$ and decreases the surface 12C/13C from about 70 to 45. The [C/N] ratio is barely affected by the first dredge-up (top right panel). Dredge-up events generally cannot explain CEMP stars since (1) they tend to deplete the carbon while we look for the opposite and (2) some CEMP stars are still unevolved (Fig. 2.5) meaning that they did not experienced any dredge-up episode. Quantifying this process for each CEMP star is nevertheless important in order to correct the surface abundances of evolved stars and recover their initial surface abundances, that reflect more directly the abundances in their natal cloud. This was done in Placco et al. (2014c) for the carbon abundance. Their CEMP stellar models suggest that the first dredge-up correction on the surface C abundance is about 0.5 dex (0.8 dex in the most extreme case).

Thermohaline mixing and rotation.

Thermohaline mixing occurs after the first dredge-up so that unevolved CEMP stars are not affected by this process (provided they do not accrete heavy material from a companion, cf. Sect. 2.5.1). Thermohaline mixing can occur in giant stars because of an inversion of the molecular weight around the top of the H-burning shell, just below the convective envelope. The negative $\nabla_{\mu}$ ( $\mu$ , the mean molecular weight, is growing outward) results in a mixing event, following the first dredge-up, and decreasing again the C/N and 12C/13C ratios (e.g. Charbonnel & Zahn 2007; Eggleton et al. 2008). Rotation transports the H-burning products outwards. It likely adds another mechanism to decrease the surface C/N and 12C/13C ratios. The bottom panels of Fig. 2.5 show the surface 12C/13C and [C/N] ratios during the evolution of a low metallicity 0.85 $M_{\odot}$ model including thermohaline mixing and rotation. In this case, the surface ratios are significantly reduced, particularly near the end of the evolution, where 12C/13C $\sim 8$ and [C/N] $\sim-1.6$ . According to these models, some of the evolved CEMP stars shown in Fig. 2.5 may have experienced an important modification of their surface C and N abundances (cf. also the work of Stancliffe et al. 2009). Among the unevolved CEMP stars, some have low 12C/13C ratios, like HE 1029-0546 with 12C/13C $=9$ (triangle in Fig. 2.5, Hansen et al. 2015a). Some other unevolved stars have low [C/N] ratios like CS 29528-041 with [C/N] $=-1.47$ (square in Fig. 2.5, Sivarani et al. 2006). These low ratios likely cannot be explained by internal processes. Such ratios probably reflect some processes at work in external sources (e.g. previous massive stars).

Atomic diffusion.

Such a process has the effect of separating the elements. It groups together the effects of gravitational settling, thermal diffusion and radiative acceleration (Michaud et al. 2015). Richard et al. (2002) predicted that atomic diffusion can alter the surface composition of metal-poor stars by $\sim 0.1-1$ dex. It depends on the chemical species considered, effective temperature and the evolutionary stage. For C, O, Na, Mg, Al and Si, the alteration does not exceed 0.5 dex, except in some hot models ( $T_{\rm eff}\gtrsim$ 6300 K). Richard et al. (2002) have also shown that the impact of atomic diffusion becomes very small (about $\sim 0.1$ dex) if including an additional turbulence effect that is required to account for the chemical anomalies of some stars (the AmFm stars, Richer et al. 2000).

Overall, although internal processes in CEMP stars can modify their surface abundances, these processes likely cannot account for the unevolved or relatively unevolved CEMP stars. For the most evolved CEMP stars, internal mixing processes might have erased the initial surface chemical composition (hence the signature of previous stellar generations) for some elements like C or N. An important work would be to compute a grid of CEMP stellar models including various mixing processes in order to quantify the degree of mixing experienced by each observed evolved CEMP star. The aim would be to recover the initial surface abundances of all elements. Such a correction would give the chemical composition of the CEMP natal cloud. It will establish a more direct link between the evolved CEMP stars and the ejecta of the previous generation of stars.

2.5 The origin of CEMP stars: external sources

The origin of the CEMP stars is closely linked to the origin of the elements. When investigating the origin of CEMP stars, the aim is generally to find what is the astrophysical source able to provide the carbon, nitrogen, s-, r-elements…

It really seems that external sources are needed to explain the peculiarities of CEMP stars. The external sources can be objects that lived before and enriched the cloud in which the CEMP star formed and/or companions stars that transferred material to the (future) CEMP star. In this global frame, the existing scenarios for the origin of the different classes of CEMP stars are discussed below.

2.5.1 CEMP-s stars

Near the end of their lives, stars with initial masses between about 1 and 8 $M_{\odot}$ evolve to the Asymptotic Giant Branch (AGB). AGB stars are known to be at the origin of the main s-process component (cf. Sect. 3.2) and also to produce light elements such as carbon. Are CEMP-s AGB stars? Actually no: many CEMP-s stars are still rather unevolved and therefore do not have gone through the AGB phase, where s-elements can be produced. The main scenario (see Fig. 2.6 for a schematic view) considers that CEMP-s were born as $\sim 0.8$ $M_{\odot}$ normal stars (i.e. not C-rich, not s-rich) in a binary system with a more massive companion (e.g. 1.5 $M_{\odot}$ ). During its AGB stage, the companion produces and ejects through winds a material enriched in light and s-elements. Some of the wind material is accreted by the companion, that becomes a CEMP-s star. The AGB star ends its life as a white dwarf.

In the scenario described above, the mechanism for the transfer of mass is wind mass transfer. The transfer of mass may indeed preferentially occur through wind accretion rather than through Roche-lobe111111The Roche-lobe is a distinctively shaped region that surrounds a star in a binary system. In this region, the material is gravitationally bound to the star. If the primary exceeds the Roche-lobe radius, some material can flow towards the secondary. overflow because when the donor is an AGB star, Roche-lobe overflow may be unstable (Paczyński 1965) and brings the system to the common envelope phase. In this phase, 3D hydrodynamic simulations suggest that accretion is very inefficient (Ricker & Taam 2008), meaning that the formation of CEMP-s stars might not happen. By investigating the origin of 15 CEMP-s stars with known orbital periods, Abate et al. (2015b) have shown that the wind mass transfer model generally agrees well with observations but in most of the cases, the wind accretion rate should be enhanced by a factor of $5-10$ to account for the observations.

Atomic diffusion and thermohaline mixing on CEMP-s stars are important ingredients that may induce important surface composition changes (e.g. Stancliffe et al. 2007). The accreting CEMP-s star undergoes thermohaline mixing because the material coming from the AGB companion has a larger mean molecular weight than the material at the surface of the accreting future CEMP-s star121212In this case, thermohaline mixing can occur during the main sequence.. After the accretion, thermohaline can reduce the surface carbon abundance in the CEMP-s by $\sim$ 1 dex (Stancliffe et al. 2007). A too strong thermohaline would make the s-elements sink and disappear from the stellar surface. However, if CEMP-s stars rotate, the horizontal turbulence induced by rotation may reduce or even kill the thermohaline mixing (Denissenkov & Pinsonneault 2008; Maeder et al. 2013). Models of rotating CEMP-s stars computed by Matrozis & Stancliffe (2017) supports this view by showing that even a mild rotational mixing severely inhibits thermohaline mixing (also atomic diffusion is inhibited).

Worth to mention is also that if a substantial amount of material (hence angular momentum) is accreted from the AGB companion, the CEMP-s star should spin up significantly. Matrozis et al. (2017) have shown that $\sim 0.05$ $M_{\odot}$ can be accreted before the CEMP-s reaches critical rotation and therefore stops accreting more material. However, more than $0.1$ $M_{\odot}$ is often needed to reproduce the chemical composition of observed CEMP-s stars (e.g. Abate et al. 2015a, b). This said, a generally good agreement is found between the yields of AGB stars and chemical composition of CEMP-s stars (with nevertheless several persisting discrepancies, especially for C, N, F, Na, and 12C/13C, Lau et al. 2009; Stancliffe 2010; Bisterzo et al. 2011, 2012; Lugaro et al. 2012).

The AGB binary scenario is also well supported by the fact that a large fraction of CEMP-s stars is in a binary system (cf. Sect. 2.3). The apparently single CEMP-s stars nevertheless challenge this scenario, even if one can imagine that the single CEMP-s stars have lost their AGB companion or that they are in a binary system with a very long period, explaining the non-detection of radial velocity variation.

In general, even if CEMP-s stars are explained with the AGB scenario, it does not mean that the previous generations of massive stars did not contribute. Likely, it means that the nucleosynthetic signature let by the AGB companion on the CEMP-s star is the dominant one and has blurred the nucleosynthetic signature let by the previous generation of stars. In Chapter 5, I investigate whether the nucleosynthetic imprint of previous massive stars can be identified in CEMP stars enriched in s-elements.

2.5.2 CEMP-r, -r+s, -r/s, -i stars

The origin of CEMP-r stars is tightly linked to the astrophysical site for the r-process, which is still unknown. The two main possible r-process sites are magnetorotationally driven supernovae (MRSNe, e.g. Thielemann et al. 2011; Winteler et al. 2012; Nishimura et al. 2015) and neutron star (NS) merger (e.g. Symbalisty & Schramm 1982; Freiburghaus et al. 1999; Thielemann et al. 2011, 2017; Wanajo et al. 2014). Recently, LIGO detected GW170817, the first observed binary neutron star inspiral (Abbott et al. 2017). The light curve of the electromagnetic counterpart was found to be compatible with a NS merging event producing r-elements (Smartt et al. 2017; Pian et al. 2017).

NS mergers alone may nevertheless face difficulties to explain the most iron-poor CEMP-r stars (e.g. SM 0248 $-$ 6843 with [Fe/H] $=-3.71$ and [Eu/Fe] $=1$ , Jacobson et al. 2015), as shown by inhomogeneous chemical evolution models (Argast et al. 2004; Wehmeyer et al. 2015). As summarized in the review of Thielemann et al. (2017), one important reason is that the merging of two NS requires two prior supernova events, that can already lead to a substantial floor of Fe. This floor may be too high compared to the CEMP-r stars with the lowest [Fe/H] ratios. This issue may nevertheless be solved if the two NS have undergone kicks at the time of the supernova (SN) explosion: in this case, they were removed from the SN debris and moved into a medium with low Fe pollution. With chemical evolution models, Wehmeyer et al. (2015) have also shown that if the NS-NS system takes too long to coalesce, further nucleosynthesis events can occur and enrich the interstellar medium (ISM) in Fe. When the NS-NS system finally merges, the surrounding ISM has a higher [Fe/H] than at the birth of the NS-NS system. In particular, they show that considering NS merger alone in their models cannot explain the [Eu/Fe] ratios at [Fe/H] $<-2.5$ . Considering also MRSNe as sources of r-elements can provide a solution to account for the enrichment in Eu at [Fe/H] $<-2.5$ (Cescutti & Chiappini 2014; Wehmeyer et al. 2015).

Some other stars have abundance patterns that neither a s-process pattern, nor a r-process pattern and nor a combination of both can fit the abundances. In such cases, an intermediate neutron capture process (i-process, first named by Cowan & Rose 1977), operating at neutron densities in between the s- and r-process may be the solution (e.g. Lugaro et al. 2012; Roederer et al. 2016; Hampel et al. 2016). The astrophysical sites for the i-process are unknown. Such a process may operate in AGB or super-AGB stars (Herwig et al. 2011; Jones et al. 2016), in accreting white dwarfs in close binary systems (Denissenkov et al. 2017) or in the He burning shell of Pop III massive stars (Clarkson et al. 2018). The s-process boost induced by rotation in the massive stars models of the present work (cf. Chapter 5) does not meet the required conditions (especially neutron density) for the i-process to occur.

Finally, some other stars seems to show an r+s pattern (Jonsell et al. 2006; Gull et al. 2018). Gull et al. (2018) reported the discovery of a CEMP star with [Fe/H] $=-2.2$ whose best fit is achieved by a combination of s- and r-process pattern. In this case, the CEMP star would have formed from at least two sources, one experiencing the s-process, the other experiencing the r-process.

2.5.3 CEMP-no stars

At the present day, no CEMP-s, -r, -r/s stars were found below [Fe/H] $\lesssim-3.5$ . Below this threshold, all the CEMP stars are either CEMP-no or just CEMP in case no Ba (and Eu) abundance is available to classify them. For convenience, I use the term CEMP-no also for the most iron-poor stars whose rigorous classification is just CEMP.

While interesting in the case of CEMP-s stars, the AGB binary scenario applied to CEMP-no stars (Suda et al. 2004; Suda & Fujimoto 2010; Campbell et al. 2010) faces difficulties to account for the observables. One reason is that most CEMP-no stars appear to be single stars (Hansen et al. 2016a). The self-enrichment scenario (Fujimoto et al. 2000) seems unlikely, especially to explain the unevolved stars (cf. Sect. 2.4). Venn & Lambert (2008) proposed that the high C and low Fe may be explained by the separation of gas and dust beyond the CEMP star surface, followed by the accretion of dust-depleted gas. In this case, a dusty disk should exist around CEMP stars, whose presence would be betrayed by a mid infrared excess. Later, Venn et al. (2014) have shown that no mid infrared excess was found for six out of the seven stars they examined (the exception is for HE 0107-5240, that shows a small excess). Also, this dust-gas separation process should affect in a similar way the different isotopes of a given element. The carbon isotopic ratio for instance, will not be modified by this process. The very low 12C/13C ratios on some CEMP-no stars need to be explained by another process.

In the end, this let us with the interesting possibility that CEMP-no stars are the rather direct daughters of a previous generation of stars. These previous stars should be massive since at the very low metallicity considered here, low or intermediate mass stars may not had time to contribute to the chemical enrichment yet. Also, these previous massive stars should have contributed little in iron.

The fact that the CEMP-no class of star shows very large abundances scatter suggests that they formed with the ejecta of only one or a few previous stars. If they were formed from a well mixed reservoir of many previous stars, the scatter should be much smaller, as is it observed at higher metallicities or in normal metal-poor stars. Over the past $\sim 15$ years, multiple scenarios, aiming at characterizing the nature of the CEMP-no source stars, emerged:

•

Mixing and fallback + faint SN (Umeda & Nomoto 2002, 2003, 2005; Iwamoto et al. 2005; Tominaga et al. 2007; Heger & Woosley 2010; Tominaga et al. 2014; Ishigaki et al. 2014).

•

Very low metallicity stars experiencing fast rotation (spinstars, Meynet et al. 2005, 2006, 2010; Hirschi & Maeder 2010; Maeder et al. 2015; Maeder & Meynet 2015; Choplin et al. 2016, 2017b).

•

Normal SN from 15 $M_{\odot}$ + faint SN with strong fallback from 35 $M_{\odot}$ (Limongi et al. 2003).

•

Jet-induced SN from $25-40$ $M_{\odot}$ Pop III stars (Maeda & Nomoto 2003; Tominaga 2009).

•

Rotation + faint SN (no fallback, Takahashi et al. 2014).

•

$15-40$ $M_{\odot}$ rotating Pop III stars with mixing and fallback (Joggerst et al. 2010).

•

H-ingestion event in the He burning shell of a 45 $M_{\odot}$ Pop III star (Clarkson et al. 2018).

This is a tentative list. Some scenario of the list above may be grouped together. Also, for a given scenario, some works occasionally consider slightly different methods or physical ingredients, so that they may be considered as separated scenarios.

Some works suggest that more than one class of source star is required to explain the CEMP-no stars. For instance, the A(C) $-$ [Fe/H] diagram (where A(C) = $\log(N_{\rm C}/N_{\rm H})$ + 12) suggests that the [Fe/H] $\lesssim-4$ stars separate in at least two groups (Yoon et al. 2016), so that at least two different classes of progenitor might be needed. Also, comparisons of the chemical composition of CEMP-no stars with ejecta of massive source stars often show that only one class of progenitor faces difficulty to reproduce large sample of CEMP-no stars. Placco et al. (2016) have used the yields of non-rotating Pop III stars of Heger & Woosley (2010) and shown that 5 out of the 12 investigated CEMP-no stars can be reproduced by the predicted source star yields while 7 stars are let without an acceptable source star.

The scenarios listed above all consider that (1) the surface abundances of CEMP-no stars reflect rather directly the abundances in their natal clouds and (2) the natal cloud was polluted by one or very few zero or very low metallicity massive source star (schematic view in Fig. 2.7). Each scenario has nevertheless its own specificity. Among the quoted works in the list above, frequent ingredients considered in source star models are rotation, extra mixing events (in the sense of Umeda & Nomoto 2002, see details below) and strong fallback. Occasionally, both are considered. Occasionally, refinements or additional ingredients were proposed. Below are discussed two scenarios in more detail: mixing & fallback and fast rotating massive stars.

Mixing and fallback

Mixing.

The [Zn/Fe] ratio of normal metal-poor stars was found to rise with decreasing [Fe/H] (Cayrel et al. 2004, their figure 12). Models of massive stars including explosive nucleosynthesis show that at the end of the evolution, Zn is located in deeper regions than Fe (Fig. 2.8). Consequently, if some Zn is ejected from the massive star (through a supernova event), also a large amount of Fe is ejected and the trend of [Zn/Fe] observed at low [Fe/H] cannot be explained. In order to expel some Zn without expelling too much Fe, Umeda & Nomoto (2002) have included an extra mixing event in the source star models. The mixing event occurs at the time of the massive star explosion and brings material from inner layers closer to the surface. This allows to bring some Zn upward, without having too much Fe. When considering such a mixing, the supernova yields can reproduce the observed [Zn/Fe] ratios at low [Fe/H].

Fallback.

For stars having a large [C/Fe] and low [Fe/H] (CEMP stars), the concept of faint supernova with strong fallback was also introduced (Nomoto et al. 2003; Umeda & Nomoto 2003). The idea of a strong fallback comes from the fact that in the massive source star, carbon is located closer to the surface than iron. Therefore, in order to have a large [C/Fe] ratio in the ejecta, not too deep layers should be expelled so as to eject mostly carbon and little iron. The supernova is faint because very little 56Ni (whose decay into 56Fe is mainly responsible for the luminosity of the supernova) is ejected. If too much 56Ni is ejected, one will ultimately get too much 56Fe compared to the low [Fe/H] ratios of the most iron poor stars. The concept of strong fallback and faint supernova for the source star is somewhat consistent with the fact that low-metallicity stars are more compact and hence might explode less easily.

The mixing & fallback scenario is a combination of both events. To fit the observations with a massive source star experiencing mixing and fallback, a massive source star model is evolved until the end of its evolution. Then a region inside the model, between two limiting shells (the two green dashed circles in Fig. 2.9), is considered to be fully mixed at the time of the supernova explosion. A part of the mixed region is ejected (red part in Fig. 2.9), a part is kept into the remnant (blue part). The extension of the mixed region and the fraction of this region which is expelled are chosen so as to reproduce the abundances of observed metal-poor stars.

Although the source star models with mixing and fallback are generally 1D models, Tominaga (2009) has shown that for a Pop III stellar model of 40 $M_{\odot}$ , the 1D mixing and fallback model gives similar chemical yields than a 2D jet-induced explosion with fallback (Fig. 2.10). It can be roughly understood by the fact that the mixed region is ejected differently in 1D (spherically) and 2D (along the jet axis) but has a similar chemical composition. Nevertheless, some chemical species are overproduced in the 2D jet SN model (e.g. Sc, see Fig. 2.10). This is due to the higher energy concentration in the jet-induced explosion, that leads to a bit different explosive nucleosynthesis. Overall, it suggests that the spherical mixing and fallback model is rather well mimicking a 2D jet-induced explosion.

The mixing and fallback scenario for CEMP-no stars has the advantage to well explain the iron-peak elements like Zn or Fe. One caveat is that it faces difficulties in reproducing the high N abundance of some metal-poor stars (Tominaga et al. 2007) except if additional mixing is considered between the He-convective shell and the H-rich envelope just before the supernova (Iwamoto et al. 2005; Tominaga et al. 2014).

Fast rotating massive stars

In a broad context, the fast rotating massive star scenario or spinstar131313The present work focuses on massive stars but, originally, the term spinstar also designates intermediate mass stars. scenario proposes that fast rotation at low metallicity is a dominant process that largely impacts the outputs of massive stars (especially the stellar yields). It is motivated by several aspects (see also Sect. 1.3 and 3.3). One of the aspect, further discussed in Sect. 3.3.1, is that the efficiency of the rotational mixing operating inside the star is expected to increase with decreasing metallicity. This effect arises naturally, as a result of the physics of rotation in stars (discussed in Sect. 3.3). As a consequence of this efficient rotational mixing, the yields of some elements like C, N, O (e.g. Meynet & Maeder 2002) or s-elements (e.g. Pignatari et al. 2008; Frischknecht et al. 2016) are impacted a lot by rotation in low metallicity massive stellar models. The spinstar scenario tells us that the low-mass stars that formed early in the Universe should contain mostly (but possibly among others) the nucleosynthetic signatures of previous fast rotating massive stars.

Thanks to Galactic chemical evolution models, it was shown that the N/O, C/O, 12C/13C and Sr/Ba ratios of very metal-poor (mostly normal, i.e. not carbon-enhanced) halo stars are better reproduced if including the yields of fast rotating massive stars (Chiappini et al. 2006, 2008; Cescutti et al. 2013). The spinstar scenario has also been proposed to explain the abundance anomalies (particularly the Mg-Al anticorrelation) in Globular Clusters (Decressin et al. 2007).

When applied to CEMP stars, the spinstar scenario proposes that most CEMP stars have formed from the material ejected through winds and/or supernova by a previous fast rotating massive source star. Meynet et al. (2006) have shown that the [C/Fe], [N/Fe] and [O/Fe] ratios in the ejecta (wind + supernova) of a very low-metallicity fast rotating 60 $M_{\odot}$ are similar to the surface ratios of the unevolved CEMP stars G77-61 and HE 1327-2326 (with [Fe/H] $<-4$ ). In the same line, Hirschi (2007) has shown that the CNO abundances of HE 1327-2326 can be explained by the wind of a low metallicity fast rotating 40 $M_{\odot}$ model, whose ejecta was diluted 600 times with ISM (i.e. 600 times more ISM material than stellar ejecta). Meynet et al. (2010) have predicted that CEMP stars formed from a fast rotating massive source star should be helium rich, provided the ejecta was little diluted with pristine ISM. Maeder et al. (2015) and Maeder & Meynet (2015) proposed that the back-and-forth, partial mixing at work between the He- and H-regions of the rotating source star may account for the wide variety of CEMP-no stars abundances (more details in Sect. 4.1).

It is important to make the difference between the two different kinds of mixing at work in the spinstar and mixing & fallback scenarios:

•

Spinstar: the mixing is induced by rotation and occurs progressively during the evolution of the star.

•

Mixing & fallback: the mixing arises only at the time of the supernova.

Contrary to the mixing & fallback process, the process of rotation, which is at the heart of the spinstar scenario, was not introduced in stellar models so as to explain the abundances of MP or CEMP stars. As mentioned, spinstars are expected to exist at very low metallicity, as a result of the physics of rotation (more details in Sect. 3.3). One strength of the spinstar scenario is that it provides a natural physical process to explain the abundances of most elements in CEMP stars. Another strength is that spinstars can account for other observables like the abundances of normal halo stars (cf. previous discussion). Rotation may also be a key process to explain the variation of surface abundances observed in solar metallicity, nearby massive stars (e.g. Martins et al. 2015). Rotation is linked to different observables, one of which could be CEMP stars.

The spinstar scenario alone does not offer a solution to explain the little enrichment in iron-peak elements of CEMP stars (e.g. Fe, Zn). For instance, in the material ejected by the stellar winds of a rotating Pop III star, no iron is ejected so that [Fe/H] $=0$ . Iron, zinc, … can be explained by the mixing process in the sense of Umeda & Nomoto (2002) or they can come from another source. Overall, the spinstar scenario proposes that rotation in massive stars played a major role in the chemical enrichment of the early Universe. It does not exclude other ingredients like mixing & fallback. As noted in Maeder et al. (2015), spinstar and mixing & fallback scenarios are more complementary than contradictory: one can imagine a rotating star experiencing an additional mixing event at the end of its evolution.

2.6 Summary

Carbon-Enhanced Metal-Poor (CEMP) stars are peculiar MP stars observed in the halo of the Galaxy and showing overabundances in light and sometimes heavy s- and/or r- elements. CEMP stars are more frequent at low [Fe/H]: about 80 % of stars with [Fe/H] $<-4$ are CEMP. The most iron-poor stars are generally weakly enriched in s- and/or s-elements (CEMP-no). They can be used to constrain the very early chemical evolution of the Universe.

Evolved CEMP stars probably underwent internal mixing processes (especially the first dredge-up and thermohaline mixing), altering their surface abundances. Although important, these processes are likely not able to explain the peculiar abundances of this class of stars (especially the unevolved stars). The abundances of CEMP-s stars may be explained by an accretion episode from the material (enriched in carbon and s-elements) ejected from an AGB companion. The fact that many CEMP-s stars are in a binary system supports this scenario. CEMP-no stars are generally single stars so that another scenario should be invoked. CEMP-no stars (and generally the most iron-poor stars) are thought to have kept the nucleosynthetic imprint of only one or very few previous massive source stars. In some cases however, this imprint may have been blurred by internal mixing processes in the CEMP-no star itself. Rotation, pre supernova mixing and strong fallback are among the interesting characteristics the source stars should have to account for the abundances of observed CEMP-no stars.

Chapter 3 Massive source stars: nucleosynthesis and models with rotation

This chapter first discusses the nucleosynthesis in massive stars. A section is dedicated to the s-process in AGB stars for completeness. The theoretical and modeling aspects of massive stellar evolution that are relevant for this work are then presented. Emphasis is placed on the specificities of stellar evolution at low metallicity.

3.1 Nucleosynthesis processes in massive stars

3.1.1 Stellar fusion

Core hydrogen burning.

The first burning stage, lasting for $\sim 1$ Myr to several tens of Myr, is the fusion of hydrogen to helium. The pp-chains and the CNO-cycle both contribute to transform H into He. Above 17 MK (corresponding the H-burning temperatures of a $\sim 1.2$ $M_{\odot}$ star), the CNO cycle becomes more efficient than the pp-chain. Provided a little bit of CNO elements are available, this is the CNO-cycle that dominates the production of energy during the H-burning stage of massive stars. The main CNO loop (CNOI) is shown by the colored loop in Fig. 3.1. One loop transforms four protons into one 4He. As shown by the colors of the arrows, 14N( $p,\gamma$ ) is the slowest reaction, followed by 12C( $p,\gamma$ ) and 13C( $p,\gamma$ ). After a timescale determined by 14N( $p,\gamma$ ) (the slowest reaction) the CNOI cycle reaches an equilibrium where 12C/14N $=0.025$ and 12C/13C $=$ $3.3$ . Because 14N( $p,\gamma$ ) is the bottleneck reaction, the main effect of CNOI is to transform the initial C nuclei into 14N. The branching point at 15N is the starting point of other CNO loops that take place at higher temperatures and that allow the synthesis of other isotopes, particularly 16O.

During this first stage, the Ne-Na and Mg-Al chains (Fig. 3.2) can also be activated for temperatures higher than $\sim 35$ MK for Ne-Na and $\sim 50$ MK for Mg-Al. The rates of the reactions at work in these chains are more uncertain than the reactions rates of the CNO-cycle. At the branching point 23Na, the 23Na( $p,\alpha$ )/23Na( $p,\gamma$ ) ratio equals 159 and 7 at 40 and 70 MK respectively according to Iliadis et al. (2010). For the rates of Cyburt et al. (2010), these ratios are 0.3 and 0.6 (still at 40 and 70 MK). We see that depending on the literature source used and of the temperature, the Ne-Na and Mg-Al chains can either be considered as closed loops or not. They are closed loops if the 23Na( $p,\alpha$ )/23Na( $p,\gamma$ ) ratio is high.

Generally, the production of Ne, Na, Mg and Al in massive stars can be significantly affected if considering nuclear reaction rates from different sources. Decressin et al. (2007) have shown that multiplying the rate of 24Mg( $p,\gamma$ ) by $10^{3}$ around 50 MK changes the production of Mg-Al isotopes during the main sequence of low metallicity massive stars by $0.5-1$ dex.

Core helium burning.

When running out of hydrogen, the core contracts until the central temperature is hot enough (about 100 MK) for the $3\alpha$ process to start. The second burning stage is the core helium burning phase. It lasts for $\sim 0.1-1$ Myr, which is about 1/10 of the core hydrogen burning phase. At the beginning of core He-burning, the 14N synthesized during core H-burning through the CNO cycle (cf. previous discussion) is quickly transformed into 22Ne via the chain 14N( $\alpha,\gamma$ )18F( $e^{+}\nu_{e}$ )18O( $\alpha,\gamma$ )22Ne. The 22Ne( $\alpha,n$ )25Mg reaction, activated at $T\sim 220$ MK releases free neutrons that can be captured by seeds like iron and heavier elements. This is the slow neutron capture process (s-process) which is discussed below in Sect. 3.1.2.

During core He-burning, a hydrogen shell burns above the helium core. The H-shell burns at a slightly higher temperature than the H-core. It induces a somewhat different nucleosynthesis in the H-shell. For instance, the Ne-Na and Mg-Al cycles are more active in the H-shell. Rotational mixing can transport elements from the He-burning core to the H-burning shell (and vice-versa) and trigger a rich and varied nucleosynthesis (Sect. 4.1).

Advanced burning stages.

At the end of the core He-burning stage, the most abundant species in the core are 12C and 16O. Since the 12C + 12C reaction has the lowest coulomb barrier, the next burning stage is core carbon burning. After carbon burning comes neon photodisintegration, oxygen and then silicon burning. The advanced stages last for $10-1000$ yr (C), $0.1-1$ yr (Ne), $0.1-1$ yr (O) and $0.1-10$ days (Si, e.g. Heger et al. 2000; Hirschi et al. 2004). During these stages, most of the energy goes out from the star in the form of neutrinos. To compensate for this strong energy loss, the rates of nuclear reactions increase. This leads to a quick burning of chemical species, explaining the short duration of the advanced stages. During these stages, the core is decoupled from the rest of the star. It implies that the star does not move anymore in the Hertzsprung-Russell (HR) diagram. The main products of C-burning are 20Ne, 23Na and 24Mg. Neon photodisintegration produces mainly 16O, 24Mg and 28Si, oxygen burning mostly 28Si and 32S and silicon burning 56Ni (cf. Woosley & Weaver 1995, especially their Table 19). At the end of each core burning phase, the burning continues in a shell. As evolution proceeds, more and more different burning regions are present in the massive star.

3.1.2 The weak s-process

Massive stars are generally associated to the weak s-process, mainly responsible for the elements with $A<90$ . Cameron (1960) identified that at the beginning of the core He-burning phase of massive stars, the secondary111An isotope is synthesized through the secondary channel if it comes from the initial metal content of the star. It is formed through the primary channel if produced from the initial hydrogen and helium content of the star. 14N (synthesized during the main sequence thanks to the CNO-cycle) is converted into 22Ne by successive $\alpha-$ captures and can provide a source of neutrons with the 22Ne( $\alpha,n$ ) reaction. This reaction is efficiently activated at $T>220$ MK. It was later recognized that the s-process in massive stars occurs principally in the He-burning core of massive stars (Peters 1968; Couch et al. 1974; Lamb et al. 1977; Langer et al. 1989; Prantzos et al. 1990; Raiteri et al. 1991a). In solar metallicity stars with $M_{\rm ini}\gtrsim 30$ $M_{\odot}$ , some 22Ne is left at the end of core He-burning phase so that s-process can occur during later stages (Couch et al. 1974). The carbon shell burning is the second efficient s-process production site inside massive stars (it contributes to $\sim 20$ % at solar metallicity, Raiteri et al. 1991b; The et al. 2007). Neutrons are released by 22Ne( $\alpha,n$ ) with the $\alpha$ particles provided by the 12C(12C, $\alpha$ )20Ne reaction. The neutron density is typically $\sim 10^{11}$ cm*-3*, which is $\sim 4$ dex higher than in the He-burning core. He-burning shell and C-burning core do not contribute significantly in producing s-elements (Arcoragi et al. 1991). At low metallicity, the 13C( $\alpha,n$ )16O reaction provides a small burst of neutrons at the very beginning of the core He-burning phase that can synthesize some light s-elements ( $A\lesssim 85$ , Baraffe et al. 1992).

The synthesis of s-elements (Sr, Ba…) is due to neutron capture on heavy seeds (e.g. Fe). However, neutrons are also captured by light elements. 12C and 16O are abundant in the He-core and are important poisons for the s-process. 16O captures neutrons via 16O( $n,\gamma$ ). Then, either the neutron is recycled with 17O( $\alpha,n$ ) or it is definitely lost with 17O( $\alpha,\gamma$ ). The ratio of these two reaction rates plays an important role on the efficiency of the s-process. At low metallicity, the poisoning effect of 16O is stronger because the ratio of 16O to s-process seeds (e.g. iron) is higher (Prantzos et al. 1990; Rayet & Hashimoto 2000). During the shell carbon burning phase, important additional neutron poisons (20Ne and 24Mg) limit the efficiency of the s-process.

Meynet et al. (2006) and Hirschi (2007) have shown that extra 22Ne can be synthesized during the core He-burning phase of massive rotating stars (the interplay between rotation and nucleosynthesis in low-metallicity massive stars is discussed in Sect. 4.1). Compared to non-rotating models, rotation gives more neutrons (source) with the same amount of seed. A higher source over seed ratio shifts the production of s-elements towards higher atomic masses (Gallino et al. 1998). Pignatari et al. (2008) have shown that rotational mixing would allow the production of s-elements up to $A\simeq 140$ . Frischknecht et al. (2012, 2016) started to explore the s-process in rotating massive stars, by computing models (about 30 models in total) of different masses ( $15<M_{\rm ini}<40$ $M_{\odot}$ ) and metallicities ( $10^{-7}<Z<Z_{\odot}$ ) while following the complete s-process during the evolution. The Chapter 5 of this thesis aims at extending this work by computing a new grid of models and compare the yields to low mass metal-poor stars enriched in s-elements.

3.1.3 Explosive nucleosynthesis

The chemical composition of the massive star can be further modified by explosive nucleosynthesis (e.g. Thielemann et al. 1996). It is activated by a shock wave that heats the material, processes it and finally ejects the envelope of the star while the central part will form a neutron star or a black hole. The innermost layers, from the center to the C-shell can burn explosively. The outer stellar layers are mostly unprocessed by explosive nucleosynthesis. Thielemann et al. (1990) reported that above the mass coordinate $\sim 2$ $M_{\odot}$ of a 20 $M_{\odot}$ model (corresponding roughly to the location of the O-burning shell), the material is not significantly altered by explosive nucleosynthesis. In the region affected by explosive nucleosynthesis, the abundances of elements lighter than neon and heavier than zinc are marginally modified. By contrast, the iron-peak elements are the most affected (Woosley & Weaver 1995; Thielemann et al. 1996; Woosley et al. 2002; Chieffi & Limongi 2003; Limongi et al. 2003; Nomoto et al. 2006). The s-elements produced during the evolution (cf. Sect. 3.1.2) are not expected to be strongly affected by the explosion (Rauscher et al. 2002; Tur et al. 2009). The shock of the explosion may nevertheless affect the isotopic distribution of heavy nuclei in the He-shell of the progenitor (Meyer et al. 2000; Pignatari et al. 2013). In some cases, massive stars may also experience magneto-rotational supernovae, which is a possible site for the r-process (Winteler et al. 2012).

In this work, the explosive nucleosynthesis is not calculated. Pre-supernova models provide nevertheless a good estimation for the many species that are not much affected by the explosion. Likely, pre-supernova models also provide a good estimate of the nucleosynthesis of all elements above the carbon or oxygen burning shell, where explosive burning may not operate significantly.

3.2 The s-process in AGB stars

The present work focuses on massive stars but the s-process in AGB stars is also discussed for completeness. Thermally pulsing AGB stars are associated to the main s-process component, responsible for the elements with $90<$ A $<209$ . The AGB corresponds to the last stage of the life of stars having initial masses between about 1 and 8 $M_{\odot}$ (e.g. the reviews of Iben & Renzini 1983; Busso et al. 1999; Herwig 2005; Karakas & Lattanzio 2014). At this phase, the star becomes larger and more luminous and strong mass loss episodes may occur (up to $10^{-4}$ $M_{\odot}$ yr*-1*). AGB stars have a degenerate carbon-oxygen core. The core is surrounded by the helium and hydrogen shells, separated by the intershell region. Above is a convective envelope. The energy production is dominated by the H-burning shell. The He shell stays quiet most of the time. As H is burning in its shell, helium is synthesized, making the intershell region growing in mass (Fig. 3.3). When a critical value is reached, He-burning is suddenly ignited and a thermal pulse occurs. The energy produced drives convection so that the products of He-burning are brought upward, to the intershell region. The energy produced also expands the outer layers of the star. It has the effect of moving the H-burning shell outward and therefore stopping the burning in the H shell. It also makes the inner boundary of the convective envelope moving inward and eventually reaching the intershell region. Then, products of internal nucleosynthesis are brought up to the surface (this episode is called third dredge-up or TDU, Fig. 3.3). The process described above occurs cyclically ( $\sim 50000$ yrs between 2 thermal pulses) until the convective envelope is entirely removed through winds.

During the TDU, protons are mixed down to the intershell region and they are directly captured by the abundant 12C to form 13C through the chain 12C( $p,\gamma$ )13N( $\beta^{+}$ )13C. It forms a 13C pocket. During the next thermal pulse, the reaction 13C( $\alpha,n$ )16O occurs, providing neutrons and thus triggering the s-process. If too many protons are mixed in the intershell region, 14N is also significantly formed from 12C (thanks to the CNO cycle) and suppresses the s-process by capturing the neutrons via 14N( $n,p$ )14C.

The 22Ne( $\alpha,n$ )25Mg reaction is not expected to contribute much in producing the main s-process component in AGB stars. One reason is that this reaction is activated in AGB stars with initial masses $M_{\rm ini}\gtrsim 3$ $M_{\odot}$ (Truran & Iben 1977) while the solar s-only abundances are best reproduced by $1.5-3$ $M_{\odot}$ AGB models (e.g. Gallino et al. 1988; Hollowell & Iben 1988). This said, a contribution of 22Ne( $\alpha,n$ ) is nevertheless expected to occur in low mass AGB stars (e.g. Straniero et al. 1995), and particularly in the low metallicity regime, for initial masses above about 2 $M_{\odot}$ (Lugaro et al. 2012).

With time, more and more sophisticated AGB stellar models with different initial masses, metallicities, reaction networks, etc… were computed (e.g. Renzini & Voli 1981; Gallino et al. 1998; Herwig 2004; Karakas 2010; Cristallo et al. 2011; Lugaro et al. 2012; Doherty et al. 2014; Cristallo et al. 2015). Several important uncertainties remain like for instance the formation mechanism of the 13C pocket222In AGB models, a partial mixing zone is added artificially in a post-processing algorithm in order to mix protons with 12C into the intershell region (Lugaro et al. 2004). It forms the 13C-pocket which is needed to produce the neutrons required for the s-process. which is a critical ingredient and is not fully understood yet (e.g. Lattanzio & Lugaro 2005), the third dredge-up (more generally the convection) or the mass loss (cf. Sect. 4 of Karakas & Lattanzio 2014, for an extensive discussion about uncertainties in AGB models).

Despite these uncertainties, the detection of CNO and s-elements at the surface of observed AGB stars provides evidences of the ongoing nucleosynthesis in such stars (e.g. Smith & Lambert 1990). The best evidence is probably the detection of the unstable element Tc at the surface of AGB stars (Merrill 1952; Smith & Wallerstein 1983): the longest-lived Tc isotope (99Tc) has a mean life of about 1/10 of the duration of the AGB phase, meaning that it has to be synthesized by the AGB star itself.

3.3 Massive stellar models including rotation

To study the nucleosynthetic processes mentioned in the previous section, and more generally the evolution of stars, stellar models are required. Although stars are 3D objects, following their entire life and structure using multi dimensional codes is computationally too expensive. At the present day, only specific stages/zones of a star can be followed using multi dimensional codes (e.g. Herwig et al. 2014; Cristini et al. 2017). In stellar evolution models, a star is often considered as a spherically symmetric object. This greatly simplifies the modeling since reducing the problem to one dimension. Compared to multi dimensional codes, 1D codes have the advantage to be able to model the entire life of stars and to explore a large parameter space. They have the disadvantadge to use a parametrized physics to describe the multi dimensional processes (e.g. turbulence).

Interestingly, rotating stars can also be modeled with 1D codes, following the theory of shellular rotation (Zahn 1992). The fundamental assumption of this theory is that in rotating stars, the horizontal turbulence (on an isobaric surface, i.e. surface of same pressure) is much stronger than the vertical one. This is motivated by the stable density stratification in the vertical direction, opposing a strong force to vertical fluid motions. In this theoretical frame, internal rotation depends essentially on the distance to the stellar center and little on latitude. The generalized 1D equations of hydrostatic equilibrium, mass conservation, energy conservation and energy transport, describing a star in shellular rotation are (Meynet & Maeder 1997):

[TABLE]

with

$f_{P}=\frac{4\pi r_{P}^{4}}{GM_{P}S_{P}}\frac{1}{\langle g_{\rm eff}^{-1}\rangle}$ and $f_{T}=\left(\frac{4\pi r_{P}^{2}}{S_{P}}\right)^{2}\frac{1}{\langle g_{\rm eff}\rangle\langle g_{\rm eff}^{-1}\rangle}$

and $M_{P}$ the mass enclosed by the sphere of radius $r_{P}$ , $g_{\rm eff}$ the effective gravity (resulting from both gravitational and centrifugal acceleration), $\nabla_{\rm rad}$ and $\nabla_{\rm ad}$ the radiative and adiabatic temperature gradients, $\bar{\rho}$ the average density between two isobars, $\epsilon_{\rm nucl}$ , $\epsilon_{\nu}$ , $\epsilon_{\rm grav}$ the rates of nuclear energy production, neutrino losses, and gravitational energy (energy released/absorbed by contraction/expansion of the star). The quantities in brackets are averaged over an isobar according to

[TABLE]

where $S_{P}$ is the surface of the isobar, defined by $S_{P}=4\pi r_{P}^{2}$ with $r_{P}$ the radius of the equivalent sphere, having the same volume than the oblate isobar. d $\sigma$ is a small surface element on the isobar.

In this work, the Geneva stellar evolution code genec (Eggenberger et al. 2008) is used. It was mainly developed and used for the computation of massive stellar models (e.g. Maeder 1987, 1992) with a sophisticated treatment of rotation (Meynet & Maeder 1997). The physical and modeling ingredients relevant for this work are discussed in the following sections.

3.3.1 Transport induced by rotation

In a differentially rotating star, the equipotentials are differently spaced as a function of the colatitude $\theta$ because the star is distorted by the centrifugal effect. The centrifugal force makes the equatorial radius larger than the polar radius so that the equipotentials are closer to each other at the poles and more spaced at the equator. Consequently, the effective gravity is larger at the poles. The radiative flux is proportional to the local effective gravity (von Zeipel 1924) meaning that there is an excess of flux along the polar axis and a deficiency close to the equatorial plane. This imbalance triggers global circulation motions called meridional circulation. Such currents, which are advective, contribute to the transport of angular momentum and chemical elements in rotating stars. In differentially rotating stars, because the stellar layers have different angular velocities, shear instabilities arise and also contribute (in a diffusive way) to the transport of angular momentum and chemical elements.

Transport of angular momentum

In the radial direction, the transport of angular momentum obeys the advective-diffusive equation (Chaboyer & Zahn 1992)

[TABLE]

where $\bar{\Omega}$ is the angular velocity of a shell, $\rho$ the density, $D$ the total diffusion coefficient, taking into account the various instabilities transporting angular momentum (especially convection and shear turbulence) and $U(r)$ the amplitude of the radial component of the meridional velocity (Maeder & Zahn 1998). A large333 $U(r)$ can be positive or negative. Here the absolute value is considered. $\textbar U(r)\textbar$ implies an efficient transport of angular momentum in the radial direction. $U(r)$ scales with $E_{\Omega}$ , a term of particular importance in the expression of $U(r)$ and that can be approximated by

[TABLE]

The second term in brackets is the Gratton-Öpik term. In the outer layers of stars, the density $\bar{\rho}$ is small so that $E_{\Omega}$ , hence $U(r)$ , can become largely negative (see solid line in Fig. 3.4). It contributes to redistribute efficiently the angular momentum and therefore smooth the $\Omega$ -profile.

Low metallicity stars contain less metals so they are less opaque and therefore more compact. Consequently, $\bar{\rho}$ is larger so that the Gratton-Öpik term is generally smaller. This reduces $U(r)$ (see Fig. 3.4), meaning that the angular momentum is less redistributed inside the star. It leads to steeper internal $\Omega$ -profiles. This tends to produce larger $\Omega$ -gradients which lead to stronger shear instabilities and then to a more efficient shear mixing.

Transport of chemical elements

Chaboyer & Zahn (1992) have shown that for chemical elements, the combination of meridional circulation and horizontal turbulence can be described by a pure diffusive process. The associated diffusion coefficient is

[TABLE]

with $D_{\rm h}$ the horizontal (i.e. on an isobaric surface) shear diffusion coefficient from Zahn (1992). It is written as $D_{\rm h}=c_{\rm h}^{-1}r\textbar 2V-\alpha U(r)\textbar$ with $\alpha=\frac{1}{2}\frac{\text{d}\ln(r^{2}\bar{\Omega})}{\text{d}\ln r}$ and $c_{\rm h}=1$ . As a consequence, in contrast with the angular momentum transport equation (Eq. 3.6), the equation for the change of abundance of a given chemical element $i$ in a given shell at coordinate $r$ is a pure diffusive equation:

[TABLE]

The last term accounts for the changes due to the nuclear reactions (cf. Sect. 3.3.3). In radiative zones, $D=D_{\rm shear}$ with $D_{\rm shear}$ the diffusion coefficient accounting for the shear instabilities. Several prescriptions exist in the literature (Maeder 1997; Talon & Zahn 1997; Maeder et al. 2013). The one used in this work is from Talon & Zahn (1997). It can be expressed as

[TABLE]

where $K$ is the thermal diffusivity, and $f_{\rm energ}=2Ri_{\rm c}$ with $Ri_{\rm c}$ the critical Richardson number below which the medium becomes dynamically unstable and turbulent. Although the canonical value for $Ri_{\rm c}$ is 1/4 some works have shown that turbulence may happen for larger Richardson number. Canuto (2002) has shown that turbulence may arise for $Ri$ $\leq$ $Ri_{\rm c}\sim 1$ . Brüggen & Hillebrandt (2001) have done numerical simulations suggesting that shear mixing occurs already at $Ri\sim 1.5$ . The physical range of values may be around $0.25<Ri_{\rm c}<2$ , corresponding to $0.5<f_{\rm energ}<4$ .

I computed two 15 $M_{\odot}$ models at solar metallicity with $\upsilon_{\rm ini}=300$ km s*-1* and with $f_{\rm energ}=1$ and 4. At core H depletion, the surface N/H ratios are enhanced by a factor of 2 ( $f_{\rm energ}=1$ ) and 3 ( $f_{\rm energ}=4$ ) compared to the initial surface N/H ratio. Such surface enrichments qualitatively agree with observation of $10-20$ $M_{\odot}$ rotating stars (e.g. Gies & Lambert 1992; Villamariz & Herrero 2005; Hunter et al. 2009). In this work, except stated explicitly, $f_{\rm energ}=4$ . The effect of $f_{\rm energ}$ on the internal mixing of low metallicity massive stars is investigated in Sect. 4.3.3.

A comparison of 3 different prescriptions for the shear mixing

Although not used in the present work, I have included in genec the global diffusion coefficient proposed by Maeder et al. (2013), taking into account different instabilities together and their possible interaction (see Appendix A.2 for calculation details).

Fig. 3.5 shows the tracks of 20 $M_{\odot}$ models with $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.4$ , $Z=10^{-5}$ and computed with various $D_{\rm shear}$ coefficients: from Maeder (1997), from Talon & Zahn (1997) and the global coefficient from Maeder et al. (2013). The new coefficient $D_{\rm global}^{\rm M13}$ combining the different instabilities leads to a bluer and more luminous evolution, characteristic of stars experiencing a high degree of mixing. The surface 4He mass fraction at the end of the main sequence is the highest in the $D_{\rm global}^{\rm M13}$ model (0.56 against 0.25 and 0.31 for the $D_{\rm shear}^{\rm TZ97}$ and $D_{\rm shear}^{\rm M97}$ models, respectively), which is also a signature of an efficient rotational mixing. An estimation of the mixing efficiency in the deep stellar interior can be obtained with the amount of central 22Ne after the main sequence (more details in Sect. 4.1). 22Ne in the center reaches a much higher mass fraction in the $D_{\rm shear}^{\rm TZ97}$ and $D_{\rm global}^{\rm M13}$ models. It suggests that, after the main sequence, a more efficient mixing in the deep interior is at work in these two models compared to the $D_{\rm shear}^{\rm M97}$ model. The efficiency of the s-process in massive stars is impacted by the amount of 22Ne (main neutron source, cf. Sect. 3.1.2). From Fig. 3.5, we see that the s-process should operate similarly in the $D_{\rm shear}^{\rm TZ97}$ and $D_{\rm global}^{\rm M13}$ because of the similar 22Ne content. On the opposite, the $D_{\rm shear}^{\rm M97}$ model predicts a less efficient operation of the s-process.

The dashed track in Fig. 3.5 shows the main sequence of the $D_{\rm shear}^{\rm TZ97}$ model but with $f_{\rm energ}=$ 40 instead of 4. In this case, the track is rather close to the track of the model with the global diffusion coefficient. A higher $f_{\rm energ}$ value for the $D_{\rm shear}^{\rm TZ97}$ model may mimic the more complex physics contained in the $D_{\rm global}^{\rm M13}$ coefficient. It shows that finally, even if $f_{\rm energ}=4$ was proposed as a possible upper limit for the $D_{\rm shear}$ of Talon & Zahn (1997), a higher $f_{\rm energ}$ (i.e. higher mixing efficiency) probably cannot be excluded.

3.3.2 Convection

In a star, a heat excess with respect to what radiation can transfer drives turbulent convective motions. It provides an additional and efficient way of transporting the energy. In this work, the Schwarzschild criterion is used to determine the stability of a given stellar layer.

In the interior of the Sun, the turnover timescale $t_{\rm turn}$ (timescale for an element of material to complete a loop in a convective cell) can be estimated using the mixing-length theory. It is about 0.5 yr (Maeder 2009), suggesting that chemical homogeneity is quickly reached in a convective zone. Since the lifetime of a star is much longer than the turnover timescale, the convective mixing can be considered as instantaneous during most of the stellar life. The last stages of massive stars (after central carbon burning) are however very short (less than 1 yr, e.g. Hirschi et al. 2004) so that the approximation of instantaneous convective mixing is no more valid. In this case, the convection is treated as a diffusive process.

During the H- and He-burning phases of the models computed in the present work, overshoot is considered: the size of the convective core is extended by $d_{\rm over}=\alpha H_{\rm P}$ where $H_{\rm P}$ is the pressure scale height and $\alpha=0.1$ for initial masses above $1.7$ $M_{\odot}$ . $\alpha$ was calibrated so as to reproduce the observed main-sequence width of stars with $1.35<M<9$ $M_{\odot}$ (Ekström et al. 2012).

3.3.3 Nuclear network

In a stellar evolution code, to follow the abundance changes due to nuclear reactions, one has to express the nuclear term in Eq. 3.9 (last term). It is written as

[TABLE]

where $A_{i}$ , $A_{j}$ , $A_{k}$ and $A_{l}$ are the mass number of isotopes $i$ , $j$ , $k$ and $l$ , $N^{i}_{j}$ , $N^{i}_{j,k}$ and $N^{i}_{j,k,l}$ are the number of particles of isotope $i$ destroyed $<0$ or produced $>0$ in a particular reaction, $f_{j;k}$ and $f_{j;k;l}$ the screening factors, $\Delta_{ijk}=\delta_{jk}+\delta_{jl}+\delta_{kl}+2\delta_{jkl}$ and $\delta$ ’s are factors preventing double counting. 1-body reactions refer to photo-disintegrations, $\beta$ -decays, $\nu$ -, $e^{-}$ - and $e^{+}$ captures. $\lambda_{j}$ , $\langle\sigma v\rangle_{j;k}$ and $\langle\sigma v\rangle_{j;k;l}$ are the nuclear reaction rates. These rates are estimated experimentally (e.g. Caughlan & Fowler 1988) or theoretically (e.g. Rauscher & Thielemann 2000) and tabulated over a certain range of temperature.

The set of differential equation 3.11 is called stiff because of the strong variety of reaction timescales, ranging from fraction of seconds to Gyr. An explicit method is not possible to solve these equations because it would require extremely small timesteps in order to follow the fastest reactions. In the new version of genec, these equations are solved in a implicit manner by the backward Euler method444Details can be found in the Sect. 3.5 of Frischknecht, PhD thesis (2012, https://edoc.unibas.ch/21287/)..

In Chapter 4 of this work, I rely on models computed with a small nuclear network, that follows 31 species in total: $n$ , 1H, 3,4He, 12,13,14C, 14,15N, 16,17,18O, 18,19F, 20,21,22Ne, 23Na, 24,25,26Mg, 26,27Al, 28Si, 32S, 36Ar, 40Ca, 44Ti, 48Cr, 52Fe and 56Ni. It allows to track the reactions that contribute significantly to generate nuclear energy. This network is also enough to follow the nucleosynthesis of the main species beyond Fe until the ultimate stages of evolution. Finally, this network is well suited for investigating the origin of CEMP-no stars since such stars do not show strong overabundances in heavy elements. In Chapter 5 instead, a network of 737 isotopes is considered, from 1H to 212Po (Fig. 3.6), that allows to follow the full s-process nucleosynthesis. Some of the reactions linking the isotopes are shown by the blue segment in Fig. 3.6. The nucleosynthesis is followed thanks to the BasNet code (Basel Network, Arnett & Thielemann 1985; Thielemann & Arnett 1985) which is coupled to genec555Details can be found in the Sect. 3.7 of Frischknecht, PhD thesis (2012, https://edoc.unibas.ch/21287/).. It allows to follow consistently all the nucleosynthesis during the entire evolution.

3.3.4 Initial composition and opacity tables

In this work, the initial composition of the low metallicity massive source stars is taken $\alpha$ -enhanced. Details are given below. In genec, the initial abundances are in mass fraction. The solar mass fraction $X_{\rm i,\odot}$ of an isotope $i$ , associated to an element $e$ can be written as

[TABLE]

where $\log\epsilon_{\rm e,\odot}$ is the solar abundance of element $e$ taken from Asplund et al. (2005), except for Ne, which is from Cunha et al. (2006). $f_{\rm i}$ is the isotopic fraction in the solar system (Lodders 2003). $A_{\rm i}$ is the mass number of isotope $i$ and $X_{\rm H,\odot}=0.7399$ is the solar hydrogen mass fraction, at the present day and corresponding to the Asplund+Cunha mixture. As a remark, since the Sun is 4.57 Gyr old, it has likely experienced atomic diffusion since its birth. Atomic diffusion progressively decreases the surface helium and increases the surface hydrogen. Then, the initial solar abundances are different than the present-day abundances. Ekström et al. (2012) have calibrated a 1 $M_{\odot}$ model including atomic diffusion to reproduce the solar radius, luminosity and surface chemical composition at the age of the Sun. It gives an initial hydrogen and helium mass fraction of 0.720 and 0.266 respectively. The associated initial solar metallicity is $Z_{\odot}=0.014$ .

In case the initial metallicity $Z$ of the model is not solar, $X_{\rm He}$ is calculated according to the relation $X_{\rm He}=X_{\rm He,p}+\Delta X_{\rm He}/\Delta Z\times Z$ where $X_{\rm He,p}$ is the primordial helium abundance and $\Delta X_{\rm He}/\Delta Z=(X_{\rm He,\odot}-X_{\rm He,p})/Z_{\odot}$ the average slope of the helium-to-metal enrichment law. I set $X_{\rm He,p}=0.2484$ (Cyburt et al. 2003). Once the helium mass fraction is calculated, the initial hydrogen mass fraction is deduced from $X_{\rm H}=1-X_{\rm He}-Z$ .

When $Z$ is not solar, if the mixture of metal remains solar-like, the mass fractions of metals are just multiplied by $Z/Z_{\odot}$ i.e. $X_{\rm i}=X_{\rm i,\odot}~{}Z/Z_{\odot}$ with $X_{\rm i,\odot}$ from Eq. 3.12. This leads to a solar-scaled mixture, meaning that [X/Fe] $=0$ . However, at [Fe/H] $<0$ , it appears that [ $\alpha$ /Fe] $>0$ where $\alpha$ represent the $\alpha$ -elements (e.g. Reddy et al. 2006). In genec, for $-1<$ [Fe/H] $<0$ , [ $\alpha$ /Fe] $=-B_{\rm\alpha}$ [Fe/H] with $B_{\rm\alpha}$ = 0.562, 0.886, 0.500, 0.411, 0.307, 0.435, 0.300, 0.222 and 0.251 for the $\alpha$ -elements 12C, 16O, 20Ne, 24Mg, 28Si, 32S, 36Ar, 40Ca and 48Ti respectively. These numbers were derived by fitting the abundance trends [ $\alpha$ /Fe] versus [Fe/H] from halo and thick disc F- and G-dwarfs stars with $-1\lesssim$ [Fe/H] $\lesssim 0$ (Reddy et al. 2006). At [Fe/H] $<-1$ , [ $\alpha$ /Fe] $=B_{\rm\alpha}$ is set (i.e. no dependance on metallicity). The mass fractions of the $\alpha$ -isotopes are calculated according to

[TABLE]

where $X_{\rm Fe}$ is the sum of the mass fractions of all Fe isotopes. The mass fraction of the non $\alpha$ -isotopes are calculated with the same equation but with $B_{\rm\alpha}=0$ . Accordingly to this $\alpha$ -enhanced mixture, the opacity tables were computed with the OPAL tool666http://opalopacity.llnl.gov.. They are complemented at low temperatures by the opacities from Ferguson et al. (2005).

In general, at low metallicity, the initial mixture is poorly known and other initial mixtures cannot be excluded. An $\alpha$ -enhanced mixture may be the most natural choice. However, it is worth noting that for most of the elements and low-metallicity models considered in this work, the abundances in the ejecta of the massive star models are very different from the initial ones. It implies that the dependance of the chemical yields on the initial composition is weak.

Also worth to mention is that with Galactic chemical evolution models, Chiappini et al. (2008) have shown that if massive fast rotators were common in the early Universe, 12C/13C would be between about 30 and 300 in the (almost) primordial ISM. Without fast rotators, 12C/13C would be between about 4500 and 31000. Here I take 12C/13C $=300$ . Lower or higher values cannot be excluded. This is discussed in the next chapters.

3.3.5 Mass loss

AGB and massive stars show spectroscopic evidences of stellar winds (Kudritzki & Puls 2000, for a review). Stellar winds are mainly driven by the absorption of UV-photons by metal lines. Winds are consequently stronger in hot metal-rich stars. The radiation pressure expels stellar material. It can make a 120 $M_{\odot}$ solar metallicity star losing more than 70 % of its initial mass (Ekström et al. 2012). At low metallicity, radiative winds are weaker because of the smaller content in metals. Radiative mass loss rates follow a scaling relation with metallicity $Z$ :

[TABLE]

where $\dot{M}(Z_{\odot})$ is the solar metallicity mass loss rate and $0.5<a<0.85$ (Vink et al. 2001). In this work, radiative mass-loss rates are from Vink et al. (2001) when $\log(T_{\rm eff})\geq 3.95$ and from de Jager et al. (1988) when $\log(T_{\rm eff})<3.95$ . For the models of Sect. 4.5.2 however, the prescription of Kudritzki & Puls (2000) is used instead of Vink et al. (2001). Radiative winds at low metallicity are generally small so that no big impact is expected. Also, for $\log(T_{\rm eff})<3.95$ , de Jager et al. (1988) is used in any case.

The stellar surface can also reach the Eddington luminosity $L_{\rm EDD}$ (luminosity when the radiative force balances the gravitational force) which triggers additional mass loss. In genec, the mass-loss rate is increased by a factor of 3 when the luminosity of any layer in the stellar envelope becomes higher than five times the Eddington luminosity (Ekström et al. 2012).

Another recent mass loss mechanism was proposed for metal-free stars with $M_{\rm ini}\geq 150$ $M_{\odot}$ (Moriya & Langer 2015): if $\log(T_{\rm eff})<3.7$ the envelope of such stars may become pulsationally unstable near the end of their evolution and undergo extreme mass-loss events, of the order of $10^{-4}-10^{-2}$ $M_{\odot}$ yr*-1*. Although not used in the models of this work, I have added this prescription in genec (details in Appendix A.3).

Effect of rotation on mass loss

Rotation is expected to affect the mass loss of stars. First, it makes the stellar winds anisotropic by favoring an ejection of matter through both the poles and the equator (Maeder 1999). The reason is that the polar regions are hotter than the equatorial regions (cf. Sect. 3.3.1) so that the radiation pressure, hence the mass loss rate is stronger at the poles. Also, for stars with equatorial temperatures $T\lesssim 23000$ K (rotation tends to reduce the temperature at the equator), the high opacity around the equator triggers enhanced radiative winds that push the matter outward and produce an equatorial ring.

When the stellar surface reaches the critical velocity, the outer layers are no longer bound and some mass is removed mechanically. In rotating stars having an Eddington factor $\Gamma=L/L_{\rm EDD}>0.639$ , because of the interplay between radiation and rotation, the critical velocity is reduced (Maeder & Meynet 2000). The consequence is that mechanical mass loss occurs more easily (i.e. at a smaller rotation rate). Mechanical mass losses on the rotating massive Pop III models of Ekström (2008) removes $<10$ % of the total stellar mass.

More generally, if considering 2 stars of same mass $M$ , one rotating at $\Omega$ and one non-rotating, at about the same location in the HR diagram, the mass loss ratio $\dot{M}(\Omega)$ / $\dot{M}(0)$ is greater than one and depends, among other, on $\Omega$ and $\Gamma$ (Maeder & Meynet 2000). Models including rotation are corrected by this factor, that becomes very high for large $\Gamma$ factors.

Also, by changing the distribution of the chemical species in the stellar interior, rotation modifies the tracks in the HR diagram. Since radiative mass loss rates depend on $L$ and $T_{\rm eff}$ , the mass loss experienced by the star is changed. For instance, rotation tends to produce bigger cores, increasing the luminosity $L$ of the star hence increasing the mass loss rate $\dot{M}$ , that varies as $L^{2.2}$ (Vink et al. 2001).

Fast rotation may also induce extreme radiative winds during the core He-burning stage of very low massive metallicity stars. It occurs if a large amount of metals from the stellar interior is brought up to the surface. In this case, the surface metallicity increases dramatically so that strong radiative winds are triggered (Eq. 3.14). It can make a very low metallicity ( $Z=10^{-8}$ ) massive star to lose about 70 % of its mass (Hirschi 2007). Such strong mass loss episodes are however not happening in all low/zero metallicity rotating models (Hirschi 2007; Ekström et al. 2008) and are sensitive to different parameters (see Sect. 4.8 for additional discussions).

3.3.6 Chemical composition of the ejecta

For a stellar model, the ejected mass $m^{\rm ej}_{\rm i}$ in $M_{\odot}$ under the form of an isotope $i$ is given by

[TABLE]

where the bounds $\tau$ , $M_{\rm{fin}}$ , and $M_{\rm{cut}}$ are the total lifetime, mass at the end of the evolution and mass cut777At the end of the evolution, the mass cut is the mass coordinate that delimitates the part of the star which is expelled from the part which is kept into the remnant. of the model, respectively. $X_{\rm i,s}(t)$ and $\dot{M}(t)$ are the surface mass fraction and the mass loss rate at time $t$ respectively. $X_{\rm i}(M_{\rm r})$ is the mass fraction of the isotope $i$ at coordinate $M_{\rm r}$ , at the end of the evolution. From Eq. 3.15 and knowing the solar composition, the [X/Y] ratios in the ejected material can be computed888In the bracket notation, X and Y are in number so that the mass ejected $m_{\rm i}^{\rm ej}$ of an isotope $i$ has to be divided by its atomic mass $A_{\rm i}$ . For instance, [C/H] $=\log\left(\frac{m_{{}^{12}\textrm{C}}^{\rm ej}/12+m_{{}^{13}\textrm{C}}^{\rm ej}/13}{m_{{}^{1}\textrm{H}}^{\rm ej}}\right)-\log(\frac{\textrm{C}}{\textrm{H}})_{\odot}$ . .

The stellar yield of an isotope $i$ is expressed as

[TABLE]

with $X_{\rm i,0}$ the initial mass fraction of isotope $i$ . The only difference with Eq. 3.15 is that the mass under the form of the isotope $i$ that was initially present in the star is deduced. Hence, $m_{\rm i}$ can be either positive or negative.

Finally, for an isotope $i$ , the production factor $f_{\rm i}$ is defined as

[TABLE]

with $M_{\rm ej}$ the total mass ejected by the star, $M_{\rm ini}$ the initial mass and $X_{\rm i,ej}$ the mass fraction of isotope $i$ in the ejecta. It expresses, for a given isotope, the ratio of what is given back by the star divided by what was present initially in the whole star.

3.4 Axions and their impact on Pop III stars

This section presents a side project of the thesis, related to the evolution of metal-free massive stars including axion cooling. Axions are hypothetical elementary particles that are of interest as possible components of cold dark matter (Preskill et al. 1983; Abbott & Sikivie 1983; Dine & Fischler 1983). They interact weakly with matter. In stars, they can be considered as an energy sink, taking away the energy, like neutrinos. An axion loss rate as a function of the stellar temperature and density can be derived and introduced in stellar evolution codes in order to see how such losses affect the life of stars. Friedland et al. (2013) found that axion losses can shorten and eliminate the blue loop phase of solar metallicity $8-12$ $M_{\odot}$ stars.

In collaboration with Alain Coc (Centre de Sciences Nucléaires et de Sciences de la Matière (CSNSM), France), Keith A. Olive (William I. Fine Theoretical Physics Institute, School of Physics and Astronomy, University of Minnesota, USA), Jean-Philippe Uzan and Elisabeth Vangioni (Institut d’Astrophysique de Paris (IAP), France), I have studied the effects of axions on Pop III stars in the article (the full paper can be found page C of this thesis):

[ **Effects of axions on Population III stars

**A. Choplin, A. Coc, G. Meynet, K. A. Olive, J.-P. Uzan & E. Vangioni, 2017 A&A 605, 106](http://adsabs.harvard.edu/abs/2017A%26A...605A.106C)

First, I introduced the axion losses $\epsilon_{\rm ax}$ in genec. The derivatives of $\epsilon_{\rm ax}$ as a function of the pressure $P$ and temperature $T$ were also introduced in genec so as to help for convergence when solving the structure equations (see Appendix A.1 for more details and calculations). Then, I computed a grid of non-rotating Pop III massive stars with initial masses of 20, 25, 32, 40, 60, 85, 120 and 150 $M_{\odot}$ , with and without axion losses, until the end of the core C-burning phase.

During the main sequence, the energy is mainly transported by radiation and convection. Axion losses have a modest effect: the main sequence lifetime is shorten by less than 3 % in models including axions. Although still modest, axion losses are stronger during the core He-burning stage, because of higher temperature. Consequently, the core He-burning lifetime is reduced by $7-10$ %. The phase from core He depletion to core C-burning ignition lasts for $10^{3}-10^{4}$ yr. During this phase, the carbon-oxygen core contracts so that the central temperature increases and axion losses become important. Neutrino losses are not strong yet. This is during this short axion-dominated phase that axions are likely inducing the most significant changes in the evolution. From core C-burning ignition to the end of the evolution, axion losses become negligible compared to neutrino losses so that stellar evolution is no more altered.

We found that globally, the effects of axions on stellar evolution are very modest and will be very hardly observable. The strongest effect of axions arises in the 85 and 120 $M_{\odot}$ models. Differences in central temperature, density and chemical composition appear after core He depletion, for a short period of time, as a transitory reaction of the model to the increased loss of energy in the central regions (cf. previous discussion). Such differences might prevent the 85 and 120 $M_{\odot}$ models with axion losses to experience a pulsational pair-instability supernova (PPISN), as it may be expected for stars with initial masses between 70 and 140 $M_{\odot}$ (Woosley 2017). If so, such stars with axions could produce black holes in a mass range where standard stellar models do not predict them. It might induce a potential signature in gravitational waves. As discussed in the paper, however, the uncertainties of different stellar model parameters produce effects at least as strong as axions on the structure of the star, particularly during the late evolution stages. We are therefore still far from a situation where Pop III stellar models can be used as a physics laboratory to verify the presence of axions or constrain their properties.

3.5 Summary

A quick summary of nucleosynthesis, modeling and theoretical aspects important for what follows is given. In the H-burning region of massive stars, the operation of the CNO cycle, Ne-Na and Mg-Al-Si chains can synthesize elements from C to Si. The 14N transformed in 22Ne at the core He-burning ignition will later (when the central temperature $T>220$ MK) provides free neutrons. It leads to the principal component of the weak s-process in massive stars (the other and smaller component comes from the C-burning shell), able to synthesize elements with A $<$ 90. Rotation-induced mixing provides additional 22Ne, which can shifts the s-process pattern towards heavier elements. Among others light elements, 16O, which is abundant in the He-burning core, can poison the s-process by capturing neutrons. The main s-process, responsible for elements with $90<$ A $<209$ is associated with thermally pulsing AGB stars, having initial masses between about 1 and 8 $M_{\odot}$ .

Some important physical ingredients were presented in Sect. 3.3 for the modeling of massive stars including rotation. At low metallicity, a natural effect of the physics of rotation in stars is that the rotation-induced mixing of chemical elements is more efficient. One reason is due to the less efficient redistribution of the angular momentum by meridional currents. Rotation enhances the mass loss in different ways, particularly because of the interplay of radiation and rotation. The mass loss is generally reduced at low metallicity but extreme mass loss events can nevertheless happen in fast rotating massive models (Fig. 3.7 for a schematic view). The nuclear network considered in this work comprises either 31 isotopes (Chapter 4) or 737, from 1H to 212Po (Chapter 5). While the small network is suitable for the study of CEMP-no stars, the second is required to study CEMP stars enriched in heavier elements like strontium or barium.

Chapter 4 Mixing in CEMP-no source stars

In this chapter, the origin of the CEMP stars with [Fe/H] $<-3$ is investigated. The recognized CEMP-s, -r/s and -r stars are not considered. For convenience, the stars considered here are referred to as CEMP-no stars, even if strictly speaking, some of them are just CEMP (because of missing abundance data to classify them). Sections 4.2 and 4.5 include the results published in the first and second articles mentioned below, respectively (the full papers can be found page C and C of this thesis).

[ **Constraints on CEMP-no progenitors from nuclear astrophysics

**A. Choplin, A. Maeder, G. Meynet, & C. Chiappini, 2016 A&A 593, 36](http://adsabs.harvard.edu/abs/2016A%26A...593A..36C)

[ **Pre-supernova mixing in CEMP-no source stars

**A. Choplin, S. Ekström, G. Meynet, A. Maeder, C. Georgy, & R. Hirschi, 2017 A&A 605, 63](http://adsabs.harvard.edu/abs/2017A%26A...605A..63C)

4.1 The back-and-forth mixing process

In the previous chapter, some aspects regarding the nucleosynthesis and the physics of rotation were discussed. The interplay between rotation and nucleosynthesis in rotating massive stars is now discussed.

During the core H-burning and He-burning phase, the mixing induced by rotation changes the distribution of the chemical elements inside the star. In advanced stages (C-burning and after), the burning timescale becomes small compared to the rotational mixing timescale so that rotation barely affects the distribution of chemical elements. During the core He-burning phase, two different burning regions exist in the star (He-burning core and H-burning shell). The rotational mixing triggers exchanges of material between the convective He-burning core and the convective H-burning shell: He-burning products are transported to the H-burning shell, processed by H-burning, transported back to the He-burning core, etc… The main steps of this mixing process are (see Fig. 4.1 for a schematic view):

In the He-burning core, the triple alpha process synthesizes 12C. 16O is formed by 12C( $\alpha,\gamma$ )16O. 2. 2.

12C and 16O are mixed into the H-burning shell. It boosts the CNO cycle and creates primary CNO elements, especially 14N (and 13C to a smaller extent). 3. 3.

The products of the H-burning shell (among them primary 13C and 14N) are mixed back into the He-core. From the primary 14N, the reaction chain 14N( $\alpha,\gamma$ )18F( $e^{+}\nu_{e}$ )18O( $\alpha,\gamma$ )22Ne allows the synthesis of primary 22Ne. The reactions 22Ne( $\alpha,n$ ) and 22Ne( $\alpha,\gamma$ ) make 25Mg and 26Mg respectively. The neutrons released by the 22Ne( $\alpha,n$ ) reaction produce 19F, 23Na, 24Mg and 27Al by 14N( $n,\gamma$ )15N( $\alpha,\gamma$ )19F, 22Ne( $n,\gamma$ )23Ne( $e^{-}\bar{\nu}_{e}$ )23Na, 23Na( $n,\gamma$ )24Na( $e^{-}\bar{\nu}_{e}$ )24Mg and 26Mg( $n,\gamma$ )27Mg( $e^{-}\bar{\nu}_{e}$ )27Al, respectively. Free neutrons can also be captured by heavier seeds like 56Fe and boost the s-process (cf. Sect. 3.1.2). This point is investigated in details in Chapter 5. 4. 4.

The newly formed elements in the He-burning core can be mixed again into the H-burning shell. It boosts the Ne-Na and Mg-Al chains: additional Na and Al are produced.

A very fast rotator will go through all the steps while a slow rotator only through the first one. An important effect (not shown in Fig. 4.1) is the growth of the convective He-burning core that helps reaching layers that had been previously enriched in H-burning products (e.g. 13C, 14N). Both the growing of the convective He core and the backward diffusion of chemical elements impact the nucleosynthesis in the He-burning core of rotating models.

Fig. 4.2 shows the results of this mixing process in a 20 $M_{\odot}$ stellar model, when the central 4He mass fraction is about 0.2. The 14N and 13C peaks can be seen and to a smaller extent, the 23Na peak (at $M_{\rm r}\sim 8$ $M_{\odot}$ ). In the He-core, 22Ne has been enhanced because of the ingestion of the extra 14N. Complete stellar models are discussed in more details in Sect. 4.3.

4.2 Nucleosynthesis in a box

Maeder et al. (2015) suggested that the wide range of abundances covered by CEMP-no stars could come from a material ejected by massive source stars having experienced various degree of rotational mixing. In this scenario, the variety of CEMP-no star abundances are mainly explained by the interplay between rotation and nucleosynthesis at work during the core He-burning phase of the massive source star (described in Sect. 4.1). Maeder & Meynet (2015) built a new classification scheme for CEMP-no stars by considering the successive steps in the back-and-forth mixing process. Five classes were proposed, the first one showing a complete absence of mixing and the fifth one a high degree of mixing (see Fig. 4.3). For instance, HE 1327-2326, with [Fe/H] $=-5.7$ (Frebel et al. 2008) and showing strong overabundances in light elements (e.g. CNO) as well as in strontium, is belonging to class 4. In Maeder & Meynet (2015), they considered 46 stars, 4 appeared to be of class 2, 17 of class 3, 9 of class 4 and 16 unclassified because of missing abundance data. No star belonging to class 0 or 1 were found.

In Choplin et al. (2016), we aimed at investigating quantitatively the effect of the back-and-forth mixing process using a one-zone (or box) nucleosynthesis code I developed. This code allows the injection of chemical species in the box while nucleosynthesis is calculated. It mimics the effect of rotational mixing at work in complete rotating stellar models. In the paper, I used the one-zone code to mimic the hydrogen burning shell of a massive rotating star in which 12C, 16O, 22Ne, and 26Mg are injected (these species are supposed to come from the He-burning core of the rotating massive star). We studied the nucleosynthesis of the CNO cycle and the Ne-Na Mg-Al chains at different temperatures, densities, and with different nuclear reaction rates while injecting chemical species.

Initial setup

For the initial composition of the box, a rotating 60 $\rm M_{\odot}$ model is used, with $Z=10^{-5}$ (corresponding to [Fe/H] $=-3.8$ ) and computed with an $\alpha-$ enhanced mixture. The initial abundances in the box are taken from the H-burning shell of this stellar model, when it starts the core He-burning stage (central 4He mass fraction equals to 0.98). The corresponding initial [X/Fe] ratios in the box are shown in Fig. 4.4 by the patterns with squares. The initial composition of the box is different than the initial composition of the stellar model since some nuclear burning has already operated in the stellar model during the H-burning phase. In particular, CNO burning has operated (that mainly transforms C and O into N) explaining the high initial [N/Fe] and lower [C/Fe] and [O/Fe] in the box. The nuclear reaction rates of the CNO cycle are from Angulo et al. (1999) except for 14N( $p,\gamma$ )15O which is from Mukhamedzhanov et al. (2003) if $T\leq 0.1$ GK and Angulo et al. (1999) otherwise. The rates related to the Ne-Na and Mg-Al chains are from Iliadis et al. (2001). Only 20Ne( $p,\gamma$ )21Na and 22Ne( $p,\gamma$ )23Na are taken from Angulo et al. (1999) and Hale et al. (2002), respectively. For $20-60$ $M_{\odot}$ stellar models at such metallicity, $T\sim 50$ MK and $\rho\sim 1$ g cm*-3* in the H-burning shell. There are the default temperature and density taken in the box. The box simulations are stopped either at H-exhaustion (1H mass fraction is below $10^{-8}$ ) or when the time exceeds 10 Myr.

Four separate injection experiments were carried out: (1) no injection, (2) injection of 12C and 16O, (3) injection of 12C, 16O and 22Ne and (4) injection of 12C, 16O, 22Ne and 26Mg. The species are injected at a constant rate. During a time $\Delta t$ , a mass $\Delta m_{\rm i}=R_{\rm i}\Delta t$ under the form of the isotope $i$ is injected in the burning box. $R_{\rm i}$ is the injection rate of the isotope $i$ expressed in $M_{\odot}$ yr*-1*. $R_{\rm i}$ was calibrated using results from complete stellar models. Details on this calibration are now given (see also the appendix of Choplin et al. 2016, page C of this thesis).

Injection of chemical species

The rate $R_{\rm{}^{12}C}$ at which 12C is injected in the box was calibrated by quantifying $M_{\rm{}^{14}N}^{\rm prim}$ which is the mass of primary 14N formed during the core helium burning phase of a rotating massive star. Primary 14N during the core helium burning phase of rotating stars is formed because of the arrival of 12C and 16O from the helium core (cf. Sect. 4.1). $M_{\rm{}^{14}N}^{\rm prim}$ can be expressed as the total amount of 14N in the star at core helium exhaustion minus the amount of 14N that can be formed with the initial CNO content (the secondary 14N):

[TABLE]

where $Y_{\rm c}$ is the central 4He mass fraction, $X_{\rm{}^{14}N}(M_{\rm r})$ the mass fraction of 14N at coordinate $M_{\rm r}$ , $X_{\rm C,ini}$ , $X_{\rm N,ini}$ , $X_{\rm O,ini}$ the initial mass fractions of the CNO elements in the stellar model, and $M$ the total mass of the star at the end of the core helium burning phase. Let us suppose that all the 12C and 16O diffusing from the helium core to the hydrogen shell are transformed into 14N. In this case, an average injection rate $R_{\rm{}^{12}C+^{16}O}$ of 12C + 16O can be defined

[TABLE]

where $\tau_{\rm HeB}$ is the duration of the core helium burning phase. It gives the average rate at which 12C + 16O should be injected in the H-burning shell so as to obtain $M_{\rm{}^{14}N}^{\rm prim}$ in the model at the end of core helium burning. For a 60 $\rm M_{\odot}$ model at $Z=10^{-5}$ and with111The critical velocity $\upsilon_{\rm crit}$ is reached when the gravitational acceleration is counterbalanced by the centrifugal force. It is expressed as $\upsilon_{\rm crit}=\sqrt{\frac{2}{3}\frac{GM}{R_{\rm p,c}}}$ with $R_{\rm p,c}$ the polar radius at the critical limit. $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.7$ , $R_{\rm{}^{12}C+^{16}O}$ is equal to $5~{}10^{-8}$ $M_{\odot}$ yr*-1*.

Of course, the amount of primary nitrogen synthesized, hence the value of $R_{\rm{}^{12}C+^{16}O}$ , can change significantly depending on the rotation, the mass of the stellar model, or the prescription for the rotational mixing for instance. The $R_{\rm{}^{12}C+^{16}O}$ rate estimated above gives an idea of possible values but other injection rates around this value are possible. Here I set $R_{\rm{}^{12}C}=R_{\rm{}^{16}O}=10^{-8}$ $M_{\odot}$ yr*-1*. The two rates are taken equal since there is roughly as much 12C as 16O in the helium core so that roughly as much 12C as 16O will enter in the H-burning shell. Finally, $R_{\rm{}^{22}Ne}=R_{\rm{}^{26}Mg}=R_{\rm{}^{12}C}/100=10^{-10}$ $M_{\odot}$ yr*-1*. The factor 100 between the two rates accounts for the fact that 22Ne and 26Mg are about 100 times less abundant than 12C and 16O in the helium burning core so that about 100 times less 22Ne and 26Mg will enter by rotational mixing into the H-burning shell. Injection rates divided and multiplied by 100 were also investigated: $10^{-10}$ and $10^{-6}$ $M_{\odot}$ yr*-1* for $R_{\rm{}^{12}C}$ and $R_{\rm{}^{16}O}$ and therefore $10^{-12}$ and $10^{-8}$ $M_{\odot}$ yr*-1* for $R_{\rm{}^{22}Ne}$ and $R_{\rm{}^{26}Mg}$ .

Results

As shown in Fig. 4.4, C, N, O and F are boosted by $\sim 4$ dex when injecting 12C, 16O because of the injection and the effect of CNO cycle. Injection of 22Ne gives Ne, Na and Mg with Na being the main product. With the nuclear rates considered, the 23Na( $p,\alpha$ )20Ne reaction is just 1.6 stronger than the 23Na( $p,\gamma$ )24Mg reaction. It means that 23Na goes almost 50 $-$ 50 to 20Ne and 24Mg. It allows a significant production of 24Mg. No Al is produced because the 24Mg( $p,\alpha$ )25Al reaction, activating the Mg-Al cycle, is too slow at the considered temperature. Injection of 26Mg boosts Mg and Al. The [12C/13C] ratio222[12C/13C] = $\log$ (12C/13C)⋆ $-$ $\log$ (12C/13C)⊙. In the Sun, (12C/13C $)_{\odot}$ = 89, i.e. $\log$ (12C/13C)⊙ = 1.95. stays always around $-1.5$ (equivalent to 12C/13C $\sim 3$ ), which is the CNO-equilibrium value. At $T=50$ MK, the timescale for the 12C/13C ratio to reach CNO-equilibrium is about $10$ yr, i.e. reached almost instantaneously.

This simple one-zone model gives a good estimation of what happens in complete stellar models: green patterns in Fig. 4.4 are from complete 20 $M_{\odot}$ stellar models with $\upsilon_{\rm ini}/\upsilon_{\rm crit}=$ 30 % and 70 %, at the end of the core He-burning phase. The abundances are taken in the stellar shell where the energy released by hydrogen burning is the highest. These patterns are close enough to the results obtained with the box model.

Comparison with CEMP-no stars of classes 2 and 4

From the classification done in Maeder & Meynet (2015), the classes 2 and 4 CEMP-no stars were selected (13 stars). These classes of stars are made of a material that was processed by H-burning, with various degree of enrichment (Fig. 4.3). I considered only stars having a [Fe/H] ratio close to the [Fe/H] $=-3.8$ of the box. HE 0057-5959 was classified as a class 2+Na star since it shows the characteristics of a class 2 star, except for Na, which is overabundant ([Na/Fe] = 1.98).

The best match between models and observations is when 12C and 16O are injected for the class 2 and when 12C, 16O and 22Ne are injected for the class 4. Injecting only 12C and 16O does not allow to reproduce the stars of class 4, which are generally Na- and Mg-rich. Injecting additional 26Mg raises the [Al/Fe] ratio and leads to a larger discrepancy between models and observations. In any case, the models overestimate the [Al/Fe] ratios. Below are discussed the uncertainties on the observed and predicted [Al/Fe] ratios.

Uncertainties on the aluminum abundance of CEMP-no stars.

The first point is that the CEMP sample is not homogeneous333A sample is homogeneous if the same procedure is used to obtain all observations and abundances.. The abundance data considered comes from several sources. Ideally, an homogeneous sample is needed because a mixture of abundances from various authors sometimes adds an undesirable scatter that makes harder the use of the sample to constrain the models. However very metal-poor stars are very rare and no large homogeneous sample exists yet. The second point is that in the sample considered, most of the abundances are derived based on 1D LTE atmosphere models. For turnoff stars at [Fe/H] $\simeq-3$ , Andrievsky et al. (2008) derived a correction $\Delta$ [Al/Fe] $=$ [Al/Fe]NLTE $-$ [Al/Fe] ${}_{\rm LTE}\simeq 0.6$ dex. In addition to NLTE, 3D effects can add another correction factor. Nordlander & Lind (2017) have shown that the difference between 3D NLTE and 1D LTE for Al in metal-poor stars can amount $+0.5$ dex. In the stars plotted in Fig. 4.4, there is for instance CS 22949-037 with [Al/Fe] $=0.02$ . This ratio was derived based on 1D LTE model-atmosphere analyses (Norris et al. 2013). According to the previous discussion, NLTE/3D effects could rise [Al/Fe] up to $\sim 0.6$ dex. This is still $\sim 1$ dex below the values predicted by the models.

Uncertainties on the aluminum abundance predicted by the models.

As mentioned, the initial [Al/Fe] $\simeq 1.5$ in the box comes from the H-burning shell of a complete stellar model at core He-ignition. The initial [Al/Fe] of this stellar model is 0 (i.e. solar). The nucleosynthesis during the main sequence and very beginning of core He-burning has synthesized some Al (especially through the Mg-Al chain), up to [Al/Fe] $\simeq 1.5$ . I have investigated how the Al production is affected (considering both the stellar model and the box model) when varying some specific nuclear reaction rates. Several literature sources provide nuclear reaction rates for the three major reactions involving 27Al in H-burning zones: 26Mg( $p,\gamma$ )27Al, 27Al( $p,\gamma$ )28Si and 27Al( $p,\alpha$ )24Mg. For instance, there are six sources for 27Al( $p,\gamma$ )28Si spanning $\sim 4$ order of magnitude at $T\sim 50$ MK (according to the JINA reaclib444http://jinaweb.org/reaclib/db/.). Using the rates in the literature that favor the destruction (or smallest production) of 27Al leads to a final [Al/Fe] in the box of about 0, i.e. $\sim 1.5$ dex below the [Al/Fe] ratio shown in Fig. 4.4. It would match better the observations. Finally, because of important uncertainties existing on some nuclear rates, caution is required when interpreting the nucleosynthetic predictions of some elements like Al.

The 12C/13C ratio.

The CEMP-no stars in Fig. 4.4 have low 12C/13C ratios compared to the Sun: $-1.5\lesssim$ [12C/13C] $\lesssim-1$ , which is equivalent to $3\lesssim$ 12C/13C $\lesssim 9$ (in the solar system, the carbon isotopic ratio is about 90, Lodders 2003). Some CEMP-no stars are giants and may therefore have experienced mixing events like the first dredge-up. In this case, the observed 12C/13C may have changed since the formation of the CEMP-no star. If so, the link between the CEMP-no star and its source star is more difficult to establish (further discussions in Sect. 4.4.2, cf. also Sect. 2.4). By contrast, the surface composition of unevolved CEMP-no stars reflects more directly the composition of the cloud in which they formed, hence the composition of the material ejected by the previous source star. Some CEMP-no stars in the considered sample are still rather unevolved: CS 22958-042 for instance, has $T_{\rm eff}=6250$ K, $\log~{}g=3.5$ and 12C/13C $=9$ . Such a 12C/13C ratio is consistent with a material processed only by H-burning in the previous massive source star. In He-burning regions of massive stars, 13C is destroyed so that 12C/13C $\sim\infty$ . Consequently, it is unlikely that this CEMP-no star formed from a source star material processed by He-burning. This will be discussed in more details while considering yields from complete source star models (Sect. 4.3 and 4.4).

Conclusion

The conclusion from this box experiment is that the range of abundances of class 2 and 4 CEMP-no stars is overall well reproduced by a material processed by H-burning at a temperature and density characteristic of $20-60$ $M_{\odot}$ source stars. During its burning, the material was enriched in He-burning products: 12C, 16O for class 2, 12C, 16O and 22Ne for class 4. This is consistent with the scenario of Maeder & Meynet (2015) proposing that CEMP-no stars are made of a material ejected from a massive star having experienced various degree of rotational mixing.

4.3 Massive source stars with rotation

As a next step, complete stellar models with various initial rotation rates are considered. It allows to give more realistic abundance predictions than with a one-zone model. Other source star parameters such as mass and metallicity are also investigated.

4.3.1 Physical ingredients

I computed 20 $M_{\odot}$ models at a metallicity $Z=10^{-5}$ with555The critical velocity $\upsilon_{\rm crit}$ is reached when the gravitational acceleration is counterbalanced by the centrifugal force. It is expressed as $\upsilon_{\rm crit}=\sqrt{\frac{2}{3}\frac{GM}{R_{\rm p,c}}}$ with $R_{\rm p,c}$ the polar radius at the critical limit. $\upsilon_{\rm ini}/\upsilon_{\rm crit}=$ 0, 0.1, 0.2, 0.3, 0.4, 0.5 and 0.7. I also computed a 40 and a 60 $M_{\odot}$ model at $Z=10^{-5}$ and with $\upsilon_{\rm ini}/\upsilon_{\rm crit}=$ 0.4 to explore different initial masses. Finally, a 20 $M_{\odot}$ at $Z=0$ and with $\upsilon_{\rm ini}/\upsilon_{\rm crit}=$ 0.4 was computed to evaluate the effect of metallicity. The nuclear reaction rates are the same than for the box model. The evolution is stopped at the end of core carbon burning. The very last burning stages (also explosive nucleosynthesis, cf. Sect. 3.1.3) significantly modify only the abundances of the most inner layers. The yields of the models presented here provide good predictions, provided the most inner layers of the star are not ejected and considered in the yields. More details on the other physical ingredients (shear mixing, mass loss, initial composition…) can be found in Sect. 3.3.

4.3.2 Evolution with rotation

This section discusses the effects of rotation by focusing on the 20 $M_{\odot}$ models with various initial rotation rates.

The effective gravity of the stellar core is decreased by rotation because of the effect of the centrifugal force. It decreases the temperature in the convective core and tends to make it smaller. On the other hand, rotation tends to produce bigger cores because of the rotational mixing that provides additional fuel to the core. Overall, in the models presented here, rotation produces bigger cores at the end of the evolution (Fig. 4.5). For instance the size of the carbon-oxygen core (CO-core, defined where the 4He mass fraction drops below $10^{-3}$ ) increases by about 1.5 $M_{\odot}$ from the non rotating model to the fast rotating one. A consequence is that the base of the H-rich envelope and the He-rich region are shifted towards higher mass coordinates when initial rotation increases (Fig. 4.6, top panels).

As the initial rotation increases, the He-burning products (e.g. 12C, 16O, 22Ne) transit quicker and in greater amount to the H-burning shell so that more 13C, 14N, 19F, 23Na are synthesized (Fig. 4.6 and 4.7). Around the mass coordinate 7 $M_{\odot}$ , 13C and 14N are boosted by $\sim 4$ dex from $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0$ to 0.7. Rotation increases the production of 19F, 22Ne, 23Na, 24,25,26Mg and 27Al in the He-burning core (cf. Sect. 4.1). Near the end of the core He-burning phase, 19F is also destroyed in the central regions (below 5 $M_{\odot}$ ) by 19F( $\alpha,p$ )22Ne. While the Ne-Na chain is boosted in the H-burning shell of rotating models (see the peak of 23Na at $\sim 8$ $M_{\odot}$ ), the Mg-Al chain is not efficiently activated (no similar peak in the H-burning shell). This is mainly because the temperature in the H-burning shell is too low ( $T\lesssim 45$ MK). Another reason is that the synthesis of extra Al in the H-burning shell needs extra Mg, which is only built in the He-core when $T\gtrsim 220$ MK (through an $\alpha$ -capture on 22Ne). In a 20 $M_{\odot}$ model, this temperature corresponds to the end of core He-burning phase. The extra Mg created in the core has then little time to be transported to the H-burning shell and boosts the Mg-Al chain. 28Si is the only isotope that is barely affected by rotation (bottom right panel of Fig. 4.7).

As initial rotation increases, the surface is enriched in H-burning products. This is because of the rotational mixing that transports these elements from H-burning layers up to the surface. We indeed see that (1) the surface 4He is increased in the faster rotating model, (2) the effect of CNO burning appears at the surface (less 12C and 16O, more 14N) and (3) the products of the Ne-Na and Mg-Al cycles are more abundant (mostly 23Na, 24Mg and 27Al). The surface abundances change mostly during the main sequence phase because of its longer duration (the chemical species have more time to be transported). When reaching the stellar surface, chemical species are potentially expelled through winds. In these models however, the mass loss metallicity relation ( $\dot{M}\propto Z^{0.85}$ , cf. Sect. 3.3.5) plays a major role and thus prevents significant radiative mass loss episodes. Also the mechanical mass loss (cf. Sect. 3.3.5) stays small for these models. The 20 $M_{\odot}$ model with $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.7$ loses about 0.12 $M_{\odot}$ through mechanic mass loss and 0.6 $M_{\odot}$ through radiative mass loss. The total mass lost through winds is < 1 $M_{\odot}$ for all the 20 $M_{\odot}$ models. We note that the mass loss may be strongly enhanced for higher mass stars.

4.3.3 Composition of the ejecta

The effect of varying the initial rotation, mass cut, dilution, efficiency of rotational mixing, mass and metallicity on the chemical composition of the source star ejecta is considered.

Initial rotation

Composition of the wind.

Fig. 4.8 shows the [X/H] ratios in the wind of the models. For all models, the wind contribution is less than 1 $M_{\odot}$ and comes from the H-rich region. The non-rotating model (red) is superimposed with the ISM pattern since the ejected material has kept exactly the same composition as the ISM. As rotation increases, the wind is overall more and more enriched in a material processed by the CNO cycle, Ne-Na and Mg-Al chains (cf. Sect. 4.3.2). For the faster rotators, the 12C/13C ratio is equal to the CNO equilibrium value of $\sim 4$ (equivalent to [12C/13C] $=-1.35$ ).

Composition of the H-rich material.

Fig. 4.9 shows the chemical composition of the ejecta when considering the wind plus all the material above the bottom of the H-rich region. In this case, $M_{\rm cut}=M_{\alpha}$ , where $M_{\alpha}$ is the mass of the helium core set where the mass fraction of 1H drops below 10*-3*. From the top left panel of Fig. 4.6 we see that it corresponds to a total ejected mass of $\sim 12-14$ $M_{\odot}$ , depending on the model. The typical CNO pattern appears for all the models (more N, less C and O) but the sum of CNO elements increases with rotation, as a result of 12C and 16O having diffused to the H-burning shell. [Na/H] spans $\sim 2$ dex while [Mg/H], [Al/H] and [Si/H] do not vary more than 0.5 dex. Mg and Al are overproduced with rotation (Fig. 4.7) but only in the He-rich region, which is not consider in the yields of Fig. 4.9. 12C/13C is very close to the CNO equilibrium value.

Composition of the H-rich + He-rich material.

Fig. 4.10 is similar as Fig. 4.9 but it considers the wind plus all the material above the bottom of the He-rich region. In this case, $M_{\rm cut}=M_{\rm CO}$ . The total ejected mass is about $15-16$ $M_{\odot}$ , depending on the model (Fig. 4.5). Compared to the previous case, the additional $\sim 2$ $M_{\odot}$ ejected are H-free, so that is raises a bit the [X/H] ratios (by < 0.5 dex). The CNO pattern is reversed compared to Fig. 4.9 because in He-burning regions, 14N is depleted while 12C and 16O are abundant (Fig. 4.6). No or very little little additional 14N is added to the ejecta compared to Fig. 4.9. The ratios containing He-burning products ([Ne/H], [Na/H], [Mg/H] and [Al/H]) are largely boosted compared to Fig. 4.9. They also greatly increase with initial rotation as a result of the back-and-forth mixing process. In He-burning regions, 13C is destroyed by 13C( $\alpha,n$ )16O so that the 12C/13C ratio is largely enhanced compared to the case where only H-rich ejecta is considered. Considering deeper mass cuts raise again C/H, O/H, Ne/H, Mg/H, and 12C/13C but, overall, it does not change significantly the trends of Fig. 4.10.

Mass cut in the intershell region

Fig. 4.12 shows the chemical composition of the wind plus an ejecta defined with various mass cuts, for the $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.4$ model. The 5 considered mass cuts are represented in Fig. 4.11 which shows the abundance profile of the 20 $M_{\odot}$ model with $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.4$ at the pre-SN stage. The zone between $7.8\lesssim M_{\rm r}\lesssim 8$ $M_{\odot}$ corresponds to the intershell region, in between the H- and He-burning shells. As $M_{\rm cut}$ decreases, deeper layers are ejected and we move progressively from the H-rich only ejecta to a mixed H+He ejecta. Varying the mass cut from 7 to 8 $M_{\odot}$ leads to a quick increase of the [X/H] ratios, up to $\sim 5$ dex for [C/H]. It illustrates the high sensitivity of the yields on the mass cut when varying it around the intershell region.

Dilution of the source star ejecta with ISM

The material ejected from the star can be mixed with the material in the ISM. The effect of the dilution depends on the composition of the ISM, which is not known at low metallicity (a choice has nevertheless to be made when computing low metallicity models, as done in this work). Generally, in the case of the scenario proposing that CEMP-no stars were formed from one or very few source stars, we can probably just guess that the ISM is either metal-free or very metal-poor. Table 4.1 reports how are affected the different abundance ratios in the source star ejecta while considering either a dilution with a metal-poor ISM or a metal-free ISM. A dilution with a metal-free ISM adds some H so that the [X/H] ratios are affected (where X refers to metals). On the other hand, such an ISM does not modify the [X/Fe] (where X refers to metals) or the isotopic ratios. In almost all the cases, when the [X/H] or [X/Fe] ratios are affected by dilution with ISM, they are reduced (cf. Fig. 4.13 and next paragraph). This is because in the source star ejecta, the H and Fe abundances are similar to the H and Fe abundances in the ISM while light metals (C to Al) are generally strongly overproduced by the source star compared to what is present in the ISM.

In this work, when diluting the source star ejecta with ISM, I consider that the ISM material is the same than the ISM material used to form the source star ( $\alpha$ -enhanced ISM, cf. Sect. 3.3.4 for details on the initial composition). To be more quantitative, a dilution factor $D$ can be defined as

[TABLE]

with $M_{\rm ej}$ the total mass ejected by the source star and $M_{\rm ISM}$ the mass of initial ISM added to the massive star ejecta. The left panel of Fig. 4.13 shows the chemical composition of the wind plus the H-rich ejecta for the $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.7$ model. Different dilution factors are considered. $D=100$ means that there is 100 $M_{\odot}$ of ISM for 1 $M_{\odot}$ of source star ejecta. As $D$ increases, the composition is shifted towards the ISM composition. The right panel of Fig. 4.13 is similar but for the H-rich + He-rich ejecta (like in Fig. 4.10). In this case, the amount of light elements is more important in the source star ejecta so that higher $D$ values are needed to reach back the ISM pattern. The ISM considered here is $\alpha$ -enhanced, which explains why the [C/H], [O/H]… ratios are enhanced compared to the [N/H], [F/H]… ratios. Also, in this ISM, [12C/13C] $\simeq 0.5$ , which corresponds to 12C/13C $=300$ (cf. Sect. 3.3.4). A more extended discussion about the 12C/13C ratio can be found in Sect. 4.4.

At the present day, the dilution factor cannot be strongly constrained. The point explosion or Sedov-Taylor explosion can be used as an approximation to estimate how fast will a shock wave travel and what would be left behind it. For a standard explosion energy of $E_{51}=1$ ( $E_{51}$ is the SN energy in units of $10^{51}$ ergs) and typical ISM densities, the ejecta will be mixed with about $M_{\rm ISM}=10^{4}$ $M_{\odot}$ of ISM (Cioffi et al. 1988; Ryan et al. 1996; Wehmeyer et al. 2015). For the models of Fig. 4.13, the total mass ejected is between $\sim 12$ and $\sim 16$ $M_{\odot}$ . Taking $10^{4}$ $M_{\odot}$ of ISM leads to a dilution factor of $10^{4}/16<D<10^{4}/12$ , which gives $600\lesssim D\lesssim 800$ (in between the cyan and blue patterns in Fig. 4.13). This would be for standard explosions energies. In the case of a low-energetic supernova with $E_{51}=0.1$ for instance, $60\lesssim D\lesssim 80$ (i.e. $D$ is divided by 10, this is because $D\sim M_{\rm ISM}\sim E_{51}^{0.95}$ , Ryan et al. 1996, their Sect. 5.6.1).

Another way to constrain the dilution factor may be the surface Li abundance of the CEMP-no stars. We can assume that Li is completely destroyed in massive stars so that X(Li)ej, the Li mass fraction in the source star ejecta is 0. The Li mass fraction $X(\textrm{Li})_{\rm CEMP}$ in the CEMP-no star natal cloud (possibly different than the value observed today) is then

[TABLE]

where $M_{\rm ej}$ is the mass ejected by the source star, and $X(\textrm{Li})_{\rm ISM}$ the Li abundance in the ISM. The dilution factor can then be expressed as

[TABLE]

We can suppose that the Li abundance in the initial ISM is equal to the WMAP value of $A(\textrm{Li})_{\rm ISM}=2.72$ (Cyburt et al. 2008). If, as a first guess, we consider that in situ processes changing the Li abundance did not occur during the CEMP-no star life, we can take $X(\textrm{Li})_{\rm CEMP}$ equal to the observed Li abundance. If the CEMP-no star has no Li at its surface, $D=0$ and the CEMP-no star is made of pure source star ejecta. If the Li abundance is high, more ISM is needed to form the CEMP-no star. The maximal detected $A(\textrm{Li})$ for CEMP-no stars is about 2.1 (i.e. around the Spite Plateau value Spite & Spite 1982). It leads to a maximal dilution factor of $D_{\rm max}\sim 0.3$ , i.e. all CEMP-no stars would be made of almost pure source star ejecta, even the most Li-rich.

This estimation of $D$ stays correct as long as (1) in situ processes changing the Li abundance did not occur in CEMP stars and (2) the Li ISM abundance is indeed $A(\textrm{Li})_{\rm ISM}=2.72$ (value from WMAP). If instead, $A(\textrm{Li})_{\rm ISM}=2.2$ for instance, $D_{\rm max}\sim 4$ , i.e. the source star ejecta may still largely dominate compared to the ISM (see Fig. 4.13). The main uncertainty in this method are the possible internal processes changing the surface Li abundance of the CEMP-no stars. Korn et al. (2009) have used models including atomic diffusion to estimate by how much the surface Li abundance of the dwarf CEMP-no star HE 1327-2326 was depleted since its birth. At maximum, Li was depleted by 1.2 dex. It would correspond to an initial Li of $A(\textrm{Li})_{\rm ini}<1.82$ for HE 1327-2326 and lead to a small $D$ value. Overall, this method of guessing $D$ is uncertain so precaution is required. It nevertheless suggests very small dilution factors. This is inconsistent with the high $D$ values guessed from the Sedov-Taylor theory assuming standard explosions energies. It might nevertheless be more consistent with low energetic SNe ( $E_{51}<1$ ), that give smaller $D$ values (for $E_{51}=0.1$ however, there is still 1 order of magnitude of difference at least).

Efficiency of the rotational mixing

The $f_{\rm energ}$ parameter in the $D_{\rm shear}$ expression (Eq. 3.10) was taken equal to 4 in these models. It is consistent with the surface N/H enrichments of observed $10-20$ $M_{\odot}$ rotating stars (cf. Sect. 3.3.1). $f_{\rm energ}=4$ corresponds to a critical Richardson number666Physical values of $Ri_{\rm c}$ are likely between 0.25 and 2, cf. Sect 3.3.1. $Ri_{\rm c}=2$ . $f_{\rm energ}=1$ ( $Ri_{\rm c}=0.5$ ) is also a reasonable choice, likely consistent with the observations (cf. Sect. 3.3.1).

Fig. 4.14 shows the effect of changing $f_{\rm energ}$ from 1 to 4. The 2 top panels show the H-rich (left) and H-rich + He-rich ejecta (right) of the 20 $M_{\odot}$ models with $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.2$ and with various $f_{\rm energ}$ . The yields are barely affected when changing $f_{\rm energ}$ . The same plots for the 20 $M_{\odot}$ model with $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.7$ are shown below. In this case, the effect is much larger and leads to differences of $1-1.5$ dex at maximum. The $f_{\rm energ}=1$ model with $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.7$ has similar yields than the $f_{\rm energ}=4$ model with $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.3$ . Changing $f_{\rm energ}$ does not change the general trends but shifts the yields upward or downward, for a given initial rotation. To obtain similar yields as the $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.7$ , $f_{\rm energ}=4$ model while setting $f_{\rm energ}=1$ , it is probably needed to raise $\upsilon_{\rm ini}/\upsilon_{\rm crit}$ up to about 1. The $f_{\rm energ}\sim$ $Ri_{\rm c}$ parameter is important, especially for fast rotators, but its accurate value is not known.

Mass

Figure 4.15 shows the yields of 20, 40 and 60 $M_{\odot}$ models with $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.4$ at $Z=10^{-5}$ . The final yields are rather similar. The 60 $M_{\odot}$ produces more N because its H-shell is more active than in lower mass models. In the H-rich layers, more Na is produced in the 20 $M_{\odot}$ models because the back-and-forth mixing process (Fig. 4.1) is more efficient in lower masses. It is mainly because the process has more time to operate due to the longer duration of the core helium burning stage. Also, Al and Si are overproduced in the H-rich layers of the 40 and 60 $M_{\odot}$ because of the higher H-burning temperature, increasing the efficiency of the Mg-Al-Si chain. The yields of the 60 $M_{\odot}$ in the H-rich + He-rich layers show significant differences compared to the other models (right panel). It is explained by the fact that the He-burning shell becomes convective in the 20 and 40 $M_{\odot}$ models while it does not for the 60 $M_{\odot}$ model. In the 60 $M_{\odot}$ model, the H-burning shell is very active and therefore limits the activation of the He-burning shell. In the 20 and 40 $M_{\odot}$ models, while becoming convective, the He-shell engulfs some 14N from the H-rich region. It boosts the production of F and Na through the chains 14N( $n,\gamma$ )15N( $\alpha,\gamma$ )19F and 14N( $\alpha,\gamma$ )18F( $e^{+}\nu_{e}$ )18O( $\alpha,\gamma$ )22Ne( $n,\gamma$ )23Ne( $e^{-}\bar{\nu}_{e}$ )23Na. The neutrons required to activate this chain come from 22Ne( $\alpha,n$ ).

Metallicity

Figure 4.16 shows the yields (H-rich: left panel, H-rich + He-rich: right panel) of the 20 $M_{\odot}$ models with $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.4$ at $Z=10^{-5}$ (green pattern) and $Z=0$ (magenta). The two models are computed with the same physics. The [C/H], [N/H] and [O/H] ratios do not change by more than 0.5 dex from the $Z=10^{-5}$ the $Z=0$ model. The reason is that the transport by rotation of 12C and 16O from the convective He-burning core to the convective H-burning shell operates at a similar efficiency in the $Z=0$ model. In the H-rich ejecta (left panel), the elements from Ne to Si are much less abundant in the $Z=0$ model compared to the $Z=10^{-5}$ model. Considering also the He-rich ejecta raises considerably the abundances of these elements in both models. The exception is for the [Si/H] ratio in the $Z=0$ model, which stays several dex below the [Si/H] ratio of the $Z=10^{-5}$ model. The differences are mainly due to the fact that the H-burning shell of the $Z=0$ model is more active, which limits the growth of the convective He-burning core (at the middle of the core He-burning phase, the size of the convective He-cores are 3.9 $M_{\odot}$ and 2.7 $M_{\odot}$ in the $Z=10^{-5}$ and $Z=0$ models, respectively). The consequence is that less H-burning products (e.g. 14N) let in between the He-core and the H-shell are engulfed by the convective He-core of the $Z=0$ model. Globally, it has the effect of reducing the efficiency of the exchanges of material between the He-core and the H-shell. Finally, the nucleosynthesis is less rich and varied in the $Z=0$ model. Also, Si is barely affected in the models considered (see also Fig. 4.7) so that the [Si/H] ratio in the ejecta mostly reflects the initial [Si/H] ratio. In the $Z=0$ model, the initial Si abundance is zero so that [Si/H] $\sim$ $\log$ (Si/H) $\sim-\infty$ in the ejecta.

4.4 Comparison with CEMP-no stars

It is now discussed whether the abundances of observed metal-poor stars can be reproduced by the massive stellar models discussed previously. Particular attention is paid to the constraints provided by the 12C/13C ratio.

For the observations, I consider CEMP stars with [Fe/H] $<-3$ and [C/Fe] $>1.0$ . Recognized CEMP-r, -s and -r/s stars are excluded (according to the criteria of Table 2.2). I took into account the $\Delta$ [C/Fe] of Placco et al. (2014c) which allows to correct the effect of the first dredge-up of evolved stars and recover the initial C abundance. For the considered stars, $0<$ $\Delta$ [C/Fe] $<0.74$ . With this correction, 12 stars become CEMP and are then added to the sample. It gives the 69 stars of Table LABEL:tabcemp. Stars with $T_{\rm eff}\geq 5500$ K and $\log g\geq 3.25$ are classified as main-sequence stars and the other as giants stars 777With the exception of G77-61, with $T_{\rm eff}=4000$ K and $\log g=5.05$ that is considered as a main-sequence star, following Plez & Cohen (2005) and Beers et al. (2007)..

4.4.1 A global comparison

Let us first mention that $Z=0$ source star models may face more difficulties in reproducing the abundance patterns of CEMP-no stars than very low metallicity source star models: the 20 $M_{\odot}$ Pop III model in Fig. 4.16 either produces enough C, N, O but not enough Na, Mg, Al (left panel) or it produces enough Na, Mg, Al but then C, O and 12C/13C are overestimated (right panel). Also [Si/H] is underestimated by several dex.

Considering all the other source star models discussed in Sect. 4.3.3, we see that a global match can be found with the abundances of CEMP-no stars. Source star ejecta with various initial rotation rates, mass cuts and dilution factors allow to reproduce all or nearly all the range of CEMP-no star abundances. However, a global match does not mean that individual CEMP-no stars can be well reproduced. The next step is to compare source star models with individual CEMP-no stars. As it will be discussed thereafter (especially in Sect. 4.4.2), a more in-depth comparison reveals some difficulties for models to reproduce some of the abundances of individual CEMP-no stars.

Interestingly, we also note that the CNO pattern of the material ejected by the source star has generally either a $\wedge$ -shape (H-rich ejecta, Fig. 4.9) or a $\vee$ -shape (H-rich + He-rich ejecta, Fig. 4.10). It is nevertheless not always the case (e.g. Fig. 4.12). In Table LABEL:tabcemp, very few stars have C, N and O abundances available together, without upper limits. CS 29498-043 has C,N and O abundances available and it has a clear $\vee$ -shape. By contrast, HE 1327-2326 has a clear $\wedge$ -shape. Another example is the CNO pattern of HE 0107-5240, which has a different shape (it as much N as O). When considering the entire sample of Table LABEL:tabcemp, about 70 % is compatible with a $\wedge$ -shape for the CNO pattern. Similarly, about 70 % is compatible with a $\vee$ -shape. About the same fraction (70 %) of the sample is compatible with an almost flat CNO pattern. Detailed comparisons between source star models and CEMP stars are likely required to obtain more informations on the CEMP source stars (Sect. 4.5 and 4.6).

References. 1 - Placco et al. (2014a); 2 - Roederer et al. (2014a); 3 - Ito et al. (2013); 4 - Venn et al. (2004); 5 - Roederer et al. (2014b); 6 - Cayrel et al. (2004); 7 - Spite et al. (2006); 8 - Cohen et al. (2013); 9 - Spite et al. (2012); 10 - Sbordone et al. (2010); 11 - Bonifacio et al. (2009); 12 - Andrievsky et al. (2007); 13 - Andrievsky et al. (2010); 14 - Andrievsky et al. (2008); 15 - Sivarani et al. (2006); 16 - Beers et al. (2007); 17 - Plez & Cohen (2005); 18 - Hollek et al. (2011); 19 - Bessell et al. (2004); 20 - Christlieb et al. (2004); 21 - Hansen et al. (2015a); 22 - Hansen et al. (2014); 23 - Norris et al. (2013); 24 - Yong et al. (2013); 25 - Norris et al. (2012); 26 - Norris et al. (2007); 27 - Aoki et al. (2007); 28 - Barklem et al. (2005); 29 - Zhang et al. (2011); 30 - Frebel et al. (2007b); 31 - Ren et al. (2012); 32 - Frebel et al. (2008); 33 - Aoki et al. (2006); 34 - Cohen et al. (2006); 35 - Placco et al. (2014b); 36 - Li et al. (2015); 37 - Li et al. (2015); 38 - Aoki et al. (2013); 39 - Aoki et al. (2008); 40 - Bonifacio et al. (2015); 41 - Spite et al. (2013); 42 - Frebel & Norris (2015); 43 - Behara et al. (2010); 44 - Caffau et al. (2013); 45 - Jacobson et al. (2015); 46 - Keller et al. (2014)

Constraints from the 12C/13C ratio

The CEMP-no stars with a measured 12C/13C ratio have $3<$ 12C/13C $<35$ . Two stars are still dwarfs, with 12C/13C $\sim 6$ . As mentioned previously (Sect. 4.2), the 12C/13C ratio at the surface of an unevolved CEMP-no star is probably similar to the 12C/13C ratio in the cloud in which the star formed, hence similar to the 12C/13C ratio in the source star ejecta.

The 12C/13C ratios of the CEMP-no star sample are well reproduced by the H-rich ejecta of the source star models (Fig. 4.9). By contrast, they are largely overestimated by the H-rich + He-rich ejecta (Fig. 4.10, cf. also Choplin et al. 2016, Sect. 5.1, page C of this thesis). Of course one could imagine to dilute the H-rich + He-rich ejecta, having a high 12C/13C, with an ISM having a very low 12C/13C (as discussed in Sect. 3.3.4, here I take 12C/13C = 300 in the ISM but a lower value may also be chosen). The final mixture may present a low 12C/13C ratio, consistent with observations. In this case however, it just pushes back the problem: the need for a source producing a large amount of 13C in the early Universe remains and has to be explained by some mechanism.

It is worth mentioning here that Galactic evolution models predict that a standard population of very low metallicity massive source stars will lead to a 12C/13C ratio of $4500-31000$ in the (almost) primordial ISM (Chiappini et al. 2008). If instead, this population is dominated by massive fast rotators, Galactic evolution models predict $30<$ 12C/13C $<300$ . Rotation in massive stars is indeed a way to produce large amounts of 13C (e.g. Fig. 4.6). The fact that it exists CEMP-no stars (especially unevolved stars) with a 12C/13C ratio even lower that 30 suggests that a very special material is required to form them, maybe coming from the relatively external layers of one specific rotating massive source star.

As a remark, let us mention that the fact that there is no CEMP star with a 12C/13C ratio below the CNO-equilibrium value (which is about 4) suggests that the dominant source of 13C in the early Universe comes from CNO burning. If there was another important source of 13C, we should observe CEMP-no stars with lower 12C/13C ratios. Moreover if such stars exist, they should be observable since low 12C/13C ratios are easier to detect: if the ratio is low, 13C is abundant and then 13C lines are stronger. This last point also shows that it can exist a bias towards low 12C/13C. Some CEMP-no stars have a lower limit for 12C/13C (e.g. HE 1201-1512 and HE 1327-2326 with 12C/13C $>20$ and $>5$ respectively, Aoki et al. 2006; Norris et al. 2013). Future observations may reveal a population of stars with higher 12C/13C ratios.

Can the H-rich material of massive source stars explain the abundances of CEMP-no stars?

In the previous discussion and in Sect. 4.2, it was proposed that CEMP-no stars could have formed with only the H-rich material of the source star. However, if considering only the H-rich source star ejecta, several issues arise (see Fig. 4.9):

The ranges of Mg/H, Al/H and Si/H ratios are not covered by source star models (also N and Na to a smaller extent). 2. 2.

The predicted [Al/H] ratios are too high (also true if considering the H- + He-rich ejecta, Fig. 4.10). 3. 3.

Such an ejecta shows a clear CNO processed signature with a very characteristic CNO pattern ( $\wedge$ -shape), while some CEMP-no stars are not compatible with this pattern. 4. 4.

The most C-rich CEMP-no stars, with [C/H] $\gtrsim-1.5$ cannot be explained.

First, some scatter in the CEMP star abundances is probably induced by the fact that the abundance data is not homogeneous, together with the possible 3D/NLTE corrections on abundances (cf. Sect. 2.2.2 and 4.2). This could alleviate the issue 1.

Second, some nuclear reaction rates of the Ne-Na and Mg-Al chains are uncertain (cf. Sect. 4.2). Changing these rates will change the predicted Na/H, Mg/H, Al/H ratios but in a similar way for all the models, i.e. the predicted scatter will not change. I computed again the $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.4$ model with the nuclear rate of 27Al( $p,\gamma$ )28Si from Cyburt et al. (2010) instead of Iliadis et al. (2001). This is an extreme case, favoring Al destruction, since the rate of Cyburt et al. (2010) is the highest one below 100 MK. At $T=50$ MK, the Cyburt et al. (2010) rate is $\sim 100$ times larger than the Iliadis et al. (2001) rate. The orange dashed line in Fig. 4.9 shows that the [Al/H] ratio in the ejecta of the model with the Cyburt et al. (2010) decreases by $\sim 1$ dex compared to the standard case. We note that the [Si/H] is barely modified. Nuclear rate uncertainties can lead to significant differences in the predicted yields and make the [Al/H] consistent with the bulk of observed abundances. This helps with the issue 2.

The issues 3 and 4 can be solved if considering the H-rich + He-rich ejecta (Fig. 4.10), which gives much more carbon and reverses the CNO pattern. Some dilution with the ISM might provide abundance patterns able to reproduce the observations (right panel of Fig. 4.13). However, in this case, the predicted 12C/13C is too high. The difficulty here is to get a high enough C/N ratio together with a low 12C/13C ratio, as it is observed on many CEMP-no stars (Fig. 4.17). This issue is discussed in the next section.

4.4.2 The C/N $-$ 12C/13C puzzle

Standard source star models

In source star models, either both C/N and 12C/13C ratios are low (H-rich ejecta), or both ratios are high (H-rich + He-rich ejecta). The crosses in Fig. 4.17 show the ratios in the total wind of some source star models discussed in the previous section. The tracks show the variation of the ratios in the ejecta with $M_{\rm cut}$ let as a free parameter. A specific $M_{\rm cut}$ value gives one point in such a track. Here, for a given source star model, all possible mass cuts are considered: in Eq. 3.15, $M_{\rm cut}$ is varied between 0 and $M_{\rm fin}$ . It gives a collection of points, which can be seen as a line.

We see that whatever the source star ejecta considered, none can match the bulk of observed stars (the tracks are nevertheless consistent with some lower limit 12C/13C ratios). All models show a similar behavior. CNO processed material gives $\log$ (12C/13C) $\sim 0.6$ and [C/N] $\sim 2$ and He-processed material $\log$ (12C/13C) $\gg 1$ and [C/N] $\gg 1$ . A mix of CNO and He-processed material gives something in between, but not in the region where most of the CEMP-no stars lie.

Effect of the first dredge-up in CEMP-no stars

Some CEMP-no stars in Fig. 4.17 are giants (big grey circles) and have likely experienced the first dredge-up. This process can change the location of the stars in the C/N $-$ 12C/13C diagram. Below is investigated by how much and in which direction the first dredge-up can move a CEMP-no star in this diagram.

First, I started from a reference 0.8 $M_{\odot}$ model having the composition of the star CS 22958-042 at the Zero-Age Main-Sequence (ZAMS). CS 22958-042 is a subgiant with [Fe/H] $=-2.99$ , [C/Fe] $=2.15$ , [N/Fe] $=2.25$ and 12C/13C $=7$ (Roederer et al. 2014a). Then, 9 other 0.8 $M_{\odot}$ models were computed with different initial [C/N] and 12C/13C ratios. Table 4.3 gives the initial ratios of the 10 models. The standard model, having the composition of CS 22958-042, initially has $\log$ (12C/13C) $=0.85$ and [C/N] $=$ $-0.1$ .

The evolution is stopped after the first dredge-up. The thermohaline mixing is not considered. The surface $\log$ (12C/13C) and [C/N] ratios after the first dredge-up are reported in Table 4.3. The effect of the first dredge-up on the surface [C/N] and $\log$ (12C/13C) ratios of these models is also shown in Fig. 4.17 by the orange arrows. In all the cases, the surface abundance ratios are decreased. The decrease ranges from 0 to 0.63 dex. The lower the initial 12C/13C and C/N ratios, the smaller the effect of the dredge-up. This is because if starting with 12C/13C and C/N ratios already close to CN equilibrium in the stellar envelope, then, adding some material at CN equilibrium barely affects the ratios. On the opposite, if the initial 12C/13C and C/N ratios are far from equilibrium, adding a bit of CN-processed material in the envelope has a stronger impact on the ratios. These results suggest a rather modest effect of the first dredge-up, except for the CEMP stars that were formed from a material in which the C/N and 12C/13C ratios were very far from CN equilibrium (see the biggest orange arrow in Fig. 4.17).

Other mixing processes in CEMP-no stars

In Fig. 4.17, some observed evolved CEMP-no stars may also have experienced other mixing processes like thermohaline (cf. Sect. 2.4). As discussed, however, a significant fraction of CEMP-no stars may not have experienced too much mixing, except the most evolved stars (cf. Fig. 2.5). Also, it has to be noted that unevolved CEMP-no stars lie globally at similar positions than evolved CEMP-no stars in Fig. 4.17. If the internal mixing processes had a strong impact on the surface C/N and 12C/13C ratios, we should probably see distinct groups of CEMP-no stars: the bulk of evolved CEMP-no stars on the one hand, the bulk of unevolved CEMP-no stars on the other hand. The fact that it is not the case may finally indicate that the composition of the evolved CEMP-no stars shown in Fig. 4.17 reflects quite well the composition of the cloud in which they formed.

4.5 The late mixing process in the source star

A solution to the C/N $-$ 12C/13C puzzle is to introduce a late mixing process in the source star, occurring between the H- and He-burning shell, about 200 yr before the end of the evolution. Below I give more details on this process and discuss how it can naturally produce a material with a high C/N ratio and a low 12C/13C ratio, able to improve the fit between models and observations. In Sect. 4.8, I investigate whether other models available in the literature can provide a solution. This mixing process was investigated in Choplin et al. (2017b, page C of this thesis). The main points of the paper are summarized in this section.

4.5.1 General idea

Figure 4.18 shows the time it takes for the C/N, O/N and 12C/13C ratios to reach their CNO equilibrium value in a H-burning zone at $30<T<80$ MK. Results are obtained using the one-zone model described in Sect. 4.2. Equilibrium values are reached quicker when the temperature increases. Whatever the temperature, 12C/13C reaches equilibrium $\sim 10$ times faster than C/N, and C/N reaches equilibrium $100-1000$ times faster than O/N. In the H-burning shell of a complete stellar model, there is a gradient of temperature and the temperature $30\lesssim T\lesssim 80$ MK. The global equilibrium timescale of the shell cannot be deduced directly from Fig. 4.18. However, the relative difference between the different timescale stays the same.

Let us now assume that some 12C is injected in a single burning zone at $T=30$ MK which is at CNO equilibrium. The extra 12C disturbs the CNO equilibrium. Fig. 4.18 tells us that after 2000 yr, 12C/13C will have reached back its equilibrium value while C/N and O/N will not. It means that if the H-burning shell of the massive star is burning at 30 MK and some 12C is injected 2000 yr before the end of the evolution, then, at the pre-SN stage, the H-shell will have C/N above equilibrium and 12C/13C at equilibrium. The average temperature in the H-burning shell of a massive source star is about $40$ MK. Then, to obtain a partially processed CN material, with C/N above equilibrium and 12C/13C at equilibrium, some 12C has to be injected in the H-burning shell $\sim 100-200$ yr before the end of the evolution. At this time, the source star burns carbon in its core. For $20-60$ $M_{\odot}$ models, the core carbon burning stage lasts for $10-1000$ yr (grey area in Fig. 4.18).

4.5.2 Implementation in source star models

This mixing process was investigated for a grid of six models whose characteristics are given in Table 4.4. Small differences exist between the input parameters of these models and the models of the previous section. First, when $\log(T_{\rm eff})\geq 3.95$ , the mass-loss rates are from Kudritzki & Puls (2000), instead of Vink et al. (2001). Radiative winds are generally small at low metallicity so that no big impact is expected. Second, following the study on Al discussed in Sect. 4.2, the nuclear rates from the literature that minimize the production of Al are selected: Angulo et al. (1999) for 26Mg( $p,\gamma$ )27Al, Cyburt et al. (2010) for 27Al( $p,\gamma$ )28Si and 27Al( $p,\alpha$ )24Mg. Third, $f_{\rm energ}$ in the expression of $D_{\rm shear}$ (Eq. 3.10) was taken equal to 1 instead of 4.

First, the models were computed normally (without late mixing) until the end of the central silicon-burning phase. The computation is stepped when the mass fraction of 28Si in the core is less than $10^{-8}$ . For rotating models, the effects of rotation were taken into account until the end of the carbon burning phase. Last stages were computed without rotation. It saves a lot of computational time and leads to only very small differences in the abundance profiles since the duration of the last stages is short ( $\sim 1-300$ days, cf. Table 4.4) compared to the rotational mixing timescale. In a second step, I have computed again the end of the evolution for the six models while triggering the late mixing process $\sim$ 200 yr before the end of the evolution (Fig. 4.19 for a schematic view). For these models, the evolution was stopped at the end of core carbon burning. Last stages are very short and change only the composition of the most inner layers. It gives four categories of models: (1) no rotation, no late mixing, (2) no rotation, late mixing, (3) fast rotation, no late mixing and (4) fast rotation, late mixing.

To model the late mixing process in rotating models, the shear diffusion coefficient $D_{\rm shear}$ is multiplied by a factor of 100 in between the H- and He-shell. In non-rotating models, an artificial and constant diffusion coefficient $D_{\rm no~{}rot}=10^{9}\,\text{cm\,s}^{-1}$ is set in the mixing zone. This is a typical value of the diffusion coefficient found in rotating models including late mixing. Although modeled through the shear diffusion coefficient, it is not assumed that the physical origin of the late mixing process is linked to the shear. Its possible physical origin is discussed in Sect. 4.5.4.

4.5.3 Comparison with CEMP-no stars

When the late mixing process is included, additional 12C and 16O enter into the H-shell, boosting the CNO cycle and then releasing more energy. The H-shell becomes convective, extends in mass so that more He-burning products are engulfed. The fresh 12C starts to be transformed into 13C and 14N in the H-shell. However, the time remaining before the end of the evolution being short, the [C/N] equilibrium value of $\sim-2.3$ is not reached. The right panel of Fig. 4.20 shows the abundance profile of the rotating 20 $M_{\odot}$ model with late mixing, at the end of core carbon burning. We see that the convective H-shell contains a lot of CNO elements, and has X(C)/X(N) $>1$ while X(12C)/X(13C) is at equilibrium, around 4. This process builds a zone which is, at the end of evolution, partially processed by the CN cycle in the source star, where C/N is high and 12C/13C at equilibrium.

Fig. 4.21 shows the ejecta of the non-rotating (left panel) and rotating (right panel) 20, 32 and 60 $M_{\odot}$ models including the late mixing process. With increasing mass, the tracks in Fig. 4.21 are shifted to the left, away from observations. This is mainly due to the fact that higher-mass models have a higher temperature in the H-burning shell. This implies that the CN cycle operates faster. In this case, the injected 12C is transformed more rapidly into 14N. Then, the [C/N] ratio in the H-burning shell is closer to the equilibrium value ( $\sim-2$ ) at the end of evolution. It finally implies that the ejecta of higher-mass models cannot reach high [C/N] ratios together with low 12C/13C ratios. There are several reasons that may make the late mixing process more likely to occur in $\sim 20$ $M_{\odot}$ source stars than in $\sim 60$ $M_{\odot}$ source stars:

•

In a $60$ $M_{\odot}$ model, the late mixing process should occur very late in the evolution, so as to end up with a high C/N (see above). If it occurs too early, C/N has enough time to reach back equilibrium. It means that the time window for the late mixing to operate is shorter in a 60 $M_{\odot}$ model than in a $20$ $M_{\odot}$ model.

•

In more massive stars, the mixing process should be extremely strong so as to compensate for the short time available.

•

In more massive stars, the distance between the H- and He-burning shells is greater, so that the connection between the two shells might be less likely.

Overall, $\sim 20\,M_{\odot}$ source stars might be better candidates for the late mixing process, hence for reproducing the observations.

Fig. 4.21 shows that both the non-rotating and rotating 20 $M_{\odot}$ models can reproduce the bulk of observations. These two kind of models show however important differences regarding other elements. In fact, the late mixing process changes the distribution of chemical species in the source star (Fig. 4.20) but in the models presented here, it implies further nucleosynthesis almost only for the elements888This process may also form heavy elements through neutron captures, see Sect. 4.8. 12C, 13C and 14N. This is because the burning timescales for the other species considered in the network (e.g. O, Ne, Na, Mg, Al) are longer compared to the remaining time before the end of the evolution. For instance, there is little time for the Ne-Na cycle to operate and produce additional 23Na in models including late mixing. Instead, a progressive mixing, achieved by rotation during the core helium burning stage can form extra 23Na (Sect. 4.3.2 and Fig. 4.7). This is an important difference between non-rotating (little Na) and rotating models (high Na) including late mixing. Many CEMP-no stars are enriched in Na. It may suggest that, at least for a part of the CEMP-no star sample, two kind of mixing are needed: rotational mixing (for Na) and the late mixing process (for a high C/N with a low 12C/13C).

4.5.4 Physical origin

In the present work, the late mixing process is triggered artificially. It has to be noted that in some cases, similar events occur naturally. Indeed, various authors reported sudden ingestion events of H-burning material into the He-burning core or shell in low or zero metallicity massive stellar models (with or without rotation, Hirschi 2007; Ekström et al. 2008; Heger & Woosley 2010; Limongi & Chieffi 2012, see also Sect. 4.8). Although observed in some stellar models, the occurrence conditions and physical process(es) responsible for such events remain unknown. No specific behaviour is observed with any stellar parameter.

The treatment of the convection in stellar evolution codes may impact the shell/shell interaction or the core/shell interaction and thus the occurrence of the late mixing event. In genec, the convective boundaries are determined using the Schwarzschild criterion. The boundaries of the convective zones are sharp (step functions). During the main sequence and core He-burning phase, the convective core is extended using a penetrative overshoot. The overshoot is applied neither for the more advanced phases of stellar evolution, nor for the intermediate convective shells. This prescription probably does not capture the whole physics of convection (Arnett et al. 2015). Multi-dimension hydrodynamics numerical simulations of convection in deep stellar interior show that the chemical composition of each side of the convective boundary makes a smooth transition and is not a step function. (Herwig et al. 2006; Meakin & Arnett 2007; Arnett & Meakin 2011; Cristini et al. 2017). Fig. 4.22 shows a comparison between 1D code (genec) and 3D simulations, for the carbon burning shell. We see that in 3D, the carbon shell extends further in mass compared to 1D models. Multi-D simulations of H/He burning-zones during earlier stages (e.g. core He-burning stage) do not exist since they are computationally too expansive, mainly because the burning timescales are long.

It might be that improving the way convection is treated in classical 1D codes to follow more closely the behavior observed in multi-dimensional simulations strengthens the exchanges between the H- and He-burning shells. This could naturally induce the creation of the late mixing zone. If so, the late mixing invoked in this work would result from an overly poor description of the convective boundaries in 1D stellar evolution models.

4.6 A systematic study of the CEMP-no source star population

I now investigate what is the best source star model for each individual CEMP-no star. All the 69 CEMP stars of Table LABEL:tabcemp are considered. To fit the abundance pattern of each CEMP star, I consider the 12 source star models of Table 4.4 and vary the dilution factor and mass cut for each models. The final structure of the source star is taken at the end of the core carbon burning stage for all the 12 models since ultimate stages were not computed for the 6 models including late mixing. Four dilution factors are considered : $D=0$ , 10, 100 and 1000. It gives 12 $\times$ 4 = 48 combinations. For each of these 48 cases, the mass cut of the given source star model is varied between its final mass (i.e. only winds) and $M_{\rm rem}$ (cf. Table 4.4). The mass cut is chosen so as to minimize the sum of the residuals (in absolute value):

[TABLE]

$\textrm{A}^{\rm obs}_{i}$ are the [C/H], [N/H], [O/H], [Na/H], [Mg/H] and $\log(^{12}$ C/13C) ratios of the CEMP-no star to fit999Table LABEL:tabcemp reports the [X/Fe] ratios. For the present analysis, I used the [X/H] ratios (taken from the SAGA database).. $\textrm{A}^{\rm mod}_{i}$ are the same ratios but in the source star ejecta, after the eventual dilution with ISM. $\xi$ is then evaluated using 1 to 6 abundance ratios. When no abundance or just an upper limit is available for a CEMP star, the abundance is not considered to estimate $\xi$ . For rotating and non-rotating source star models, the number of possible mass cuts is about 1000 and 500 respectively (it depends on the resolution, which is higher in rotating models). In total, there are about 35000 possible ejecta compositions.

For each of the 48 cases, the ejecta composition with the mass cut that minimizes $\xi$ is saved. Among these 48 ejecta, the 3 best ones (the 3 lowest $\xi$ ), are shown in Fig. 4.23 for two CEMP stars. This procedure was applied for the 69 CEMP stars (all the plots are shown in Appendix B). In this sample, I selected the cases where $\xi$ was estimated with at least 3 abundances. Fits using only 1 or 2 abundances can lead to a high degree of degeneracy (many source star models provide a good solution). After this selection, it gives a subsample of 50 CEMP-no stars (19 stars excluded). In this new sample, the CEMP-no stars for which no satisfactory fit was found were excluded: fits with $\xi\geq 1.5$ are excluded. It finally gives 43 stars. The parameters of the best source star models for these 43 CEMP-no stars are reported in Table 4.5.

Figures 4.24, 4.25 and 4.26 show the results. 20 $M_{\odot}$ source stars are preferred in 70 % of the cases, before the 60 $M_{\odot}$ (23 %) and 32 $M_{\odot}$ (7 %) source stars. Rotation gives the best fit for 74 % of the sample. The late mixing process appears in 72 % of the best models. $D\leq 10$ in 79 % of the cases. Figure 4.25 shows that rotation + late mixing gives the best fit in 58 % of the cases. The histogram of Fig. 4.26 shows the distribution of the sum $f_{\rm H}+f_{\rm He}+f_{\rm CO}$ (i.e. the sum of the ejected fraction of the H-rich envelope, He-shell and CO-core, cf. Table 4.5) for the best source star models. This sum varies between 0 (no material ejected from the source star) and 3 (all the material is ejected). A value of 1.5, for instance, means that 100 % of the H-rich envelope plus 50 % of the He-shell of the source star was ejected. The sum $f_{\rm H}+f_{\rm He}+f_{\rm CO}$ can also be seen as a mass cut value normalized to 3. Figure 4.26 shows that in most of the cases (about 70 %), $f_{\rm H}+f_{\rm He}+f_{\rm CO}$ is about 1 or just above 1. It means that the CEMP-no stars mostly formed with the H-rich envelope of the source star plus possibly a small part of the He-shell. In other other words, a mass cut located around the bottom of the H-rich region of the source star is preferred. It corresponds to $M_{\rm cut}=M_{\alpha}$ . In $15-20$ % of the cases, $f_{\rm H}+f_{\rm He}+f_{\rm CO}\geq 2$ . In this case, it suggests a deeper mass cut in the source star, located around the top or in the CO core.

The results suggest that the CEMP-no source stars are preferentially rotating $20$ $M_{\odot}$ models experiencing the late mixing process. In most cases, only the outer layer of the source star should be expelled. Also, the results suggest a modest dilution with ISM. In Choplin et al. (2017b), we investigated the individual abundances of only six CEMP-no stars in details but reached similar conclusions.

It is worth noting that the late mixing process, developed to explain the abundances of a small sample of CEMP-no stars in the C/N vs. 12C/13C diagram (cf. Sect. 4.5), is still favored when considering a larger sample of CEMP stars that often do not have a measured 12C/13C ratio and/or the N abundance available. One reason is that standard models with or without rotation tend to give either much more N than C or much more C than N while numerous CEMP-no stars have roughly as much C as N. The late mixing process allows to get as much C as N in the ejecta. Also to note is that, even if both non-rotating and rotating models including late mixing can provide a solution in the C/N vs. 12C/13C diagram (cf. Fig. 4.21), rotating source stars models are preferred. One reason is that rotation can provide the additional Na and Mg needed to reproduce some CEMP-no stars while the late mixing process cannot.

Possible improvements

This analysis can be improved in different ways. Only the best source star models were considered here. The second best models could also be considered with smaller weights than the best models. It can also be done for the third best models, etc… This would allow to also include the good (but not best) models. It may increase the statistics of the results. An other improvement could be to attribute weights to the different abundances used to perform the fit. For instance, the abundances that are strongly affected by NLTE/3D effects should have a lower weight. The abundances that are the most affected by nuclear rate uncertainties in stellar models should also have a lower weight.

In the future, it would be interesting to do the same analysis while considering larger grids of source star models with more initial masses and rotation rates, and with different initial metallicities. This could allow to derive a initial mass or velocity function for the early generations of massive stars. However, the sample of CEMP-no stars may still be quite small. Larger (and homogeneous) samples are required so as to obtain meaningful statistic results.

Finally, let us mention that among the 50 stars fitted (69 in total but 19 were excluded because of a too small abundance data) 7 stars could not be fitted correctly.

•

3 out of these 7 stars (HE 0107-5240, HE 0557-4840 and SDSS J131326.89) have very low [Na/H] and [Mg/H] ratios, at least 1 dex below the ISM values considered here. No solution can give such low values. Zero metallicity source star models may provide a better solution. As discussed at the end of Sect. 4.3.3, zero metallicity source stars may produce as much CNO as low metallicity source stars but less Na, Mg, Al and Si. This remains to be tested.

•

3 other stars (HE 1506-0113, HE 1012-1540 and HE 2139-5432) have high [Na/H] together with low [N/H] ratios. This is difficult to explain with the present source star models, where N and Na are rather well correlated. In particular, both are produced in rotating models.

•

The last star (CS 29498-043) has a CNO pattern very typical of an He-burning material but a very low 12C/13C ratio, typical of an H-burning material (see Fig. 4.27). Although the models with extra mixing can approach the solution closer than standard models, no satisfactory fit can be found.

Overall, these seven stars may require different kinds of progenitors. In any case, these stars will require further attention. This is among the next steps of this analysis.

4.7 Are CEMP-no stars helium-rich?

A signature of the operation of the CNO cycle is an enrichment in helium. Thus, the CEMP-no stars that formed with almost only the envelope of massive source stars (i.e. $D\simeq 0$ ) should be He-rich (Meynet et al. 2010). If instead the source star ejecta was significantly mixed with ISM, the mass fraction of helium $X$ (He) in the CEMP-no star should be around the primordial value of 0.248 (Cyburt et al. 2003).

Table 4.5 reports the predicted helium mass fraction in the ejecta (after dilution) of the best source star models. It shows for instance that the star CS 22960-053 should have formed with 0.39 of helium in mass fraction. Fig. 4.28 shows the distribution of helium mass fractions. While $\sim 60$ % of the CEMP star sample is predicted to have formed with rather normal helium mass fractions ( $X$ (He) $\leq 0.3$ ), about 40 % should have formed with $X$ (He) $>0.3$ . I discuss below what are the effects on the evolution of CEMP stars if changing the initial He. The specific case of the He-rich candidate CS 22949-037, with $X$ (He) = 0.38, is then investigated.

Low-mass metal-poor models enriched in helium

Chantereau et al. (2015) have investigated the evolution of $0.3-1$ $M_{\odot}$ stars at [Fe/H] $=-1.75$ with an initial He mass fraction $Y_{\rm ini}$ between 0.248 and 0.8. As $Y_{\rm ini}$ increases, the opacity in the stellar interior is reduced, making the star more compact. This shifts the evolutionary tracks towards higher $T_{\rm eff}$ . The higher compactness of the star makes the central temperature higher, increasing the rate at which hydrogen is burnt. This, together with the fact that there is less hydrogen fuel in helium rich stars, lead to shorter main sequence lifetimes for the helium rich models. Their 0.8 $M_{\odot}$ models with $Y_{\rm ini}=0.248$ (standard), $0.4$ and $0.8$ spend 12.9, 4.62 and 0.16 Gyr on the main sequence, respectively.

To investigate the specific case of the CEMP-no star CS 22949-037, I computed non-rotating 0.5, 0.6, 0.7, 0.8 and 0.9 $M_{\odot}$ stellar models starting with the chemical composition of CS 22949-037. For each mass, different initial helium mass fractions are tested: 0.25, 0.3, 0.4 and 0.5. What is added to the initial helium mass fraction is removed from the initial hydrogen mass fraction. The OPAL tool was used to compute new opacity tables accordingly to the particular composition of CS 22949-037. For the other input parameters, I followed Ekström et al. (2012).

Fig. 4.29 shows the tracks of these models. The observations of CS 22949-037 are better reproduced by the tracks having $Y_{\rm ini}$ $=0.4$ and $0.5$ . This is consistent with the analysis of Sect. 4.6 which predict $Y_{\rm ini}=0.38$ for CS 22949-037. However, because of uncertainties on both the modeling and observational sides, it is difficult to make meaningful comparisons between the observations and the tracks of Fig. 4.29.

Considerations on the age of CS 22949-037 can give additional hints. The color of the track shows the age of the model. To match the observables, the tracks of Fig. 4.29 have to reach the $\log g$ and $T_{\rm eff}$ of CS 22949-037 at the age of CS 22949-037. For instance, while the 0.9 $M_{\odot}$ model with $Y_{\rm ini}=0.4$ seems a good candidate, it reaches the $\log g$ and $T_{\rm eff}$ of CS 22949-037 after only $\sim 4$ Gyr. It is unlikely that CS 22949-037 is only 4 Gyr old. On the other hand, the 0.5 $M_{\odot}$ model (still with $Y_{\rm ini}=0.4$ ) is not a solution since it would still be unevolved today, with a much higher $\log g$ than CS 22949-037. We can see that if CS 22949-037 has $Y_{\rm ini}=0.4$ , it should be between 0.6 and 0.7 $M_{\odot}$ .

We see here that the scenario investigated in this work to explain CEMP-no stars predicts that some of the CEMP-no stars (the ones that are He-rich) will have rather small masses, due to their He-richness. Both the determination of the helium abundance and the mass of the CEMP-no stars may provide further clues on their origin.

Measuring the helium abundance and the mass of CEMP-no stars

Helium is challenging to detect and direct measurements are rare. One possibility is to focus on the HeI line at $1.08$ $\mu$ m that forms in the upper chromosphere of cool stars. In doing so, Pasquini et al. (2011) managed to measure the difference in helium abundance for two giants stars ([Fe/H] $=-$ 1.22 and $-1.08$ ) in the globular cluster NGC 2808. With their chromospheric model, they found a difference of 0.17 in helium mass fraction, meaning that if one of the two star has a solar He abundance, the other would have $Y\sim 0.42$ . Also, Dupree & Avrett (2013) reported an helium abundance of $Y<0.22$ and $0.39<Y<0.44$ in two other giant stars ([Fe/H] $=-1.86$ and $-1.79$ ) belonging to the globular cluster $\omega$ Centauri. In CEMP-no stars and generally in very iron-poor stars, no helium measurements has been performed yet.

Let us mention that asteroseismology may provide the mass of giants CEMP-no stars. The asteroseismic information (hence the mass) of cool giant stars with $1.9<\log~{}g<3.2$ may be obtained with the Kepler K2 mission (e.g. Stello et al. 2015). Another way to have a direct estimation of the mass is if the CEMP-no star is in an eclipsing binary system: since the inclination of an eclipsing system is known, masses of the two stars can be determined from the Kepler’s laws. Tracks of stellar models computed with the right masses and with various helium abundances may allow to get an estimation of the helium abundance of these observed stars.

Proxies for the helium abundance

Some abundances of other elements may give a proxy for the helium abundance. A high helium abundance requires a small dilution factor otherwise the helium abundance goes back towards the ISM value of $\sim 0.25$ . A small dilution factor might be related to a low Li abundance (Sect. 4.3.3, paragraph about dilution), meaning that He-rich CEMP stars could also be Li-poor (caution is required since Li is a fragile element that can be heavily affected by various processes in the CEMP star itself). Interestingly, the He-rich candidate CS 22949-037 has a very low Li abundance (A(Li) $<0.13$ ). Two other He-rich candidates, CS 22960-053 ( $X$ (He) $=0.39$ ) and HE 2331-7155 ( $X$ (He) $=0.39$ ), have A(Li) $<0.55$ and A(Li) $<0.37$ , respectively. He-rich candidates are nevertheless not always Li-poor (e.g. CS 22960-053 with a predicted helium abundance of $X$ (He) $=0.42$ and a Li abundance, deduced from observations, of A(Li) $=1.71$ ).

It is also worth noting that the He-rich CEMP stars should probably not be searched among the CEMP stars having a $\vee$ -shape CNO pattern (cf. Sect. 4.4.1). It may be surprising since it is a pattern characteristic of a material processed by He-burning, hence potentially He-rich. However, when a CEMP star is predicted to be formed with the He-processed material of the source star, a high dilution factor is generally also predicted (often $D=1000$ , see Table 4.5) so that the final helium abundance (the one of the CEMP) is close to the ISM value of 0.25. Instead, it is predicted here that many He-rich CEMP stars should have a $\wedge$ -shape CNO pattern. This pattern is characteristic of an ejecta processed by H-burning. Such an ejecta is also enriched in helium (provided the dilution with ISM is small).

4.8 Other CEMP-no source star models

4.8.1 An energetic H-ingestion event in the source star

Let us first mention the recent work of Clarkson et al. (2018), that investigated the origin of the 3 most iron-poor stars with a non-rotating 45 $M_{\odot}$ source star model experiencing an energetic H-ingestion event during shell He burning. It is interesting in the frame of the present work since the ingestion process they consider is similar to the late mixing process described in Sect. 4.5. In their work, nucleosynthesis was calculated in post-processing, using a one-zone model. They found that after the H-ingestion event, neutron densities of $10^{-13}$ cm*-3* are reached (typical of the i-process), leading to neutron captures on light seeds. These neutron captures allow the synthesis of small amounts of heavier elements like Ca (not much heavier elements than Ca are synthesized). Globally they found a reasonable agreement for 2 out of the 3 iron-poor stars considered. One difficulty is that neutron captures in the source star model do not produce enough Fe so that an additional enrichment process is required. Also, one of the star they reproduce (HE 1327-2326) has [Sr/Fe] $=1.08$ . It is not mentioned if their models can account for it. The origin of Sr in HE 1327-2326 is investigated in the Sect. 5.4.2 of this work.

4.8.2 Other source star models in the C/N $-$ 12C/13C diagram

It is now investigated whether various massive source star models from different authors can provide a solution in the C/N $-$ 12C/13C diagram. Low or zero metallicity massive star models with available yields are considered. Some intermediate mass models are also included (see the legend of Fig. 4.30 for the complete list of models). In the non-rotating $10-100$ $M_{\odot}$ Pop III models of Heger & Woosley (2010), explosive nucleosynthesis is calculated and various assumptions for the mixing (in the sense of the mixing & fallback process of Umeda & Nomoto 2002) and the explosion energy are considered. Explosive nucleosynthesis is also calculated in the non-rotating $13-80$ Pop III stars of Limongi & Chieffi (2012) .

The composition of the ejecta of all the considered models is shown in Fig. 4.30. The observations lie in a very small zone (black frame) compared to the region occupied by the source star models. Worth to remind is that some CEMP-no stars have an upper limit for N and/or a lower limit for 12C/13C. It means that it might exist an unseen population of stars with higher 12C/13C and C/N ratios. For what regards the observations without upper/lower limits, only a small fraction of the source star models could possibly account for them.

Fig. 4.31 shows a zoom in the region where observations lie. Models of Limongi & Chieffi (2012) consider standard core collapse supernovae, with $E_{51}\sim 1$ and deep mass cuts. As they say (see also Fig. 4.30 and 4.31), this assumption likely cannot account for the majority of the most metal-poor stars. It is similar for the models of Ekström et al. (2008) where a deep mass cut is considered, following the relation of Maeder (1992). Higher mass cut values (closer to the stellar surface) in the models of Limongi & Chieffi (2012) and Ekström et al. (2008) may improve the fit between models and observations. AGB models may account for some observations but there are generally away from the majority of CEMP-no stars. Models approaching the most the bulk of observed stars are (1) some non-rotating $50-100$ $M_{\odot}$ Pop III models from Heger & Woosley (2010), represented by big blue circles, and (2) fast-rotating 40 and 85 $M_{\odot}$ models with $Z=10^{-8}$ from Hirschi (2007).

A fast rotating massive source star with extreme mass loss

Let us first summarize the peculiar evolution of the fast rotating 85 $M_{\odot}$ model of Hirschi (2007), that leads to [C/N] $\simeq 0$ and $\log$ (12C/13C) $\simeq 1.1$ in the ejecta (big red star in Fig. 4.31). From the beginning of the core helium burning stage, 12C and 16O diffuse progressively to the radiative H-shell. At the middle of the core helium burning phase, the helium convective core encroaches the H-shell so that the CNO cycle is suddenly boosted in the H-shell and a copious amount of 14N and 13C is quickly formed. The energy released makes the H-shell convective. This CNO-rich convective zone quickly reaches the stellar surface so that the surface metallicity is enhanced and dramatic mass loss occurs, removing about 60 $M_{\odot}$ from the star. The material ejected is only partially processed by the CNO cycle because the convective zone extends very quickly in cold regions where the CNO cycle operates slowly or does not operate at all. In addition, the strong mass loss episode occurs also quickly after the encroaching of the H-shell, saving definitely the material from further processing. From the instant of the encroaching of the H-shell to the instant where strong mass loss stops, only $\sim 0.03$ Myr have past. Finally, the model (which is now about 25 $M_{\odot}$ ) finishes to burn helium in its core (and then subsequent burning stages occur normally). The big red star in Fig. 4.31 shows the chemical composition in the wind of this model, which is indeed partially CNO processed.

H/He interaction in non-rotating massive source stars

Some $50-100$ $M_{\odot}$ models of Heger & Woosley (2010, blue circles) experience a similar encroaching (cf. previous paragraph) of the He-core with the H-shell, as they mention in their paper. Also, as they note, in some models, the encroaching occurs during the core carbon burning stage, between the He- and H-burning shells (like for the late mixing process, cf. Sect. 4.5). In both cases, it produces a lot of 13C and 14N. Mass loss was taken equal to zero in their models so that no material is ejected through winds. However, some material is likely saved in cold regions from further CNO processing until the end of the source star evolution. It leads to a partially processed CNO material in the ejecta as shown by some of the blue points in Fig. 4.31 that approach the bulk of observed CEMP-no stars.

A strong H/He interaction: a characteristic shared by the best source star models?

All the models able to fit the observations in the [C/N] $-$ 12C/13C diagram (including the models of this work discussed in Sect. 4.5) likely share a common feature: a strong interaction between the H- and He-region occurred in the source star, boosting the CNO cycle, but right after, the material was saved from further CNO processing (either by being ejected quickly, or by being saved in cold regions of the source star until a supernova expels these layers). The fact that this interaction occurs also in non-rotating models (e.g. Heger & Woosley 2010) may indicate that the origin of the phenomena is not entirely due to rotation. Rotation may facilitate such interactions. As discussed in Sect. 4.5.4, the main ingredient might be convection. Convection constitutes a major uncertainty that should be better constrained in the future thanks to multi-D simulations.

This said, the present work suggests that this strong interaction between the H- and He-regions is required but not sufficient to explain the CEMP-no stars. The special nucleosynthesis induced by the progressive rotational mixing at work in the source star also appears to be needed to account for the abundances of CEMP-no stars (e.g. Sect. 4.6).

The mass of the source stars

Models of Hirschi (2007) and Heger & Woosley (2010) in Fig. 4.31 suggest that the CEMP-no source stars could have initial masses of $50-100$ $M_{\odot}$ while this work suggest lower masses, about 20 $M_{\odot}$ (e.g. Fig. 4.24). Heger & Woosley (2010) investigated the origin of the CEMP stars HE 0107-5240 and HE 1327-2326 with their Pop III massive models. In both cases, the best fits are given by their $10.5-25$ $M_{\odot}$ source star models. Similarly to Umeda & Nomoto (2003), an artificial mixing episode is included is their models at the time of the supernova in order to mix a little bit of iron in upper stellar layers. The iron is then expelled and the little iron content of HE 0107-5240 and HE 1327-2326 can be reproduced. Placco et al. (2016) have used the models of Heger & Woosley (2010) to investigate the origin of 12 stars with [Fe/H] $<-4$ . They found that the best fits are given by $12.6-41$ $M_{\odot}$ models (in both studies, the 12C/13C ratio is not considered). Also, in these works, comparisons are made through the [X/H] ratios but no dilution with primordial ISM was considered. It likely means that the yields of the source stars models considered should be seen as upper limits since any dilution with primordial ISM will decrease the [X/H] ratios. Some caution is therefore required.

From Fig. 4.30 and 4.31, we see that the $10-40$ $M_{\odot}$ of Heger & Woosley (2010) are not reproducing the bulk of observations. Fig. 4.31 rather suggests that their models with $M>40$ $M_{\odot}$ may be better source stars. In the present section, since the comparison is made using only few abundances (C and N), it is not possible to conclude further. It suggests that tensions probably exist and that the preferred masses of the CEMP-no source stars may require further investigations.

4.9 Summary

This chapter has investigated the origin of the CEMP stars with [Fe/H] $<-3$ and not significantly enriched in s- and/or r-elements (CEMP-no stars). The main results are summarized below.

The high abundance scatter (especially for C, N, O, Na, Mg and Al) of these stars was suggested to originate from a material ejected by previous massive source stars that experienced various degree of rotational mixing. A part of the CEMP-no star sample is thought to have formed mainly with the H-burning shell of the massive source star. During the core He-burning phase of rotating source stars, He-burning products are transported to the H-burning shell by the operation of the rotational mixing. Once into the H-shell, these products are further processed by H-burning and transported back to the He-burning core, etc. I developed a one-zone nucleosynthesis model that mimics the H-burning shell of a rotating massive star. The effect of rotation was modeled by progressively injecting He-burning products (12C, 16O, 22Ne and 26Mg) in the burning zone. The ranges of abundances of the considered CEMP-no stars were found to be overall well reproduced by a material processed by H-burning at a temperature and density characteristic of $20-60$ $M_{\odot}$ source stars. To reproduce the observations, this material should be enriched, while burning, in 12C, 16O and occasionally 22Ne. This suggests that the CEMP-no source stars experienced mid to strong rotational mixing.

Source stars models with various initial masses, rotation rates and metallicities were computed. As the result of the rotation induced mixing during the core He-burning phase, the yields of elements from C to Al scale with initial rotation. In the fastest rotating model, the [X/H] ratios in the ejecta can be boosted by $\sim 2$ to $\sim 5$ dex compared to the non-rotating model. The mass cut and the dilution of the source star ejecta with ISM are important and weakly constrained parameters, that strongly affect the source star yields. Overall, a global match between the abundances of CEMP-no stars and very low metallicity 20 $M_{\odot}$ source star models with various initial rotation rates can be found. The low 12C/13C ratio (especially on unevolved CEMP-no stars) requires that no or little material processed by He-burning was expelled from the source star. In this case however, [C/N] $\sim-2$ , which does not account for the bulk of CEMP-no stars, that generally have higher [C/N] ratios. The source star ejecta either have low 12C/13C ratios together with low [C/N] ratios or high 12C/13C ratios together with high [C/N] ratios. It cannot fit the bulk of CEMP-no stars.

A solution to improve the fit is to include a late mixing process in the massive source star, operating in between the H-burning and the He-burning shell, about 200 yr before the end of the source star evolution. It may occur preferentially in $\sim 20$ $M_{\odot}$ source stars (both rotating and non-rotating). This additional process was studied by computing new source star models with initial masses of 20, 32 and 60 $M_{\odot}$ , without and with fast rotation, without and with the late mixing process (12 models). Using the yields of these 12 source star models, an automatic abundance fitting procedure was applied to the CEMP-no stars with [Fe/H] $<-3$ . I found that the best CEMP-no source stars are preferentially rotating 20 $M_{\odot}$ models that experienced the late mixing process, that ejected the layers above or just below the interface between the H-rich and He-rich region and whose ejecta underwent a modest dilution with the ISM.

Finally, to avoid confusion, I recall the three different kinds of mixing that may arise in the source star:

•

The mixing induced by rotation that occurs progressively and everywhere, during the entire life of the source star.

•

The late mixing process (Sect. 4.5) arising between the H-burning shell and He-burning shell, shortly before the end of the evolution101010It may also occur earlier in the evolution, between the H-burning shell and He-burning core, cf. Sect. 4.8..

•

The mixing in the sense of Umeda & Nomoto (2002) that occurs between two limiting shells, at the time of the supernova.

Chapter 5 The s-process in CEMP source stars

The previous chapter focused on light elements, from C to Si. These elements are of particular interest for studying the origin of the most iron poor stars (with [Fe/H] $<-3$ ) that are mostly CEMP-no stars. The reason is that these stars are often strongly enriched in such elements while, by definition, they are generally little enriched in heavier elements.

Many CEMP stars show overabundances in s-elements, especially at higher metallicities ( $-3\lesssim$ [Fe/H] $\lesssim-2$ ), but also sometimes at very low metallicity (e.g. HE 1327-2326 with [Fe/H] $<-5$ and [Sr/Fe] $=1.08$ ). The weak s-process is expected to occur in massive stars (provided the metallicity is not zero). As mentioned in Sect. 3.1.2 (also Fig. 4.1), the effect of rotation in massive stars can alter the production of s-elements. At very low/zero metallicity, the amount of seed (especially iron) is very low so that little s-elements can be produced. At higher metallicities, there are more seeds, hence possibly more s-elements.

The main purpose of this chapter is to extend the study to heavier elements that can be formed in the source stars through the s-process. The s-process is studied in a new grid of massive source stars at [Fe/H] $\sim-2$ together within lower metallicity source star models. Then, I investigate whether the nucleosynthetic signatures of these massive stars can be recognized in observed metal-poor stars. A very recent paper (in Sect. 5.2) and a letter (in Sect. 5.3) are directly included in this chapter. Additional results and discussions are included, particularly in Sect. 5.4.

5.1 The weak s-process in a box

Before investigating complete stellar models, the s-process in a single burning zone is discussed. Using a similar code as in Sect. 4.2 but that now mimics the He-burning core of massive stars (this is mostly where the s-process operates, cf. Sect. 3.1.2), the s-process in massive stars can be studied qualitatively. The single burning zone considered burns at $T=300$ MK and $\rho=500$ g cm*-3*, as characteristic values of the He-burning core of massive stars. The initial mass fractions in the zone are $\sim 0.4$ for 4He, $\sim 0.3$ for 16O, $\sim 0.3$ for 12C and $10^{-7}$ for 56Fe (in mass fraction). The initial mass fraction of 22Ne is varied from $10^{-4}$ to 0.05. The calculation is stopped when all the 4He is burnt. The final chemical patterns in the burning zone are shown in Fig. 5.1.

When increasing the initial 22Ne, heavier s-elements are produced at the expense of lighter s-elements. If little 22Ne is available, the neutron flux is small and only light s-elements are produced. When the initial 22Ne mass fraction is 0.05, the pattern becomes flatter. It shows the effect of changing the source (22Ne) over seed (56Fe) ratio. If this ratio increases (provided some reasonable amount of seed is present) the hs (heavy s-elements) over ls (light s-elements) ratio increases.

Fig. 5.2 illustrates the poisoning effect of 16O by changing the initial 16O mass fraction. For higher initial 16O mass fractions, the production of s-elements is reduced. This is because if 16O is more abundant, the 16O( $n,\gamma$ )17O( $\alpha,\gamma$ )21Ne chain is boosted, so that less neutrons are available for heavy elements.

5.2 A new grid of massive stars with rotation and s-process

Grids of massive stellar models including rotation and full s-process network are needed in order to investigate the role of such stars in the chemical enrichment of the Universe. To date, only Frischknecht et al. (2016) and very recently Limongi & Chieffi (2018) have provided such grids. An important part of my work was to compute a new grid of massive rotating star with full s-process, so as to extend the study of Frischknecht et al. (2016). The final goal being to gain knowledge on the nature of such massive stars by comparing their yields to the abundances of observed low-mass metal-poor stars enriched in s-elements.

In Choplin et al. (2018) we computed a new grid of massive stars with initial masses between 10 and 150 $M_{\odot}$ , at a metallicity $Z=0.001$ in mass fraction (corresponding to [Fe/H] $=-1.8$ ). The models were computed either without rotation or with $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.4$ . We considered only one metallicity but significantly extended the range of mass compared to the study of Frischknecht et al. (2016), that focused on $15-40$ $M_{\odot}$ models. We also investigated the impact of a faster initial rotation and a different 17O( $\alpha,\gamma$ )21Ne reaction rate. Most of the physical ingredients of this grid are the same than for the models discussed previously. The main change is the size of the nuclear network that now comprises 737 species, from 1H to 212Po instead of 31 species (cf. Sect 3.3.3).

The paper describing the models is directly included in the thesis (in the present section). It was very recently accepted in A&A and I have therefore almost no discussion to add yet. Before the paper itself, I discuss several aspects that were not published: several additional physical ingredients and some obstacles I had to overcome. In Appendix A.5, additional parameters, allowing to quantify the efficiency of the s-process, are defined and tabulated for the new grid of models. The table was not published in the paper but it may be useful to have these quantities for future comparisons with other models.

5.2.1 Nuclear network and reaction rates

As shown in Table 2 of the paper below, 8 important nuclear reaction rates were updated compared to the study of Frischknecht et al. (2016). Originally, the reaction rate format in stellar evolution codes is the following: one table for each reaction rate with two columns, one for the temperature, one for the associated rate. Then, interpolations are done in these tables to evaluate the rates at the desired temperatures. With large networks, it is convenient to use analytical reaction rates such as in the reaclib format (Cyburt et al. 2010) in order to save computational time. Such a format allows to express a reaction rate with $n$ sets of 7 parameters $a_{0},..,a_{6}$ . For 2-body reactions, it yields

[TABLE]

with $T_{9}=10^{-9}~{}T$ and $N_{A}$ the Avogadro number. For 1- and 3-body reactions, the left side of Eq. 5.1 is respectively equal to $\langle\sigma v\rangle N_{A}^{2}$ and $\lambda$ , where $\lambda$ represents the photodisintegration or $\beta$ -decay rate. If just the standard tabulated rate exists, one has to find the $a$ parameters that allow to fit correctly the rate. A leastsquare method is used to estimate these parameters from a temperature-rate table. $n>1$ is often required to reach a reasonable accuracy. Finding the $a$ parameters can sometime be challenging, mainly because of the large range of temperature to be covered (several orders of magnitude, it depends on the reactions). Once the $a$ parameters are determined for the forward reaction, the $a_{rev}$ parameters for the reverse reaction can be easily calculated (Rauscher & Thielemann 2000).

Best et al. (2013) provided, in the tabular form, new rate measurements for the 17O( $\alpha,n$ )20Ne and the 17O( $\alpha,\gamma$ )21Ne reactions, that are of crucial importance for the s-process in massive stars. I used the fitting method described in Rauscher & Thielemann (2000, also nucastro.org) to convert these tabulated rates into the reaclib format. For the two fits, I found that $n=3$ provides satisfactory results: the final deviation is less than 5 % (Fig. 5.3, only one of the two fit is shown).

5.2.2 The $\mu$ and $\Omega$ profiles

When first trying to reproduce the results of Frischknecht et al. (2016), I found significantly different results: many s-elements were underproduced by a factor of 100 in the new models. It was caused by strong oscillations of the $D_{\rm shear}$ coefficient in between the H- and He-burning zones, during the core He-burning stage. The green profile in the left panel of Fig. 5.4 shows such oscillations. The low values of $D_{\rm shear}$ at $M_{r}\simeq 7.5$ strongly reduces the exchanges of material between the He-core and the H-shell, leading to a smaller synthesis of primary 14N and 22Ne (Fig. 5.4, right panel, green line). Such $D_{\rm shear}$ oscillations are likely not physical since their shape change or disappear when changing the model resolution. An example is shown by the blue profiles in Fig. 5.4: the resolution of this model (res- model in Fig. 5.4) is reduced compared to the green model (res+ model) but it is still enough to see the eventual $D_{\rm shear}$ oscillations. In this case, the $D_{\rm shear}$ does not oscillate so that the mixing is not cut and more 14N and 22Ne are synthesized compared to the green model (Fig. 5.4, right panel). While the changes induced by the presence or the absence of oscillations are not huge for 14N and 22Ne (factor of about 5), they are much more significant for s-elements (factor of about 100 at maximum, as shown in Fig. 5.5). Models of Frischknecht et al. (2016) are similar to the blue lines in Fig. 5.4 and 5.5 while new models to the green lines.

To improve the stability of the code and find similar results when changing the mesh number, I improved the way of calculating $D_{\rm shear}$ (Eq. 3.10), by trying to better evaluate the derivative of $\mu$ and $\Omega$ , that appeared to be responsible for the oscillation of the $D_{\rm shear}$ coefficient. The oscillation problem is solved if properly smoothing the $\mu$ and $\Omega$ profiles when calculating their derivatives (see Appendix A.4 for more details). If applied, this technique gives similar results when changing the mesh number (see Fig. 5.4, black and red profiles). It also gives similar s-process yields compared to the models of Frischknecht et al. (2016).

See aa33283-18.pdf

5.3 The origin of the single CEMP-s stars

As discussed in Sect. 2.5, CEMP-s stars are generally explained with the AGB binary scenario. This scenario predicts that the CEMP-s should have a white dwarf companion (cf. Fig. 2.6). The CEMP-s stars that appear to be single (Hansen et al. 2016b) may challenge the AGB scenario.

5.3.1 Massive source stars

In Choplin et al. (2017c, see letter in the next section), we have investigated the origin of the four apparently single CEMP-s stars in light of the new grid of massive stars including rotation and s-process presented in the previous paper. The abundances of the apparently single CEMP-s stars are reported in Table 5.1. We found that 3 out of the 4 CEMP-s stars can be well reproduced by the yields of the fast rotating ( $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.7$ ) 25 $M_{\odot}$ model that was computed with the rate of the 17O( $\alpha,\gamma$ ) reaction divided by 10. The dilution factors $D$ are between 4 and 20 and in all the cases, the mass cut $M_{\rm cut}=M_{\rm CO}$ . In general, the other models of the grid do not provide enough s-elements. If deep layers are expelled some models may nevertheless provide enough s-elements but in this case, Na, Mg and Al are overestimated by several order of magnitudes compared to the observations. These results show that some s-rich metal-poor ([Fe/H] $\sim-2$ ) halo stars may have formed with a material that was enriched by the ejecta of a previous fast rotating massive source star. It gives support to the spinstar scenario at higher metallicities (compared to the lower metallicities considered in Chapter 4).

The late mixing process introduced in Sect. 4.5 is not considered in these new CEMP source star models. This process will mostly affect the C and N abundances. It may nevertheless also synthesize heavier elements through neutron captures (Clarkson et al. 2018, cf. also Sect. 4.8). Including the late mixing process in the models with an extended network is among the possible next steps of this work. However, it is not excluded that the late mixing process occurs only at very low metallicity (maybe [Fe/H] $\lesssim-4$ ), and not in these new source star models, with [Fe/H] $=-1.8$ . The reason is that at very low metallicity, source stars are more compact so that the H- and He-burning shells are closer from each other. It might imply an easier interaction of these two shells. This is however speculative and deserves more investigation.

See aa31948-17.pdf

5.3.2 The AGB scenario

Below is discussed some aspects of the AGB binary scenario for the four stars of the previous letter. Abate et al. (2015a, b) have used a binary evolution and population synthesis code to predict the orbital properties of the system (CEMP-s + AGB). The chemical composition in the AGB intershell region, from AGB models of Lugaro et al. (2012), is used. The abundances are function of 3 quantities: the mass of the AGB star at the first thermal pulse, the thermal pulse number and the mass of the partial mixing zone (cf. Sect. 3.2). The procedure is discussed in details in Abate et al. (2015a, b).

Because of its high Pb abundance, the apparently single CEMP-s star CS 30301-015 discussed in the previous letter likely cannot be reproduced if considering only the massive stars ejecta computed in this work. The best AGB fit for this CEMP-s star (shown in Fig. 5.6, top panel) is a 2.6 $M_{\odot}$ AGB star with a period (at the present day) of about $10^{6}$ days. Although not perfect, the fit is improved compared to what can be done with massive stars. In particular, Pb can be reproduced. Also, the long predicted period provides a simple explanation to why this CEMP-s star appears to be single: its orbits is so wide that no radial-velocity variations can be detected. It is consistent with the statement of Hansen et al. (2016b) that reported that any undiscovered binaries among their four apparently single CEMP-s stars would have periods of at least $10^{3}-10^{4}$ days.

For HE 1045+0226 (bottom panel in Fig. 5.6), AGB star models predict too low Y and Zr. Also, the predicted period for HE 1045+0226 is about 40 days, which is too short to explain the non-detection of radial velocity variations. For this star, a massive rotating source stars provides a better solution (cf. previous letter). For the two other CEMP-s stars, only the Ba abundance is available among the heavy elements so that both massive stars and AGB star models can provide a reasonable solution.

Generally speaking, massive stars tend to produce larger light s-element (e.g. Sr) over heavy s-element (e.g. Ba, Pb) ratios than AGB stars. Another difference, as discussed in the previous letter, is the oxygen, that can be higher by $1-2$ dex in massive stars compared to AGB stars. Some CEMP-s stars are O-rich, a characteristic that AGB models may not be able to account for. For instance CS 31080-095 has [O/Fe] $=2.35\pm 0.12$ (Sivarani et al. 2006), LP625-44 has [O/Fe] $=1.8$ (Aoki et al. 2002a), HE 2258-6358 has [O/Fe] $=1.8\pm 0.1$ (Placco et al. 2013). Such high ratios do not exclude a contribution from an AGB companion but may indicate a contribution of one (or more) additional source (i.e. previous massive stars). By detailed comparisons between AGB and massive star models, it would probably be interesting to try to spot the elements like oxygen that could help probing the nature of the additional source(s).

5.4 The weak s-process at lower metallicities

With decreasing metallicity, less seed is available so that less s-elements are produced. In non-rotating models, the production of s-nuclei in massive stars becomes negligible below about $Z$ $=$ $10^{-4}$ (Prantzos et al. 1990). In rotating models, this metallicity threshold may be around $Z=10^{-7}$ : Frischknecht et al. (2016) have shown that at $Z=10^{-7}$ , rotation in a 25 $M_{\odot}$ model has a modest effect on the abundances of s-elements. At very low metallicity, the lack of iron seed implies that even if the neutron source is boosted by rotation, there is no significant s-process boost. Also, it is worth mentioning that above an given metallicity threshold, the s-process boost induced by rotation becomes very small: at $Z=Z_{\odot}$ , Frischknecht et al. (2016) have shown that the abundance patterns of rotating and non-rotating models are almost identical. This is because rotation does not provide much additional 22Ne (neutron source) at this metallicity, as a result of the less efficient back-and-forth mixing process (Sect. 4.1). Indeed, at higher metallicity the distance between the He-core and the H-shell increases and the gradient of $\Omega$ is smaller so that the shear mixing between the He-core and the H-shell is less strong.

5.4.1 A rotating 25 $M_{\odot}$ model with various initial metallicities

The computation of grids of massive star models at lower metallicities (including s-process) is a work in progress. Only 25 $M_{\odot}$ models are presented here. Fig. 5.7 shows the ejected mass (Eq. 3.15) of four isotopes for rotating 25 $M_{\odot}$ models with $Z=10^{-3}$ , $2~{}\times~{}10^{-4}$ and $10^{-5}$ . As the metallicity decreases by 2 dex, the ejected mass of the considered isotopes decreases by $2-4$ dex, depending on the chemical specie. The green and red patterns in Fig. 5.8 show the production factors (Eq. 3.17) of a non-rotating and a rotating 25 $M_{\odot}$ model at $Z=10^{-5}$ , respectively. Compared to their initial abundances, elements between Cu and Y are overproduced by $1-2$ dex in the rotating model. The black pattern shows an extreme case, with fast rotation and a lower 17O( $\alpha,\gamma$ ) reaction rate (/10). In this case, the production of elements between Fe and Eu are enhanced by 1 up to about 3 dex compared to their initial abundances. Overall, it shows that at very low metallicity, although the absolute yields are low (Fig. 5.7), rotation can strongly affect the distribution of heavy elements that are initially present in the star (Fig. 5.8). If rotation is not considered, the initial distribution of heavy elements is barely modified at this metallicity.

5.4.2 The origin of HE 1327-2326

The star HE 1327-2326 (Frebel et al. 2005a) is one of the most iron-poor star with [Fe/H] $-5.7$ and an excess of Sr compared to Fe. Red circles in Fig. 5.9 show its surface composition, according to a recent re-analysis (Ezzedine, priv. comm.). In particular, an overabundance of Zn was found ([Zn/Fe] $=0.84\pm 30$ ).

All possible chemical compositions one can obtain with the non-rotating 25 $M_{\odot}$ model at $Z$ $=$ $10^{-5}$ are shown by the purple area. This area shows the range of [X/Fe] ratios one can obtain when varying the mass cut from the final mass of the model $M_{\rm fin}=24.5$ $M_{\odot}$ (in this case only the material in the stellar winds is considered) to the remnant mass $M_{\rm rem}=2.31$ $M_{\odot}$ (according to the relation of Maeder 1992). We see that whatever the mass cut, N is underproduced by more than 2 dex and Sr by more than 1 dex.

The thick black pattern shows the [X/Fe] ratios of the fast rotating 25 $M_{\odot}$ model ( $\upsilon_{\rm ini}/\upsilon_{\rm crit}$ $=$ $0.7$ ). The mass cut is set to 10.5 $M_{\odot}$ , which is just below the H-rich envelope. No dilution with ISM was considered. In this case, the [Sr/Fe] ratio of HE 1327-2326 can be reproduced. The fit for light elements is also satisfactory. In particular, N is much closer to the observed value. It is however still underproduced by 0.5 dex. The dashed pattern, shows the yields of a model with same metallicity and rotation but with an initial mass of 20 $M_{\odot}$ and a small network (model of Sect. 4.3). This model can produce enough N, suggesting that a source star with a bit different initial mass may provide a better fit (at least for the light elements).

In Sect. 4.6, the source star model that best reproduced the abundance pattern (for light elements, C to Si) of HE 1327-2326 was a fast rotating 60 $M_{\odot}$ model without late mixing, without dilution with ISM and with a mass cut close to the bottom of the H-envelope (cf. Table 4.5). All these characteristics are consistent with the new results obtained here, except for the initial mass of the source star ( $20-25$ $M_{\odot}$ here vs. 60 $M_{\odot}$ before). The high [Sr/Fe] might favor rotating $\sim$ 25 $M_{\odot}$ instead of $\sim$ 60 $M_{\odot}$ source stars because the s-process boost induced by rotation peaks around $20-40$ $M_{\odot}$ (Choplin et al. 2018). A rotating 60 $M_{\odot}$ source star may not produce enough Sr. In the future, the computation of additional source star models at this low metallicity but with different initial masses may help to further address this point.

The source star models presented here underproduce Ti, Ni and Zn by $\sim 0.5$ dex. Such elements can be affected by explosive nucleosynthesis. Interestingly, it was shown that Ti and Zn are overproduced in jet-induced SNe (Tominaga 2009). This kind of asymmetric SN may be produced by fast rotation of the massive stellar core at the time of the explosion (Woosley 1993). Fast rotation of the core at the time of explosion may be due to fast rotation of the progenitor. The fact that HE 1327-2326 is enriched in both the product of rotation (e.g. N, Sr) and of jet-induced SNe (e.g. Zn) may indicate that its source star was a massive rotating star that experienced a jet-induced SN.

In general, the determination of the abundances of both rotation products and jet-induced SNe products in very metal-poor stars might give clues on the impact of rotation on the explosion. An interesting perspective is to study these two families of elements in very metal-poor stars. However, for some interesting elements like Zn, almost only upper limits are available at the moment since they are very challenging to detect.

5.5 Summary

By increasing the amount of available neutrons, rotation boosts the s-process in massive stars. A new grid of non-rotating and rotating ( $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.4$ ) stellar models at [Fe/H] $=-1.8$ with initial masses of 10, 15, 20, 25, 40, 60, 85, 120 and 150 $M_{\odot}$ was computed. Stellar yields are publicly available. Rotation has a strong impact on the production of s-elements (especially the first peak, e.g. Sr) for initial masses between about 20 and 60 $M_{\odot}$ . Two additional 25 $M_{\odot}$ models were computed: one with faster rotation ( $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.7$ ) and another with faster rotation ( $\upsilon_{\rm ini}/\upsilon_{\rm crit}=0.7$ ) and lower 17O( $\alpha,\gamma$ ) rate (divided by 10, it reduces the poisoning effect of 16O). In these two models, the production of s-elements is boosted again. The fast rotating model with a lower 17O( $\alpha,\gamma$ ) rate is the model where the s-process boost is the strongest. In particular, a modest amount of heavy s-elements (e.g. Pb) is synthesized. In stellar models with initial masses $M\gtrsim 60$ $M_{\odot}$ , the back-and-forth mixing is less efficient so that the production of s-elements is similar whether or not rotation is considered.

Some CEMP-s stars appear to be single stars, which may challenge the AGB binary scenario (for these specific stars). The yields of the fast rotating 25 $M_{\odot}$ model of the computed grid provide a material able to fit the abundance patterns of 3 out of the 4 apparently single CEMP-s stars.

The s-process boost induced by rotation still exists in lower metallicity massive stellar models (probably down to about $Z\sim 10^{-7}$ ). HE 1327-2326, one of the most iron-poor star known, has [Sr/Fe] = 1.08. Its abundance pattern can be reproduced by a fast rotating very low metallicity $20-25$ $M_{\odot}$ source star. The fact that this CEMP star is also enriched in Zn, which is a product of jet-induced SNe, is consistent with a scenario proposing that its source star was a fast rotator that experienced a jet-induced SN.

Chapter 6 Conclusions and perspectives

6.1 Conclusions

This work mainly aimed at better understanding the nature of the early generations of massive stars. They are crucial objects to figure out the origin of the elements in the Universe. Although long-dead, indirect clues on these stars can be obtained from the surface chemical composition of still alive and observable low-mass metal-poor stars, formed early in the Universe. Some of these low-mass metal-poor stars, very little enriched in iron and showing highly non solar-like abundance patterns (CEMP stars, especially CEMP-no) are thought to have formed from the ejecta of only one or a few previous zero or very low-metallicity massive stars (the source stars). To gain knowledge on the characteristics of the early massive stars, I computed models of massive source stars under various assumptions so as to determine what are the source star ingredients required to reproduce the abundances of CEMP stars.

Below are listed the main concrete works carried out during this PhD, followed by the main results.

•

I developed a nucleosynthetic one-zone code mimicking the effect of rotation on nucleosynthesis in stellar interiors and made comparisons with abundances of CEMP stars (Sect. 4.2 and Choplin et al. 2016).

•

I computed pre-supernovae massive source star models under various assumptions (initial mass, rotation, extra mixing…) and made comparisons with abundances of CEMP stars (Sect. 4.3, 4.4, 4.6 and Choplin et al. 2017b).

•

I developed a small module in genec allowing to generate extra mixing events in a specific zone of a stellar model (Sect. 4.5 and Choplin et al. 2017b).

•

I computed a new grid of massive stars from 10 to 150 $M_{\odot}$ , at $Z=10^{-3}$ , with and without rotation and including full nucleosynthesis so as to follow the s-process (Sect. 5.2 and Choplin et al. 2018). Stellar yields are available online111See https://www.unige.ch/sciences/astro/evolution/en/database/ or the CDS database at cdsarc.u-strasbg.fr.. Then, comparisons with CEMP stars enriched in s-elements were done (Sect. 5.3, 5.4 and Choplin et al. 2017c).

•

During a short term scientific mission with Prof. Jose Groh, I produced CMFGEN spectra for a population of main-sequence massive stars at $Z=10^{-5}$ and started to investigate the effect of fast rotation in the spectral features of such stars (see Sect. 6.2.1 for more details).

•

I included the effects of axion losses in genec and computed a grid of non rotating Pop III stars with and without axion losses (Sect. 3.4, Appendix A.1 and Choplin et al. 2017a).

•

I included in genec the new diffusion coefficient of Maeder et al. (2013) that describes the interaction between various instabilities arising in rotating stars (Appendix A.2). I carried out several tests models to compare this prescription with other prescriptions (Sect. 3.3.1).

•

I included in genec the new mass loss recipe of Moriya & Langer (2015) that considers the mass loss induced by pulsations in the late evolution of very massive metal-free stars (Appendix A.3).

•

I improved the way of treating the rotational mixing in genec by upgrading the calculation techniques of the $D_{\rm shear}$ coefficient (Appendix A.4).

•

I transformed the tabulated reaction rates of Best et al. (2013, 17O( $\alpha,\gamma$ ) and 17O( $\alpha,n$ )) into the reaclib format (Sect. 5.2.1).

The main results of these works, presented in the chapters 4 and 5, can be summarized as follow:

•

Using the one-zone nucleosynthetic code, I found that a significant fraction of the CEMP stars with [Fe/H] $<-3$ can be overall well reproduced by a material processed by H-burning at a temperature and density characteristic of $20-60$ $M_{\odot}$ source stars. While burning, this material has to be enriched in 12C, 16O and occasionally in 22Ne. It suggests that the source stars experienced mid to strong rotational mixing.

•

Complete source star models with various initial parameters (especially rotation) were computed. The efficient rotational mixing operating at low metallicity triggers exchanges of material between the He-burning core and the H-burning shell. It leads to a rich and varied nucleosynthesis, able to cover the ranges of abundances of light elements for the CEMP stars with [Fe/H] $<-$ 3.

•

Comparisons between source star models and observations in the [C/N] vs. 12C/13C diagram revealed some discrepancies that can be alleviated if a late mixing process is included in the source stars. The mixing operates in between the H-burning shell and the He-burning shell, about 200 yr before the end of the source star evolution. The mixing may also operate before, provided the material in the H-burning shell (at least some of it) is saved from further processing shortly after the mixing event (e.g. it is expelled through stellar winds).

•

The abundance fitting (for light elements, C to Si) of 69 CEMP stars with [Fe/H] $<-3$ and not significantly enriched in s- and r-elements was performed with $\sim 35000$ ejecta composition of source star models. The best source stars are preferentially fast rotators (74 % of the cases), have initial masses of 20 $M_{\odot}$ (70 %) and experienced the late mixing process (72 %). In most of the cases ( $\sim 70$ %), only the outer layers of the source stars (above or just below the interface between the H-rich and He-rich region) have to be expelled. Finally, the best abundance fits are mostly obtained with a modest dilution of the ejecta with the interstellar medium ( $\sim 0-10$ times more interstellar material than source star ejecta).

•

A new grid of massive source stars at [Fe/H] $=-1.8$ was computed with an extended nuclear network, able to follow the full s-process during the evolution. Rotation was found to strongly boost the first s-process peak (e.g. Sr) for stars with initial masses between 20 and 60 $M_{\odot}$ . If the initial rotation is high enough, models predict a significant synthesis of s-elements from the second peak (e.g. Ba). Elements from the third peak (e.g. Pb) were found to be little impacted by rotation.

•

CEMP-s stars, which often have $-3<$ [Fe/H] $<-2$ , are generally associated with the AGB binary scenario. Four CEMP-s stars were recently found to be single stars, a characteristic that may challenge this scenario. The fast rotating 25 $M_{\odot}$ model of the new grid of model including s-process provides a material able to fit the abundance pattern of 3 out of the 4 apparently single CEMP-s stars.

•

The abundances of HE 1327-2326, one of the most iron-poor star, were examined in detail with the yields of new very low metallicity source star models including the s-process. Both the excess in light elements and Sr can be explained with the ejecta of a fast rotating $20-25$ $M_{\odot}$ source star model. Interestingly, the fact that HE 1327-2326 is enriched in both the products of rotation (e.g. N, Sr) and of jet-induced supernovae (e.g. Zn), is consistent with a scenario proposing that its source star was a fast rotator that experienced a jet-induced supernova.

The results of this work suggest that rotation in the source star is a crucial ingredient, which is able to provide a solution for the abundances of light elements (C to Si) and s-elements of many CEMP stars. It supports the idea that rotation was a dominant effect in the early generations of massive stars. The results propose that in most of the cases, a strong and late mixing event operated in between the H-burning and He-burning shell of early massive stars. It was also shown that CEMP stars should be formed with only the relatively outer layers of the source stars (generally only the H-envelope or the H-envelope plus a small part of the He-rich region). This suggests that early massive stars expelled only their envelope and experienced strong fallback. The present work does not offer a specific mechanism for the ejection of the source star envelope. Although stellar wind is a good candidate for the reasons mentioned in Sect. 3.3.5, the wind material of the source star models presented here is generally not sufficiently enriched in light and heavy elements for reproducing the CEMP star abundances. An additional (generally modest) supernova contribution is required. In any case, the fact that just the envelope of the source star should be expelled is consistent with the mixing & fallback scenario that could finally co-exist with the fast rotating massive star scenario.

6.2 Perspectives

The nature of the first stars is a topic where we are still scratching the surface and where to move on, modelers and observers should go hands in hands. Below are important possible future steps or projects (mainly on the modeling side) linked to the present work.

•

The modeling of grids of source star models including s-process has to be continued, especially at very low metallicity. The aim is to get a more complete picture of the nucleosynthesis in rotating massive stars and perform extended comparisons with observations, with as much abundances as possible.

•

The new scenario for the origin of HE 1327-2326 raises the interest for studying the outputs of rotating massive stars experiencing a jet-induced supernova. A consistent prediction of the nucleosynthetic yields of a rotating massive star ending its life as a jet SN could be an interesting project. In the future, the comparison of such models with observations might give clues on how the explosion of early massive stars can be affected by rotation.

•

Although generally operating in very central regions, which may be finally locked into the remnant, the SN-shock may lead to further neutron capture nucleosynthesis in the He-shell. It could be included in source star models.

•

The late mixing process could be studied using multi dimension models. Also, when available, constraints from such multi dimension models (especially on the convective boundaries of the H- and He-burning shells) should be included in 1D stellar evolution codes so as to further test the hypothesis of the late mixing process in the source stars.

•

An important project would be to recover the initial surface composition of evolved CEMP stars by computing grids of CEMP star models including various mixing processes. To date, such a work on a large CEMP star sample has been done only for correcting effect of the first dredge-up on the C abundance (Placco et al. 2014c). Knowing well the initial surface composition of CEMP stars (especially for the most evolved CEMP stars) is crucial to connect them more consistently to their source stars.

There are also different observational perspectives. One may be to try determining the abundances of both rotation and jet-induced SN products on the most metal poor stars (cf. point 2 just above). Isotopic ratios (especially 12C/13C) are very constraining (especially on rather unevolved stars) and can provide strong clues on nucleosynthetic processes at work in source stars. Also, the oxygen is likely overproduced in massive stars compared to AGB stars (Choplin et al. 2017c) and might help to further assess the relative contribution of these sources (particularly in the case of the apparently single CEMP-s stars, cf. Sect. 5.3). As first proposed in Meynet et al. (2010), this work predicts that some CEMP stars are enriched in helium (Sect. 4.7). Detecting helium in CEMP stars is probably very challenging but it may be mentioned here as a possible observational perspective. Generally, an observation campaign able to determine rather complete abundance patterns (as for HE 1045+0226 and CS 30301-015, cf. Sect. 5.3) will help very much in choosing between the different existing models. Also, although probably tedious and challenging, radial velocity measurements of more CEMP stars over a long period of time would be very interesting (Hansen et al. 2016a, b, did such measurements for 22 CEMP-s and 24 CEMP-no stars) and would help better understanding their origin.

6.2.1 Linking the old and local with the old and distant Universe

To gain knowledge on the first generation of massive stars, the present work focused on their signatures in the local Universe. As mentioned in the introduction (Sect. 1.4), an alternative way is to observe the distant Universe: either individual explosive/transient events or the integrated light of high redshift galaxies. An interesting project would be to predict the specific signatures in the high redshift Universe of the CEMP massive source stars. It will establish a connection between the old and local Universe with the old and distant Universe. A schematic view of such a project is shown in Fig. 6.1: the source star population that best account for observations of metal-poor stars is determined using stellar models (the aim of the present thesis, for CEMP stars) and also Galactic chemical evolution (GCE) models. GCE models are suitable to investigate the origin of normal metal-poor stars, which probably formed from a reservoir well enriched by different previous sources and not just $\sim 1$ source star. Type of supernovae, supernova rates, and emergent spectrum of this massive source star population may be estimated combining the outputs of stellar evolution modeling, GCE modeling and the predictions from a radiative transfer code. Such predictions could be compared to high redshift observations, especially observations from JWST, that may be able to catch the explosion of the first generations of massive stars (Whalen et al. 2013a, b, c).

During a Short Term Scientific Mission222STSM, in the frame of the COST action ChETEC (http://www.chetec.eu/). of two weeks with Pr. Jose Groh (Trinity college, Dublin), we started to work on one aspect of this project. As a very first step, I tried to see what would be the emergent spectrum of a population of main sequence fast rotating massive source stars compared to a population of main sequence non-rotating massive source stars. I extended the small grid of massive stars presented in Sect. 4.5. In addition to the 20, 32 and 60 $M_{\odot}$ models, I computed 10, 12, 15, 25, 85 and 120 $M_{\odot}$ models. The initial rotation is either 0 or 70 % of the critical velocity. Only the main sequence was computed. To compute the output spectra of the models, the atmospheric radiative transfer code CMFGEN (Hillier & Miller 1998) is used. CMFGEN is a spherically-symmetric code that computes line and continuum formation in non-local thermodynamical equilibrium. Fig 6.2 shows the emergent spectra of the non-rotating models at the middle of the main sequence (H in the core is half burnt). Also the integrated spectrum is shown by the dashed line. After normalizing the spectra with their continuum, comparisons can be done with the rotating population. A detailed comparison of specific lines (e.g. HeI $\lambda$ 6680 or HeII $\lambda$ 4687) between the different models remains to be done.

In the future, after the analysis of these first results, it would be worth computing a more realistic emergent integrated spectrum by calculating more CMFGEN spectra (at different stages of the main sequence but also after the main sequence), by considering a non-constant star formation rate (e.g. a burst of star formation), by maybe considering additional rotational velocities, by introducing some noise and convolving the spectra with a Gaussian (corresponding to a given spectral resolution) so as to predict which kind of observing facility may be able to detect a given spectral feature predicted by the models.

Appendix A Numerical aspects

A.1 Axion cooling

The energy loss by axions can be written as

[TABLE]

where $K$ and $g_{10}$ are constants, $T_{8}=10^{-8}~{}T$ , $\rho_{3}^{-1}=10^{-3}~{}\rho$ and $Z(\xi^{2})=A(\xi^{2})\ln(B(\xi^{2}))$ with

[TABLE]

and where

[TABLE]

$\hbar$ is the reduced planck constant, $\rm c$ the speed of light and $\rm k_{B}$ the Boltzmann constant. The Debye–Hückel screening wavenumber $k_{S}$ , is given by Raffelt (2008) as

[TABLE]

where $\alpha$ is the fine structure constant, $Z_{i}$ the atomic number and $n_{i}$ the ions/electron number densities. The term $C$ in Eq. A.1 is equal to $C=\exp(-(\hbar\omega_{0})/(k_{B}T))$ with $\omega_{0}$ the plasma frequency defined as

[TABLE]

In genec, I have included the energy loss by axions $\epsilon_{\rm ax}$ by adding it to $\epsilon_{\nu}$ , the energy loss by neutrino. Axion losses are considered if the parameter iaxions=1. When solving the stellar structure equations with the Henyey method, the derivatives of $\epsilon_{\nu}$ and $\epsilon_{\rm ax}$ as a function of $P$ and $T$ are required for convergence. Most of the time, $\epsilon_{\rm ax}\ll\epsilon_{\nu}$ , so that $\epsilon_{\rm ax}$ can be neglected. At the end of He-burning however, axion losses become the dominant source of energy loss and must be included in the energy derivatives. In the case of genec, the following terms have to be evaluated:

[TABLE]

where $\epsilon=\epsilon_{\nu}+\epsilon_{\rm ax}$ . The term on the left in A.6 can be written as

[TABLE]

The derivative of $\epsilon_{\rm ax}$ as a function of $P$ is equal to

[TABLE]

At this point, the derivatives of $Z(\xi^{2})$ and $C$ have to be calculated:

[TABLE]

The derivatives of $A$ and $B$ as a function of $\rho$ are

[TABLE]

and

[TABLE]

with

[TABLE]

since $\xi^{2}\propto k_{S}^{2}\propto n\propto\rho$ . The derivative of $C$ in Eq. A.8 is non-zero because $C\propto\omega_{0}\propto n_{e}\propto\rho$ . It yields

[TABLE]

A similar derivation has to be done for the second term of A.6. Then, $\epsilon_{\rm ax}$ has to be derived as a function of $T$ (with $P$ constant but not $\rho$ , so that $\rho$ has to be derived as a function of $T$ ). It yields

[TABLE]

The derivative of $Z(\xi^{2})$ as a function of $T$ is evaluated similarly to Eq. A.9, A.10 and A.11. Then, as in Eq. A.12, one needs the derivative of $\xi$ but this time as a function of $T$ :

[TABLE]

Finally, the derivative of $C$ as a function of $T$ is

[TABLE]

From this point, all quantities are defined or available in the code so that Eq. A.8 and A.14 can be calculated and the two quantities in A.6 evaluated.

A.2 Secular shear mixing

The $D_{\rm shear}$ used in this work is the one of Talon & Zahn (1997, Eq. 3.10). The other $D_{\rm shear}$ coefficient from Maeder (1997) can be written as

[TABLE]

with $f_{\rm energ}$ the fraction of the excess energy in the shear that contributes to mixing. It is generally calibrated on observations (cf. Sect. 3.3.1).

It also exists other instabilities (e.g. thermohaline instability…) that, when included in 1D stellar evolution codes, are generally translated as individual diffusion coefficients. The global diffusion coefficient is then expressed as the sum of the coefficients of the various effects considered independently. However, it can exist physical interactions between the different instabilities, possibly leading to amplification or damping effects. Maeder et al. (2013) have proposed a global stability criterion, taking into account different instabilities together (thermohaline instability, shear instability, Rayleigh-Taylor instability, semiconvective instability, the instability characterized by the Solberg-Høiland criterion and the baroclinic instability). From the stability criterium, I have derived the global diffusion coefficient and included it genec. The global stability criterium is written as

[TABLE]

with

$A=N_{ad}^{2}+N_{\mu}^{2}+N_{\Omega-\delta v}^{2}$

$B=N_{ad}^{2}D_{h}+N_{\mu}^{2}(K+D_{h})+N_{\Omega-\delta v}^{2}(K+2D_{h})$

$C=N_{\Omega-\delta v}^{2}(D_{h}K+D_{h}^{2})$

and where

$N_{ad}^{2}=\displaystyle\frac{g\delta}{H_{p}}(\nabla_{ad}-\nabla)$

$N_{\mu}^{2}=\displaystyle\frac{g\varphi}{H_{p}}\nabla_{\mu}$

$N_{\Omega-\delta v}^{2}=\displaystyle\frac{1}{\bar{\omega}^{3}}\frac{d(\Omega^{2}\bar{\omega}^{4})}{d\bar{\omega}}\sin\theta-Ri_{c}\left(\frac{dU}{dr}\right)^{2}$

with $\bar{\omega}$ the distance to the rotational axis. It can be written $\bar{\omega}=r\sin\theta$ where $\theta$ is the colatitude. $U$ can be expressed as $U=r\Omega\sin\theta$ . Let us express the first term of $N_{\Omega-\delta v}^{2}$ :

[TABLE]

It yields

[TABLE]

In numerical calculations, one has to average $N_{\Omega-\delta v}^{2}$ over an isobar. We obtain

[TABLE]

The diffusion coefficient is $D_{\rm global}^{\rm M13}=(1/3)|v|l=2|x|$ where $x$ are the two solutions of Eq. A.18. Test models were computed with both solutions. The first solution leads to convergence issues while the second does not. The second one also gives plausible results (Fig. 3.5). In genec, the second solution was implemented as a standard choice.

A.3 Mass loss recipes

The pulsationally induced mass-loss rate derived by Moriya & Langer (2015) are

[TABLE]

where $\dot{M}$ is expressed in $M_{\odot}$ yr*-1* and with $\eta=(-8.30\pm 0.59)\times 10^{-4}~{}T_{\rm eff}+(4.15\pm 0.29)$ . In genec, this mass loss is considered and added to other kinds of mass losses (mechanical, radiative) if the parameter ipuls=1 and if $\log(T_{\rm eff})<3.698$ (it corresponds to $T_{\rm eff}=4992$ K). This is the temperature below which the stellar envelope becomes pulsationally unstable (Moriya & Langer 2015). The parameter $\eta$ is a free parameter that has to be chosen between the 4 possible values (0.1, 0.3, 0.5 or 0.8, parameter epsil in the code).

A small change was also done in the mass loss recipe of de Jager et al. (1988, imloss=1) in order to correct a bug happening for very luminous stars. In the expression of $\dot{M}$ , there is a term

[TABLE]

where $T_{j}$ is a function defined as $T_{j}(x)=\cos(j\arccos x)$ . This definition implies that the term in brackets in Eq. A.23 must be $\leq 1$ or equivalently, $\log(L/L_{\odot})\leq 6.7$ . In extreme cases (e.g. very massive stars), it happens that this condition is not verified, leading to convergence issues. To solve this issue, I just took the minimum between 1 and the bracket value in Eq. A.23.

A.4 Locally weighted scatterplot smoothing

In genec, a locally weighted scatterplot smoothing technique can be used for smoothing the profile of a quantity (e.g. $\mu$ or $\Omega$ ) when calculating its derivative. It is used at least during the main sequence of rotating models to smooth the $\Omega$ , $\mu$ and $U$ (vertical component of the meridional circulation) profiles. Without it, the code may experience convergence issues.

Fig. A.1 illustrates the technique. Let us consider $N$ data points with given coordinates $x_{i}$ and $y_{i}$ (black crosses in Fig. A.1, upper panels). Let us focus on the point at $x_{i}\simeq 9$ in the upper left panel of Fig. A.1. A window of $n=2W+1$ points around that point is selected. $W$ is a parameter to chose. In this example, $W=2$ so that $n=5$ . A linear fit with these $n=5$ points is then performed and the derivative is taken equal to the slope of the fit. Fig. A.1 (lower left) shows $y^{\prime}$ , the derivative of the data when considering just the two neighborhood values (black line) and the derivative if smoothing is done (red line). The smoothed data being more regular, the red profile is less sharp.

The size of the window $W$ used to smooth the profile plays an important role. The upper right panel of Fig. A.1 shows the same data as well as the three smoothed profiles for $W=1$ (blue), $W=2$ and $W=4$ (green). The larger the size of the window, the more damped the irregularity of the raw profile, because the fit is done using more points. It leads to smoother derivatives (Fig. A.1, lower right panel). This smoothing technique can be seen as a filter that damps the irregularity of the $y_{i}$ profile. If $W$ is small, the smoothing is weak (i.e. close to the raw data), if $W$ is large, some important (physical) features in the profile can be lost.

The effect of varying $W$ in a complete stellar model is shown in Fig. A.2. The $\mu-$ gradient calculated from just the two neighborhood values (pink line) presents strong oscillations which are likely not physical. The smoothing procedure described previously damps these features (other lines).

In genec, I introduced a mesh-adaptative $W$ parameter, defined as $W=m/a$ with $m$ the mesh number and $a=120$ , a constant selected after carrying numerical tests with various values of $a$ .

A.5 S-process parameters

I remind here some quantities that can be used to quantify the efficiency of the s-process. These quantities are tabulated in Table A.1 for the grid of models published in Choplin et al. (2018). These quantities may be useful for future comparisons with other models.

The central neutron exposure during core He-burning $\tau_{\rm c}$ is defined as

[TABLE]

where $t_{\rm ini-He}$ and $t_{\rm end-He}$ are the age of the model at the beginning and the end of the core He-burning phase, respectively, $n_{\rm n}$ the neutron density and $v_{\rm T}=\sqrt{2kT/m_{\rm n}}$ the thermal velocity (with $kT=30$ keV as a typical value in the helium burning core). Because the neutron density $n_{\rm n}$ varies with time and mass coordinate in the model, it is interesting to define the neutron exposure averaged over the He-core and over the He-burning lifetime:

[TABLE]

$\langle n_{\rm n}(t)\rangle$ is the neutron density at time $t$ averaged over the He-core. It is defined as

[TABLE]

where $M_{\rm He}(t)$ is the mass of the helium core at time $t$ and $n_{n}(M_{\rm r})$ the neutron density at coordinate $M_{\rm r}$ . Finally, the average number of neutron captures per iron seed $n_{\rm c}$ is defined as (Käppeler et al. 1990)

[TABLE]

with $Y(A)$ and $Y_{\rm 0}(A)$ the final and initial number abundance of a nucleus with nuclear mass number A and $Y_{0}$ (56Fe) the initial number abundance of 56Fe.

Appendix B Abundance fits

This appendix contains the abundance fits of the 69 CEMP stars of Table LABEL:tabcemp with the source star models presented in Sect. 4.5 and 4.6.

Appendix C Publications

This section contains the list of publication. After the list are the 3 refereed papers (page C, C and C) that are not directly included in the thesis. The 2 others papers can be found page 5.2.2 and 5.3.1 of this thesis.

Refereed articles

•

*Non standard s-process in massive rotating stars. Yields of $10-150$ $M_{\odot}$ models at $Z=10^{-3}$

*Choplin, A., Hirschi R., Meynet G., Ekström S., Chiappini C. & Laird A.

2018, A&A, 618, A133

•

Are some CEMP-s stars the daughters of spinstars?

Choplin, A., Hirschi R., Meynet G. & Ekström S.

2017, A&A, 607, L3

•

*Effects of axions on Population III stars

*Choplin, A., Coc A., Meynet G., Olive K. A., Uzan J.-P. & Vangioni E.

2017, A&A, 605, A106

•

*Pre-supernova mixing in CEMP-no source stars

*Choplin, A., Ekström S., Meynet G., Maeder A., Georgy C. & Hirschi R.

2017, A&A, 605, A63

•

*Constraints on CEMP-no progenitors from nuclear astrophysics

*Choplin, A., Maeder A., Meynet G. & Chiappini C.

2016, A&A, 593, A36

Publications in conference proceedings

•

*Toward the first stars

*Choplin, A.

Annual meeting of the French Society of Astronomy and Astrophysics, July 2017

•

*Massive stars: stellar models and stellar yields, impact on Galactic Archaeology

*Meynet, G., Choplin, A., Ekström, S. & Georgy, C.

IAU Symposium 334, Rediscovering our Galaxy 2017

•

*Evolution and Nucleosynthesis of Massive Stars

*Meynet, G., Maeder, A., Choplin, A., Takahashi, K., Ekström, S., Hirschi, R., Chiappini, C. & Eggenberger, P.

14th International Symposium on Nuclei in the Cosmos (NIC2016), id.010401, 8 pp, 2017

•

*Impact of rotation on stellar models

*Meynet, G., Maeder, A., Eggenberger, P., Ekstrom, S., Georgy, C., Chiappini, C., Privitera, G. & Choplin, A.

Astronomische Nachrichten, Vol.337, Issue 8-9, p.827 2016

•

*Nucleosynthesis in the first massive stars

*Choplin, A., Meynet, G., Maeder, A., Hirschi, R. & Chiappini, C.

Nuclear in Astrophysics Conference, 2016

•

*Clues about the first stars from CEMP-no stars

*Choplin, A., Meynet, G. & Maeder, A.

Annual meeting of the French Society of Astronomy and Astrophysics, June 2015

Poster proceedings

•

*Insights on the First Stars from CEMP-no Stars

*Choplin, A., Meynet, G., Maeder, A., Hirschi, R., Ekström, S. & Chiappini, C.

International Symposium on Nuclei in the Cosmos, 2017

•

*Clues on the first stars from CEMP-no stars

*Choplin, A., Meynet, G., Maeder, A., Hirschi, R., Ekström, S. & Chiappini, C.

IAU Symposium, Hawaii, USA, August 2016

•

*Clues about the first stars from CEMP-no stars

*Meynet, G., Maeder, A., Choplin, A., Hirschi, R., Ekström, S. & Chiappini, C.

IAU General Assembly, 2015

Other oral contributions (no proceeding)

•

Nucleosynthesis in Rotating massive stars and Abundances of metal-poor stars. (Invited talk)

Choplin, A.

the JINA-CEE Frontiers in Nuclear Astrophysics Meeting, South Bend IN, US, May 2018

•

Shedding light on the first stars with CEMP-no stars. (Invited talk)

Choplin, A., Meynet, G., Ekström, S., Hirschi, R., Maeder, A., Chiappini, C. & Georgy, C.

A Celebration of CEMP and Gala of GALAH, Melbourne, Australia, November 2017

See aa31040-17_low.pdf

See aa30182-16.pdf

See aa28083-16_low.pdf

Bibliography410

The reference list from the paper itself. Each links out to its DOI / PubMed record.

1Abate et al. (2015 a) Abate, C., Pols, O. R., Izzard, R. G., & Karakas, A. I. 2015 a, A&A, 581, A 22
2Abate et al. (2015 b) Abate, C., Pols, O. R., Karakas, A. I., & Izzard, R. G. 2015 b, A&A, 576, A 118
3Abazajian et al. (2009) Abazajian, K. N., Adelman-Mc Carthy, J. K., Agüeros, M. A., et al. 2009, Ap JS, 182, 543
4Abbott et al. (2016) Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2016, Physical Review Letters, 116, 061102
5Abbott et al. (2017) Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2017, Physical Review Letters, 119, 161101
6Abbott & Sikivie (1983) Abbott, L. F. & Sikivie, P. 1983, Physics Letters B, 120, 133
7Abel et al. (2002) Abel, T., Bryan, G. L., & Norman, M. L. 2002, Science, 295, 93
8Abohalima & Frebel (2017) Abohalima, A. & Frebel, A. 2017, Ar Xiv e-prints

TL;DR

Contribution

Findings

Abstract

Peer Reviews

Videos

Taxonomy

Abstract

Résumé

Contexte

Objectifs et méthodes

Résultats

Conclusion

Remerciements

Contents

List of Figures

List of Tables

Chapter 1 Introduction

1.1 From the Big Bang to the first stars

1.1.1 Big Bang nucleosynthesis

1.1.2 The formation of the first stars

1.2 Origin of the elements

1.3 Stellar rotation

Rotation at low and zero metallicity

1.4 Observable signatures of the early generations of massive stars

Integrated light of high redshift galaxies

Reionization

Supernovae and Gamma-Ray Bursts in distant galaxies

Gravitational waves

Pockets of primordial material

Nucleosynthetic imprints in low-mass metal-poor stars

Nucleosynthetic imprints in the metal-poor stars of the Galactic bulge

1.5 Overview of this thesis

Chapter 2 CEMP stars: observations and origins

2.1 Generalities on metal-poor stars

2.2 Observation and abundances of metal-poor stars

2.2.1 The observational steps

Step 1 : wide-angle surveys

Proper-motion surveys

Colorimetric surveys

Objective-prism surveys

Step 2 : moderate-resolution spectroscopy

Step 3 : high-resolution spectroscopy

2.2.2 Abundances and uncertainties

2.3 CEMP stars as peculiar metal-poor stars

Are CEMP stars enriched in other elements?

Are CEMP stars frequent?

Are CEMP stars in binary systems?

2.4 Internal mixing processes in CEMP stars

The first dredge-up.

Thermohaline mixing and rotation.

Atomic diffusion.

2.5 The origin of CEMP stars: external sources

2.5.1 CEMP-s stars

2.5.2 CEMP-r, -r+s, -r/s, -i stars

2.5.3 CEMP-no stars

Mixing and fallback

Mixing.

Fallback.

Fast rotating massive stars

2.6 Summary

Chapter 3 Massive source stars: nucleosynthesis and models with rotation

3.1 Nucleosynthesis processes in massive stars

3.1.1 Stellar fusion

Core hydrogen burning.

Core helium burning.

Advanced burning stages.

3.1.2 The weak s-process

3.1.3 Explosive nucleosynthesis

3.2 The s-process in AGB stars

3.3 Massive stellar models including rotation

3.3.1 Transport induced by rotation

Transport of angular momentum

Transport of chemical elements

A comparison of 3 different prescriptions for the shear mixing

3.3.2 Convection

3.3.3 Nuclear network

3.3.4 Initial composition and opacity tables

3.3.5 Mass loss

Effect of rotation on mass loss

4.4.2 The C/N $-$ 12C/13C puzzle

4.8.2 Other source star models in the C/N $-$ 12C/13C diagram

5.2.2 The $\mu$ and $\Omega$ profiles

5.4.1 A rotating 25 $M_{\odot}$ model with various initial metallicities