Nebular Spectra of 111 Type Ia Supernovae Disfavor Single Degenerate Progenitors

TL;DR

This study analyzes 227 nebular spectra of 111 Type Ia supernovae to constrain progenitor models, finding no evidence for certain companion scenarios and establishing upper limits on their occurrence rates.

Contribution

It provides the first comprehensive statistical constraints on Type Ia supernova progenitors using nebular spectra and introduces a new nebular phase Phillips relation.

Findings

No evidence of stripped companion emission in spectra

Upper limit of <5.5% on H-rich non-degenerate progenitors

Upper limit of <6.4% on He star progenitors

Abstract

We place statistical constraints on Type Ia supernova (SN Ia) progenitors using 227 nebular phase spectra of 111 SNe Ia. We find no evidence of stripped companion emission in any of the nebular phase spectra. Upper limits are placed on the amount of mass that could go undetected in each spectrum using recent hydrodynamic simulations. With these null detections, we place an observational $3\sigma$ upper limit on the fraction of SNe Ia that are produced through the classical H-rich non-degenerate companion scenario of < 5.5%. Additionally, we set a tentative $3\sigma$ upper limit on He star progenitor scenarios of < 6.4%, although further theoretical modelling is required. These limits refer to our most representative sample including normal, 91bg-like, 91T-like, and "Super Chandrasekhar" \sne but excluding SNe Iax and SNe Ia-CSM. As part of our analysis, we also derive a Nebular Phase Phillips Relation, which approximates the brightness of a SN Ia from $150-500$~days after maximum using the peak magnitude and decline rate parameter $\Delta m_{15} (B)$.

Tables

Table 1. Table 1: All telescopes and instruments utilised in this work. If a reference could not be found for a given instrument, the corresponding instrument website is provided in the table notes.

Telescope	Abbrev.a	Instrument	Abbrev.a	Ref.	$N_{\mathrm{spec}}$
Australian National University 2.3m	ANU2.3m	Wide-Field Spectrograph	WiFeS	Dopita et al. (2007, 2010)	7
Calar Alto 2.2m	CA2.2m	Calar Alto Faint Object Spectrograph	CAFOS	${\dots }^b$	1
Calar Alto 3.5m	CA3.5m	Multi-Object Spectrograph at Calar Alto	MOSCA	${\dots }^c$	2
Danish 1.54m	D1.54m	Danish Faint Object Spectrograph and Camera	DFOSC	Andersen et al. (1995)	1
du Pont Telescope	duPont	Wide Field Reimaging CCD Camera	WFCCD	${\dots }^d$	4
		Boller and Chivens Spectrograph	BC	${\dots }^e$	1
ESO 1.5m	ESO1.5m	Boller and Chivens Spectrograph	BC	${\dots }^f$	2
ESO 3.6m	ESO3.6m	ESO Faint Object Spectrograph and Camera	EFOSC1/2	Buzzoni et al. (1984)	11
Harlan J Smith Telescope	HJST	UltraViolet Image Tube Spectrograph	UVITS	Wills et al. (1980)	1
Himalayan Chandra Telescope	HCT	Himalayan Faint Object Spectrograph	HFOSC	${\dots }^g$	2
Hubble Space Telescope	HST	Faint Object Spectrograph	FOS	${\dots }^h$	1
Isaac Newton Telescope	INT	Faint Object Spectrograph (1st Gen.)	FOS1	Breare et al. (1987)	2
Gemini North/South	GN/S	Gemini Multi-Object Spectrograph	GMOS	Hook et al. (2004)	13
Gran Telescopio Canarias	GTC	Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy	OSIRIS	Cepa (2010)	1
Keck I	KeckI	Low Resolution Imaging Spectrograph	LRIS	Oke et al. (1995)	27
Keck II	KeckII	DEep Imaging Multi-Object Spectrograph	DEIMOS	Faber et al. (2003)	9
		Echelette Imager and Spectrograph	ESI	Sheinis et al. (2002)	3
Large Binocular Telescope	LBT	Multi-Object Double Spectrograph	MODS1/2	Pogge et al. (2010)	10
Magellan Baade Telescope	Baade	Inamori-Magellan Areal Camera and Spectrograph	IMACS	Dressler et al. (2011)	3
		Magellan Echellette Spectrograph	MagE	Marshall et al. (2008)	2
Magellan Clay Telescope	Clay	Low Dispersion Survey Spectrograph	LDSS	${\dots }^i$	5
Multiple Mirror Telescope	MMT	Blue Channel Spectrograph	BCS	Angel et al. (1979)	6
New Technology Telescope	NTT	ESO Multi-Mode Instrument	EMMI	D’Odorico (1990)	1
		SOFI	$\dots$	Moorwood et al. (1998)	1
Palomar 200-inch	P200	Double Spectrograph	DBSP	Oke & Gunn (1982)	4
Shane 3m Telescope	Shane3m	Kast Spectrograph	KAST	Silverman et al. (2013)	11
Southern African Large Telescope	SALT	Robert Stobie Spectrograph	RSS	Buckley et al. (2006)	3
Subaru	Sub	OH-Airglow Suppressor/Cooled Infrared Spectrograph and Camera for OHS	CISCO	Motohara et al. (2002)	3
		Faint Object Spectrograph and Camera	FOCAS	Kashikawa et al. (2002)	2
Tillinghast 1.5m	Till	FAst Spectrograph for the Tillinghast telescope	FAST	Fabricant et al. (1998)	7
Telescopio Nazionale Galileo	TNG	Device Optimized for LOw RESolution	DOLORES	Molinari et al. (1999)	2
Very Large Telescope	VLT	FOcal Reducer and low dispersion Spectrograph	FORS1/2	Appenzeller et al. (1998)	43
		Multi-Unit Spectroscopic Explorer	MUSE	Bacon et al. (2010)	8
		XSHOOTER	XSH	Vernet et al. (2011)	16
William Herschel Telescope	WHT	Intermediate dispersion Spectrograph and Imaging System	ISIS	Jorden (1990)	5
		ACAM	$\dots$	Benn et al. (2008)	1
		Faint Object Spectrograph (2nd Gen.)	FOS2	Breare et al. (1987)	6
Total	29		40		227

Table 2. Table 2: Line luminosities for both the hydrogen-rich (H-rich) model and the helium-rich (He-rich) model corresponding to the MS38 and helium models from Botyánszki et al. ( 2018 ) . Helium lines are given letter designations to ease identification in Table 14 . FWHM refers to the expected FWHM of a line profile broadened by ∼ 10 3 ​ km ​ s − 1 similar-to absent superscript 10 3 km superscript s 1 \sim 10^{3}~{}\rm{km}\,\rm s^{-1} .

Line	$\lambda$	$L_{200}$[${10}^{38}$ erg/s]	FWHM [Å]
H-rich Model
H$\gamma$	4341Å	0.271	14.5
H$\beta$	4831Å	4.38	16.1
HeI-a	5875Å	4.27	19.6
H$\alpha$	6563Å	68.0	21.9
HeI-b	6678Å	2.24	22.3
HeI-c	1.08$\mu m$	10.5	36.0
Pa$\beta$	1.281$\mu m$	14.6	42.7
Pa$\alpha$	1.875$\mu m$	14.6	62.5
HeI-d	2.06$\mu m$	8.48	68.7
He-rich Model
HeI-a	5875Å	8.26	19.6
HeI-b	6678Å	6.90	22.3
HeI-c	1.08$\mu m$	18.2	36.0
HeI-d	2.06$\mu m$	12.9	68.7

Table 3. Table 3: Statistics for each sample considered in our study (see § 4 ). N 𝑁 N is the number of SNe Ia with M s ​ t < M cut subscript 𝑀 𝑠 𝑡 subscript 𝑀 cut M_{st}<M_{\rm{cut}} and f n ​ σ subscript 𝑓 𝑛 𝜎 f_{n\sigma} is the n ​ σ 𝑛 𝜎 n\sigma fractional upper limit on their occurrence. N t ​ o ​ t subscript 𝑁 𝑡 𝑜 𝑡 N_{tot} refers to the total number of SNe Ia in that sample.

		H-rich			He-rich
		()			()
Sample	$N_{tot}$	$N$	$f_{1\sigma }$	$f_{3\sigma }$	$N$	$f_{1\sigma }$	$f_{3\sigma }$
Normal	$90$	$86$			$73$
91T-like	$5$	$5$			$4$
91bg-like	$8$	$8$			$7$
SC	$4$	$4$			$4$
Iax	$4$	$4$			$4$
Normal+91T	$95$	$91$			$77$
Normal+91bg	$98$	$94$			$80$
Normal+91T+91bg	$103$	$99$			$84$
Normal+91T+91bg+SC	$107$	$103$			$88$
All	$111$	$107$			$92$

Table 4. Table 4: Values of the coefficients for Eqs. 6 - 8 and fit statistics. N t ​ o ​ t subscript 𝑁 𝑡 𝑜 𝑡 N_{tot} is the total number of photometric points used in each filter from N S ​ N subscript 𝑁 𝑆 𝑁 N_{SN} SNe Ia.

Filter	$a_{\lambda }$	$b_{\lambda }$	$c_{\lambda }$	$d_{\lambda }$	$N_{SN}$	$N_{\mathrm{tot}}$	$\overline{x}$	$\sigma$
	$\left[{10}^{-3}{\mathrm{day}}^{-1}\right]$	[${10}^{-2}$ mag day-1]		[mag]
$B$	$-{7.66}_{-0.62}^{+0.53}$	${1.443}_{-0.005}^{+0.005}$	${0.48}_{-0.04}^{+0.04}$	${6.168}_{-0.004}^{+0.003}$	42	346	0.00	0.08
$V$	$-{13.68}_{-0.37}^{+0.33}$	${1.620}_{-0.003}^{+0.003}$	${2.58}_{-0.02}^{+0.02}$	${6.050}_{-0.002}^{+0.002}$	67	438	0.03	0.13
$R$	${4.22}_{-0.33}^{+0.41}$	${1.650}_{-0.003}^{+0.004}$	${1.00}_{-0.03}^{+0.03}$	${6.776}_{-0.002}^{+0.002}$	34	286	0.00	0.09

Table 5. Table 5: R V subscript 𝑅 𝑉 R_{V} values and references for SNe Ia with ≥ 3 ​ σ absent 3 𝜎 \geq 3\sigma deviations from the assumed R V = 3.1 subscript 𝑅 𝑉 3.1 R_{V}=3.1 .

Name	$R_V$	Ref.
SN2002bo	1.2	Phillips et al. (2013)
SN2004eo	0.8	Burns et al. (2014)
SN2006X	1.5	Wang et al. (2008); Phillips et al. (2013); Burns et al. (2014)
SN2007le	1.6	Phillips et al. (2013); Burns et al. (2014)
SN2014J	1.5	Amanullah et al. (2014); Foley et al. (2014); Gao et al. (2015); Brown et al. (2015)

Table 6. Table 6: All SNe Ia studied in this work.

Disc. Name	IAU Name	Pec?	z	Redshift Ref.	Discovery	Classification
$\dots$	ASASSN-14hr	N	$0.03362$	Jones et al. (2009)	Nicolas et al. (2014)	Morrell et al. (2014a)
$\dots$	ASASSN-14jc	N	$0.01132$	Jones et al. (2009)	Kiyota et al. (2014a)	Romero-Canizales et al. (2014)
$\dots$	ASASSN-14jg	N	$0.01483$	Jones et al. (2009)	Holoien et al. (2014)	Arcavi et al. (2014)
$\dots$	ASASSN-14jz	N	$0.01550$	This Work	Kiyota et al. (2014b)	Dimitriadis et al. (2014)
$\dots$	ASASSN-14kq	N	$0.03360$	Jones et al. (2009)	Brimacombe et al. (2014a)	Morrell et al. (2014b)
$\dots$	ASASSN-14lt	N	$0.03205$	Springob et al. (2014)	Kiyota et al. (2014c)	Zhang & Wang (2014)
$\dots$	ASASSN-14lu	N	$0.02700$	Collobert et al. (2006)	Brimacombe et al. (2014b)	Shappee et al. (2014b)
$\dots$	ASASSN-14lv	N	$0.04919$	Jones et al. (2006)	Kiyota et al. (2014d)	Shappee et al. (2015)
$\dots$	ASASSN-14me	N	$0.01800$	Shappee et al. (2015)	Stanek et al. (2014)	Shappee et al. (2015)
$\dots$	ASASSN-15be	N	$0.02190$	Colless et al. (2003)	Brimacombe et al. (2015)	Morrell et al. (2015)
$\dots$	ASASSN-15hx	N	$0.00810$	This Work	Dong et al. (2015b)	Frohmaier et al. (2015)
$\dots$	PSN J1149a	N	$0.00560$	Meyer et al. (2004)	Vladimirov et al. (2015)	Rudy et al. (2015)
$\dots$	SN1972E	N	$0.00136$	Koribalski et al. (2004)	Kowal (1972)	Herbig et al. (1972)
$\dots$	SN1981B	N	$0.00603$	Grogin et al. (1998)	Aksenov (1981)	Vettolani et al. (1981)
$\dots$	SN1986G	91bg-like	$0.00182$	Graham et al. (1978)	Evans et al. (1986)	Feast et al. (1986)
$\dots$	SN1990N	N	$0.00340$	Meyer et al. (2004)	Maury et al. (1990)	Maury et al. (1990)
$\dots$	SN1991T	91T-like	$0.00579$	Strauss et al. (1992)	Waagen et al. (1991)	Waagen et al. (1991)
$\dots$	SN1991bg	91bg-like	$0.00339$	Cappellari et al. (2011)	Kosai et al. (1991)	Kirshner et al. (1991)
$\dots$	SN1992A	N	$0.00626$	D’Onofrio et al. (1995)	Liller et al. (1992)	Liller et al. (1992)
$\dots$	SN1993Z	N	$0.00450$	Epinat et al. (2008)	Treffers et al. (1993)	Treffers et al. (1993)
$\dots$	SN1994ae	N	$0.00427$	Krumm & Salpeter (1980)	van Dyk et al. (1994)	Iijima et al. (1994)
$\dots$	SN1995D	N	$0.00656$	Cappellari et al. (2011)	Nakano et al. (1995)	Benetti et al. (1995)
$\dots$	SN1996X	N	$0.00694$	Ogando et al. (2008)	Garradd et al. (1996)	Suntzeff et al. (1996)
$\dots$	SN1998aq	N	$0.00370$	de Vaucouleurs et al. (1991)	Hurst et al. (1998)	Ayani & Yamaoka (1998)
$\dots$	SN1998bu	N	$0.00299$	de Vaucouleurs et al. (1991)	Villi et al. (1998)	Ayani et al. (1998)
$\dots$	SN1999aa	91T-like	$0.01444$	de Vaucouleurs et al. (1991)	Armstrong & Schwartz (1999)	Filippenko et al. (1999)
$\dots$	SN1999by	91bg-like	$0.00213$	de Vaucouleurs et al. (1991)	Arbour et al. (1999)	Gerardy & Fesen (1999)
$\dots$	SN2000cx	91T-like	$0.00802$	Cappellari et al. (2011)	Yu et al. (2000)	Chornock et al. (2000)
$\dots$	SN2001el	N	$0.00389$	Koribalski et al. (2004)	Monard et al. (2001)	Sollerman et al. (2001)
$\dots$	SN2002bo	N	$0.00424$	Theureau et al. (1998)	Cacella et al. (2002)	Kawakita et al. (2002)
$\dots$	SN2002cx	Iax	$0.02396$	Falco et al. (1999)	Wood-Vasey et al. (2002a)	Matheson et al. (2002)
$\dots$	SN2002dj	N	$0.00939$	Rothberg & Joseph (2006)	Hutchings & Li (2002)	Riello et al. (2002)
$\dots$	SN2002er	N	$0.00857$	de Vaucouleurs et al. (1991)	Wood-Vasey et al. (2002b)	Smartt et al. (2002)
$\dots$	SN2003cg	N	$0.00413$	van Driel et al. (2001)	Nakano et al. (2003)	Kotak et al. (2003a)
$\dots$	SN2003du	N	$0.00638$	Schneider et al. (1992)	Schwartz & Holvorcem (2003)	Kotak et al. (2003b)
$\dots$	SN2003gs	91bg-like	$0.00477$	Smith et al. (2000)	Evans et al. (2003)	Evans et al. (2003)
$\dots$	SN2003hv	N	$0.00562$	Ogando et al. (2008)	Beutler & Li (2003)	Dressler et al. (2003)
$\dots$	SN2003kf	N	$0.00739$	Theureau et al. (1998)	Li et al. (2003b)	Li et al. (2003b)
$\dots$	SN2004S	N	$0.00936$	Theureau et al. (2007)	Martin & Biggs (2004)	Suntzeff et al. (2004)
$\dots$	SN2004eo	N	$0.01570$	Theureau et al. (1998)	Arbour et al. (2004)	Gonzalez et al. (2004)
$\dots$	SN2005W	N	$0.00889$	de Vaucouleurs et al. (1991)	Nakano et al. (2005)	Elias-Rosa et al. (2005)
$\dots$	SN2005am	N	$0.00790$	Theureau et al. (1998)	Martin et al. (2005)	Modjaz et al. (2005b)
$\dots$	SN2005cf	N	$0.00646$	de Vaucouleurs et al. (1991)	Pugh & Li (2005)	Modjaz et al. (2005a)
$\dots$	SN2005hk	Iax	$0.01299$	Abolfathi et al. (2018)	Quimby et al. (2005)	Serduke et al. (2005)
$\dots$	SN2006X	N	$0.00524$	Rand (1995)	Ponticello et al. (2006)	Quimby et al. (2006a)
$\dots$	SN2006dd	N	$0.00587$	Longhetti et al. (1998)	Quimby et al. (2006b)	Salvo et al. (2006)
$\dots$	SN2006gz	SC	$0.02800$	Falco et al. (1999)	Frieman et al. (2006)	Prieto et al. (2006)
$\dots$	SN2007af	N	$0.00546$	Koribalski et al. (2004)	Nakano & Itagaki (2007)	Salgado et al. (2007)
$\dots$	SN2007gi	N	$0.00462$	Cappellari et al. (2011)	Nakano et al. (2007)	Harutyunyan et al. (2007)
$\dots$	SN2007if	SC	$0.07416$	Scalzo et al. (2010)	Akerlof et al. (2007)	Akerlof et al. (2007)
$\dots$	SN2007le	N	$0.00672$	Koribalski et al. (2004)	Monard et al. (2007)	Filippenko et al. (2007)
$\dots$	SN2007on	N	$0.00649$	Graham et al. (1998)	Pollas & Klotz (2007)	Morrell et al. (2007)
$\dots$	SN2008A	Iax	$0.01643$	Theureau et al. (1998)	Nakano et al. (2008)	Blondin & Berlind (2008)
$\dots$	SN2008Q	N	$0.00802$	Cappellari et al. (2011)	Villi et al. (2008)	Stanishev & Pursimo (2008)
$\dots$	SN2009dc	SC	$0.02139$	Falco et al. (1999)	Puckett et al. (2009)	Harutyunyan et al. (2009)
$\dots$	SN2009ig	N	$0.00877$	Meyer et al. (2004)	Kleiser et al. (2009)	Kleiser et al. (2009)
$\dots$	SN2009le	N	$0.01779$	Theureau et al. (1998)	Pignata et al. (2009)	Challis & Berlind (2009)
$\dots$	SN2010ev	N	$0.00921$	Meyer et al. (2004)	Pignata et al. (2010)	Stritzinger (2010)
$\dots$	SN2010gp	N	$0.02450$	Downes et al. (1993)	Maza et al. (2010)	Folatelli et al. (2010b)
$\dots$	SN2010hg	N	$0.00822$	Meyer et al. (2004)	Monard & Africa (2010)	Prieto et al. (2010)
$\dots$	SN2010lp	91bg-like	$0.01015$	Huchra et al. (1999)	Cox et al. (2010)	Prieto & Morrell (2011)

Table 7. Table 8: SNe Ia light curve parameters, number of late-time spectra and the corresponding phases, ordered by t max subscript 𝑡 max t_{\rm{max}} . See § 3 for fitting methods.

SN	$t_{\max }^a$	$\Delta m_{15}\left(B\right)$	$\mu$	E(B-V)	$N_{\mathrm{spec}}$	Phase
	(MJD)	(mag)	(mag)			(days)
SN1972E	$41445.9\pm 0.4$	$0.93\pm 0.06$	$27.75\pm {0.06}^1$	$-0.03\pm 0.06$	4	$205-418$
SN1981B	$44672.7\pm 0.4$	$1.12\pm 0.06$	$30.91\pm {0.05}^2$	$0.06\pm 0.06$	1	267
SN1986G	$46561.0\pm 0.4$	$1.57\pm 0.07$	$27.82\pm {0.06}^1$	$0.91\pm 0.06$	4	$256-325$
SN1990N	$48082.5\pm 0.3$	$1.09\pm 0.06$	$31.53\pm {0.07}^2$	$0.02\pm 0.06$	5	$186-333$
SN1991T	$48374.5\pm 0.3$	$0.97\pm 0.06$	$30.67\pm {0.09}^1$	$0.17\pm 0.06$	6	$258-552$
SN1991bg	$48604.1\pm 0.4$	$1.76\pm 0.06$	$31.07\pm {0.06}^3$	$0.07\pm 0.07$	2	$198-202$
SN1992A	$48639.3\pm 0.3$	$1.27\pm 0.06$	$31.22\pm {0.06}^3$	$0.04\pm 0.06$	1	292
SN1993Z	$49247.1\pm 0.8$	$0.87\pm 0.06$	$33.10\pm 0.17$	$0.00\pm 0.06$	2	$181-213$
SN1994ae	$49685.3\pm 0.3$	$1.04\pm 0.06$	$32.07\pm {0.05}^2$	$0.05\pm 0.06$	2	$219-369$
SN1995D	$49767.4\pm 0.4$	$0.90\pm 0.06$	$32.67\pm 0.18$	$0.01\pm 0.06$	2	$278-286$
SN1996X	$50189.8\pm 0.3$	$1.20\pm 0.06$	$32.29\pm 0.25$	$-0.02\pm 0.06$	2	$247-299$
SN1998aq	$50930.8\pm 0.3$	$1.11\pm 0.07$	$31.74\pm {0.07}^2$	$0.01\pm 0.06$	3	$210-240$
SN1998bu	$50951.9\pm 0.3$	$1.05\pm 0.06$	$30.11\pm {0.06}^4$	$0.41\pm 0.06$	11	$191-341$
SN1999aa	$51232.5\pm 0.3$	$0.90\pm 0.06$	$34.19\pm 0.23$	$-0.01\pm 0.06$	2	$258-284$
SN1999by	$51308.9\pm 0.3$	$1.76\pm 0.06$	$30.75\pm {0.06}^5$	$0.05\pm 0.06$	1	185
SN2000cx	$51752.8\pm 0.3$	$1.27\pm 0.06$	$32.14\pm {0.09}^6$	$0.02\pm 0.06$	2	$182-451$
SN2001el	$52182.3\pm 0.4$	$1.12\pm 0.06$	$31.31\pm {0.05}^2$	$0.22\pm 0.06$	3	$310-398$
SN2002bo	$52356.8\pm 0.3$	$1.10\pm 0.06$	$31.73\pm {0.09}^1$	$0.36\pm 0.06$	2	$227-311$
SN2002cx	$52415.1\pm 0.3$	$1.13\pm 0.06$	$35.31\pm {0.15}^7$	$0.07\pm 0.06$	4	$232-317$
SN2002dj	$52451.3\pm 0.4$	$1.02\pm 0.08$	$33.23\pm 0.16$	$0.03\pm 0.07$	2	$220-273$
SN2002er	$52525.3\pm 0.3$	$1.23\pm 0.06$	$33.15\pm 0.17$	$0.16\pm 0.06$	1	214
SN2003cg	$52729.2\pm 0.3$	$1.14\pm 0.06$	$31.83\pm {0.10}^1$	$1.32\pm 0.06$	1	385
SN2003du	$52766.6\pm 0.3$	$1.02\pm 0.06$	$32.92\pm {0.06}^2$	$0.00\pm 0.06$	6	$194-375$
SN2003gs	$52842.2\pm 0.4$	$1.59\pm 0.06$	$32.13\pm 0.20$	$0.00\pm 0.06$	1	207
SN2003hv	$52891.5\pm 0.3$	$1.55\pm 0.06$	$31.51\pm 0.20$	$0.00\pm 0.06$	2	$319-393$
SN2003kf	$52980.3\pm 0.3$	$1.03\pm 0.06$	$32.43\pm {0.10}^1$	$-0.03\pm 0.06$	1	401
SN2004S	$53039.7\pm 0.4$	$1.06\pm 0.06$	$33.41\pm 0.18$	$0.00\pm 0.06$	1	315
SN2004eo	$53278.7\pm 0.3$	$1.31\pm 0.06$	$34.03\pm 0.15$	$0.01\pm 0.06$	1	227
SN2005W	$53412.6\pm 0.3$	$1.02\pm 0.06$	$33.01\pm 0.20$	$0.23\pm 0.06$	1	213
SN2005am	$53435.0\pm 0.3$	$1.30\pm 0.06$	$32.66\pm 0.17$	$0.03\pm 0.06$	2	$300-383$
SN2005cf	$53534.3\pm 0.3$	$1.11\pm 0.06$	$32.26\pm {0.10}^2$	$-0.02\pm 0.06$	4	$266-383$
SN2005hk	$53684.8\pm 0.3$	$1.58\pm 0.10$	$33.91\pm {0.15}^7$	$\dots$	2	$378-408$
SN2006X	$53786.3\pm 0.3$	$1.08\pm 0.06$	$30.72\pm {0.06}^1$	$1.38\pm 0.06$	3	$277-360$
SN2006dd	$53918.6\pm 0.3$	$1.05\pm 0.06$	$31.52\pm 0.13$	$0.00\pm 0.06$	2	$188-195$
SN2006gz	$54021.7\pm 0.1$	$0.88\pm 0.06$	$35.22\pm {0.15}^7$	$0.20\pm 0.06$	1	339
SN2007af	$54174.0\pm 0.3$	$1.08\pm 0.06$	$31.79\pm {0.05}^2$	$0.12\pm 0.06$	1	302
SN2007gi	$54327.9\pm 0.3$	$1.21\pm 0.06$	$32.17\pm 0.12$	$0.12\pm 0.06$	1	223
SN2007if	$54340.3\pm 0.4$	$0.88\pm 0.06$	$37.55\pm {0.15}^7$	$-0.03\pm 0.06$	2	$393-421$
SN2007le	$54399.0\pm 0.3$	$1.05\pm 0.06$	$32.44\pm 0.10$	$0.30\pm 0.06$	1	307
SN2007on	$54419.8\pm 0.3$	$1.81\pm 0.06$	$31.34\pm {0.07}^3$	$\dots$	3	$286-381$
SN2008A	$54478.0\pm 0.4$	$1.55\pm 0.09$	$34.26\pm {0.15}^7$	$\dots$	3	$204-288$
SN2008Q	$54505.6\pm 0.3$	$1.09\pm 0.06$	$32.66\pm 0.18$	$0.06\pm 0.06$	1	200
SNF-012	$54682.1\pm 1.1$	$1.29\pm 0.16$	$37.66\pm {0.15}^7$	$\dots$	3	$265-319$
SN2009dc	$54946.4\pm 0.4$	$0.80\pm 0.06$	$35.07\pm {0.15}^7$	$\dots$	2	$287-380$
SN2009ig	$55080.1\pm 0.3$	$0.88\pm 0.06$	$32.50\pm {0.08}^2$	$0.12\pm 0.06$	1	405
SN2009le	$55165.6\pm 0.4$	$0.91\pm 0.06$	$34.47\pm 0.17$	$0.20\pm 0.06$	1	317
SN2010ev	$55384.8\pm 0.3$	$1.12\pm 0.06$	$33.47\pm 0.20$	$0.19\pm 0.06$	1	270
SN2010gp	$55406.0\pm 0.4$	$1.10\pm 0.06$	$34.61\pm 0.36$	$0.44\pm 0.08$	1	276
SN2010hg	$55451.0\pm 5.0$	$\dots$	$32.82\pm {0.50}^8$	$\dots$	1	203
SN2010lp	$55568.0\pm 5.0$	$\dots$	$33.04\pm {0.40}^8$	$\dots$	1	264
SN2011K	$55577.9\pm 0.3$	$1.30\pm 0.06$	$33.95\pm 0.09$	$0.01\pm 0.06$	1	344
SNhunt37	$55620.1\pm 0.6$	$1.03\pm 0.07$	$32.16\pm 0.08$	$0.05\pm 0.13$	1	306
SN2011at	$55625.0\pm 0.4$	$0.92\pm 0.06$	$32.63\pm 0.16$	$0.17\pm 0.06$	1	359
SN2011by	$55690.5\pm 0.5$	$1.11\pm 0.08$	$31.59\pm {0.07}^2$	$0.09\pm 0.07$	1	207
SN2011ek	$55788.8\pm 0.4$	$1.00\pm 0.07$	$32.47\pm 0.44$	$0.59\pm 0.06$	1	422
PTF11kly	$55815.1\pm 0.3$	$1.18\pm 0.06$	$29.14\pm {0.05}^2$	$0.04\pm 0.06$	9	$204-346$
SN2011iy	$55893.2\pm 0.4$	$1.03\pm 0.08$	$31.33\pm 0.17$	$0.25\pm 0.06$	1	205
SN2011im	$55902.3\pm 0.4$	$1.06\pm 0.07$	$34.83\pm 0.15$	$0.11\pm 0.06$	1	313
SN2011iv	$55906.0\pm 0.3$	$1.63\pm 0.05$	$31.53\pm {0.07}^9$	$0.01\pm 0.06$	5	$244-304$
SN2012Z	$55967.7\pm 0.1$	$1.43\pm 0.01$	$32.52\pm {0.06}^2$	$\dots$	4	$193-254$

Table 8. Table 10: Spectra observations.

SN	Obs. Date	Phasea	Telescopeb	Instrumentb	Range	Expt.	$v_{exp}$	Qual.	Ref.
	(MJD)	(days)			(Å)	(s)	[km s-1]
SN1972E	41651.00	205.1	P200	DBSP	$4000-10000$	$\dots$	$5100\pm 800$	Med	Kirshner & Oke (1975)
	41682.00	236.1	P200	DBSP	$3300-10300$	$\dots$	$5900\pm 400$	Med	Kirshner & Oke (1975)
	41795.00	349.1	P200	DBSP	$3400-10200$	$\dots$	$6300\pm 100$	Med	Kirshner & Oke (1975)
	41864.00	418.1	P200	DBSP	$3400-9200$	$\dots$	$6600\pm 200$	Med	Kirshner & Oke (1975)
SN1981B	44940.00	267.3	HJST	UVITS	$3400-7100$	$3600$	$6200\pm 300$	Med	Branch et al. (1993)
SN1986G	46816.50	255.5	ESO2.2m	BC	$4500-6800$	$\dots$	$5500\pm 100$	Med	Cristiani et al. (1992)
	46817.50	256.5	ESO3.6m	EFOSC	$3700-9500$	$\dots$	$4900\pm 100$	High	Cristiani et al. (1992)
	46818.50	257.5	ESO3.6m	EFOSC	$4000-9300$	$\dots$	$5000\pm 200$	High	Cristiani et al. (1992)
	46885.50	324.5	ESO3.6m	EFOSC	$3800-7000$	$\dots$	$5100\pm 400$	Med	Cristiani et al. (1992)
SN1990N	48268.50	186.0	WHT	FOS	$3400-9700$	$1880$	$5000\pm 700$	High	Gomez et al. (1996)
	48309.50	227.0	WHT	FOS	$3500-9700$	$1800$	$5800\pm 600$	High	Gomez et al. (1996)
	48337.50	255.0	WHT	FOS	$3500-9700$	$1800$	$5800\pm 800$	Med	Gomez et al. (1996)
	48362.50	280.0	WHT	FOS	$3500-9700$	$1800$	$5500\pm 500$	Med	Gomez et al. (1996)
	48415.50	333.0	WHT	FOS	$3600-9700$	$2000$	$6100\pm 400$	Med	Gomez et al. (1996)
SN1991T	48632.50	258.0	WHT	ISIS	$3200-8500$	$1800$	$7100\pm 400$	High	Gomez et al. (1996)
	48658.50	284.0	INT	FOS1	$3800-8800$	$3600$	$6500\pm 100$	Med	Gomez et al. (1996)
	48690.50	316.0	INT	FOS1	$3800-9900$	$1800$	$6200\pm 1000$	Med	Gomez et al. (1996)
	48694.93	320.4	Shane3m	KAST	$3300-10100$	$3600$	$6500\pm 700$	Med	BSNIP
	48723.86	349.3	Shane3m	KAST	$3300-10400$	$3600$	$6600\pm 200$	Med	BSNIP
SN1991bg	48802.50	198.4	WHT	FOS2	$4900-9700$	$2000$	$\left(\mathrm{3\hspace{0.17em}000}\right)$	Low	Gomez et al. (1996)
	48806.50	202.4	ESO3.6m	EFOSC2	$3800-6800$	$\dots$	$1100\pm 100$	Med	Turatto et al. (1996)
SN1992A	48931.00	291.7	HST	FOS	$1600-4800$	$2000$	$\left(\mathrm{3\hspace{0.17em}000}\right)$	Low	Kirshner et al. (1993)
SN1993Z	49428.50	181.4	Shane3m	KAST	$3100-10300$	$1800$	$6700\pm 400$	Med	BSNIP
	49460.00	212.9	Shane3m	KAST	$3100-10400$	$2700$	$6200\pm 800$	Med	BSNIP
SN1994ae	49904.71	219.4	Shane3m	KAST	$3600-10400$	$1800$	$5900\pm 500$	Med	BSNIP
	50053.97	368.7	MMT	BCS	$3200-8600$	$1200$	$6000\pm 200$	Med	CfA
SN1995D	50045.00	277.6	MMT	BCS	$3200-8200$	$1200$	$7000\pm 200$	Med	CfA
	50053.00	285.6	MMT	BCS	$3200-8800$	$1200$	$5800\pm 400$	Med	CfA
SN1996X	50437.00	247.2	ESO1.5m	BC	$3500-9200$	$\dots$	$4100\pm 100$	Low	Salvo et al. (2001)
	50489.00	299.2	ESO3.6m	EFOSC2	$3700-6900$	$\dots$	$6200\pm 200$	High	Salvo et al. (2001)
SN1998aq	51141.00	210.2	Till	FAST	$3700-7500$	$2100$	$5900\pm 300$	Med	CfA
	51161.00	230.2	Till	FAST	$3700-7500$	$2400$	$6100\pm 100$	Med	CfA
	51171.00	240.2	Till	FAST	$3700-7500$	$2400$	$6200\pm 300$	Med	CfA
SN1998bu	51143.04	191.2	Till	FAST	$3700-7500$	$2400$	$6000\pm 500$	High	CfA
	51161.04	209.2	Till	FAST	$3700-7500$	$2400$	$6200\pm 200$	High	CfA
	51169.98	218.1	Till	FAST	$3700-7500$	$2400$	$6100\pm 200$	Med	CfA
	51188.88	237.0	Shane3m	KAST	$3400-10200$	$1800$	$6300\pm 200$	High	BSNIP
	51195.96	244.1	Till	FAST	$3700-7500$	$2400$	$6100\pm 200$	Med	CfA
	51201.96	250.1	D1.54m	DFOSC	$3000-8500$	$\dots$	$6300\pm 1500$	Med	Cappellaro et al. (2001)
	51204.96	253.1	NTT	SOFI	$9400-25400$	$4800$	$3000\pm 700$	Med	Spyromilio et al. (2004)
	51232.92	281.0	Shane3m	KAST	$3400-10500$	$1800$	$6100\pm 100$	High	BSNIP
	51281.50	329.6	ESO3.6m	EFOSC2	$3400-7500$	$\dots$	$5900\pm 100$	Med	Cappellaro et al. (2001)
	51292.78	340.9	Shane3m	KAST	$3300-10500$	$1800$	$6400\pm 200$	Med	BSNIP
SN1999aa	51491.00	258.5	KeckI	LRIS	$4100-9500$	$600$	$5700\pm 1400$	Med	BSNIP
	51517.00	284.5	KeckI	LRIS	$3900-9900$	$600$	$6500\pm 100$	Med	BSNIP
SN1999by	51494.14	185.2	KeckI	LRIS	$4000-9700$	$100$	$2100\pm 900$	High	BSNIP
SN2000cx	51935.00	182.2	MMT	BCS	$3700-7100$	$2400$	$6300\pm 200$	Med	CfA
	52204.00	451.2	KeckII	ESI	$3900-10100$	$1800$	$11300\pm 1000$	Low	BSNIP
SN2001el	52492.40	310.1	VLT	FORS1	$6200-10000$	$1500$	$\left(\mathrm{3\hspace{0.17em}000}\right)$	Med	PI-Sollerman
	52500.35	318.1	VLT	FORS1	$6200-10000$	$2400$	$\left(\mathrm{3\hspace{0.17em}000}\right)$	Med	PI-Sollerman
	52580.15	397.9	VLT	FORS1	$3800-9300$	$3000$	$5300\pm 800$	Med	Mattila et al. (2005)
SN2002bo	52584.00	227.2	KeckII	ESI	$4000-10100$	$240$	$\left(\mathrm{3\hspace{0.17em}000}\right)$	low	BSNIP
	52668.00	311.2	MMT	BCS	$3200-8700$	$3600$	$5800\pm 400$	Med	Blondin et al. (2012)
SN2002cx	52647.15	232.1	KeckI	LRIS	$3200-9200$	$1800$	$\left(\mathrm{3\hspace{0.17em}000}\right)$	Low	BSNIP
	52699.11	284.0	KeckI	LRIS	$3100-9200$	$2200$	$\left(\mathrm{3\hspace{0.17em}000}\right)$	Low	BSNIP
	52699.14	284.1	KeckI	LRIS	$6100-7300$	$2200$	$\left(\mathrm{3\hspace{0.17em}000}\right)$	Low	BSNIP
	52731.81	316.7	Clay	LDSS	$3600-9300$	$3600$	$\left(\mathrm{3\hspace{0.17em}000}\right)$	Low	CfA
SN2002dj	52671.00	219.7	NTT	EFOSC2	$3400-7400$	$\dots$	$6400\pm 400$	Med	Pignata et al. (2008)
	52724.00	272.7	VLT	FORS1	$3600-8500$	$\dots$	$6500\pm 300$	Med	Pignata et al. (2008)

Table 9. Table 14: Flux limits for each line in Table 2 and the corresponding H/He mass limit.

	H-rich Model				He-rich Model
SN	Phasea	Lineb	Flux Limit	Mass Limit	Phasea	Lineb	Flux Limit	Mass Limit
	(days)		(erg/s/cm2)	($M_{\odot }$)	(days)		(erg/s/cm2)	($M_{\odot }$)
SN1972E	418.1	H$\alpha$	$2.52\times {10}^{-16}$	$4.95\times {10}^{-5}$	349.1	HeI-a	$3.07\times {10}^{-17}$	$9.84\times {10}^{-5}$
SN1981B	267.3	H$\alpha$	$5.54\times {10}^{-16}$	$1.49\times {10}^{-3}$	267.3	HeI-a	$5.86\times {10}^{-16}$	$2.25\times {10}^{-3}$
SN1986G	324.5	H$\alpha$	$1.68\times {10}^{-15}$	$2.84\times {10}^{-4}$	256.5	HeI-b	$6.57\times {10}^{-16}$	$5.29\times {10}^{-4}$
SN1990N	280.0	H$\alpha$	$9.52\times {10}^{-17}$	$5.68\times {10}^{-4}$	280.0	HeI-a	$2.35\times {10}^{-16}$	$1.53\times {10}^{-3}$
SN1991T	258.0	H$\alpha$	$1.99\times {10}^{-14}$	$4.78\times {10}^{-2}$	349.3	HeI-a	$4.84\times {10}^{-14}$	$>2.0$
SN1991bg	202.4	H$\alpha$	$1.81\times {10}^{-16}$	$1.26\times {10}^{-3}$	202.4	HeI-b	$1.35\times {10}^{-16}$	$2.39\times {10}^{-3}$
SN1992A	291.7	H$\gamma$	$1.87\times {10}^{-15}$	$2.91\times {10}^{-1}$	$\dots$	$\dots$	$\dots$	$\dots$
SN1993Z	212.9	H$\alpha$	$8.16\times {10}^{-16}$	$2.68\times {10}^{-2}$	212.9	HeI-b	$5.07\times {10}^{-16}$	$1.20\times {10}^{-1}$
SN1994ae	368.7	H$\alpha$	$5.58\times {10}^{-17}$	$2.84\times {10}^{-4}$	368.7	HeI-a	$6.44\times {10}^{-17}$	$4.20\times {10}^{-4}$
SN1995D	285.6	H$\beta$	$1.50\times {10}^{-16}$	$2.30\times {10}^{-3}$	285.6	HeI-a	$2.57\times {10}^{-16}$	$3.69\times {10}^{-3}$
SN1996X	247.2	H$\alpha$	$5.55\times {10}^{-17}$	$8.24\times {10}^{-4}$	247.2	HeI-a	$6.36\times {10}^{-17}$	$1.28\times {10}^{-3}$
SN1998aq	240.2	H$\alpha$	$7.75\times {10}^{-16}$	$4.84\times {10}^{-3}$	230.2	HeI-a	$8.05\times {10}^{-16}$	$1.40\times {10}^{-2}$
SN1998bu	329.6	H$\alpha$	$2.18\times {10}^{-16}$	$2.86\times {10}^{-4}$	281.0	HeI-b	$1.41\times {10}^{-16}$	$6.45\times {10}^{-4}$
SN1999aa	258.5	H$\alpha$	$5.41\times {10}^{-17}$	$2.82\times {10}^{-3}$	258.5	HeI-a	$4.89\times {10}^{-17}$	$3.85\times {10}^{-3}$
SN1999by	185.2	H$\alpha$	$3.05\times {10}^{-16}$	$1.74\times {10}^{-3}$	185.2	HeI-b	$2.04\times {10}^{-16}$	$3.11\times {10}^{-3}$
SN2000cx	451.2	H$\alpha$	$7.44\times {10}^{-16}$	$8.94\times {10}^{-4}$	451.2	HeI-a	$6.91\times {10}^{-16}$	$>2.0$
SN2001el	318.1	H$\alpha$	$6.84\times {10}^{-17}$	$3.00\times {10}^{-4}$	310.1	HeI-b	$2.25\times {10}^{-17}$	$4.82\times {10}^{-4}$
SN2002bo	311.2	H$\alpha$	$3.35\times {10}^{-17}$	$3.03\times {10}^{-4}$	227.2	HeI-a	$3.41\times {10}^{-17}$	$6.66\times {10}^{-4}$
SN2002cx	284.0	H$\beta$	$1.47\times {10}^{-17}$	$2.55\times {10}^{-3}$	232.1	HeI-a	$2.30\times {10}^{-17}$	$2.19\times {10}^{-2}$
SN2002dj	272.7	H$\alpha$	$9.53\times {10}^{-17}$	$1.91\times {10}^{-3}$	272.7	HeI-a	$8.24\times {10}^{-17}$	$2.47\times {10}^{-3}$
SN2002er	213.7	H$\alpha$	$7.59\times {10}^{-15}$	$>2.0$	213.7	HeI-a	$7.23\times {10}^{-15}$	$>2.0$
SN2003cg	384.8	H$\alpha$	$2.35\times {10}^{-14}$	$3.52\times {10}^{-2}$	384.8	HeI-a	$2.12\times {10}^{-14}$	$>2.0$
SN2003du	296.4	Pa$\beta$	$2.28\times {10}^{-15}$	$1.00\times {10}^{-2}$	219.4	HeI-b	$9.18\times {10}^{-16}$	$1.16\times {10}^{-1}$
SN2003gs	207.1	H$\alpha$	$5.65\times {10}^{-17}$	$1.05\times {10}^{-3}$	207.1	HeI-b	$3.77\times {10}^{-17}$	$1.80\times {10}^{-3}$
SN2003hv	319.5	H$\alpha$	$2.58\times {10}^{-17}$	$1.82\times {10}^{-4}$	319.5	HeI-a	$6.89\times {10}^{-17}$	$4.54\times {10}^{-4}$
SN2003kf	400.7	H$\beta$	$2.29\times {10}^{-17}$	$2.54\times {10}^{-4}$	400.7	HeI-a	$1.47\times {10}^{-17}$	$1.96\times {10}^{-4}$
SN2004S	315.3	H$\alpha$	$9.10\times {10}^{-17}$	$1.43\times {10}^{-3}$	315.3	HeI-a	$1.26\times {10}^{-16}$	$2.69\times {10}^{-3}$
SN2004eo	227.3	H$\alpha$	$2.24\times {10}^{-15}$	$7.38\times {10}^{-1}$	227.3	HeI-a	$2.78\times {10}^{-15}$	$>2.0$
SN2005W	213.4	Pa$\beta$	$5.28\times {10}^{-16}$	$6.59\times {10}^{-3}$	$\dots$	$\dots$	$\dots$	$\dots$
SN2005am	383.0	H$\alpha$	$2.17\times {10}^{-17}$	$2.00\times {10}^{-4}$	300.0	HeI-a	$3.50\times {10}^{-17}$	$1.05\times {10}^{-3}$
SN2005cf	352.7	H$\alpha$	$2.27\times {10}^{-17}$	$2.76\times {10}^{-4}$	265.7	HeI-a	$4.62\times {10}^{-17}$	$8.51\times {10}^{-4}$
SN2005hk	407.9	H$\alpha$	$1.48\times {10}^{-17}$	$2.69\times {10}^{-4}$	407.9	HeI-a	$1.44\times {10}^{-17}$	$3.56\times {10}^{-4}$
SN2006X	359.7	H$\alpha$	$4.13\times {10}^{-18}$	$3.43\times {10}^{-5}$	359.7	HeI-a	$3.51\times {10}^{-18}$	$4.01\times {10}^{-5}$
SN2006dd	194.7	H$\alpha$	$1.64\times {10}^{-14}$	$9.86\times {10}^{-1}$	187.7	HeI-a	$2.63\times {10}^{-14}$	$>2.0$
SN2006gz	339.0	H$\alpha$	$3.22\times {10}^{-17}$	$1.89\times {10}^{-3}$	339.0	HeI-a	$8.49\times {10}^{-18}$	$9.77\times {10}^{-4}$
SN2007af	302.0	H$\alpha$	$2.49\times {10}^{-16}$	$1.11\times {10}^{-3}$	302.0	HeI-a	$1.24\times {10}^{-16}$	$9.36\times {10}^{-4}$
SN2007gi	223.1	H$\alpha$	$5.25\times {10}^{-17}$	$8.94\times {10}^{-4}$	223.1	HeI-b	$5.32\times {10}^{-17}$	$2.10\times {10}^{-3}$
SN2007if	420.9	H$\beta$	$1.95\times {10}^{-18}$	$7.88\times {10}^{-4}$	420.9	HeI-a	$3.48\times {10}^{-18}$	$1.23\times {10}^{-3}$
SN2007le	306.5	H$\beta$	$4.99\times {10}^{-16}$	$4.34\times {10}^{-3}$	306.5	HeI-a	$3.72\times {10}^{-16}$	$3.42\times {10}^{-3}$
SN2007on	380.7	H$\alpha$	$2.79\times {10}^{-18}$	$3.33\times {10}^{-5}$	285.6	HeI-a	$3.33\times {10}^{-18}$	$3.64\times {10}^{-4}$
SN2008A	288.3	H$\alpha$	$2.96\times {10}^{-17}$	$1.40\times {10}^{-3}$	288.3	HeI-a	$3.32\times {10}^{-17}$	$2.20\times {10}^{-3}$
SN2008Q	200.4	H$\alpha$	$1.13\times {10}^{-16}$	$2.82\times {10}^{-3}$	200.4	HeI-b	$1.18\times {10}^{-16}$	$8.04\times {10}^{-3}$
SNF-012	319.4	H$\alpha$	$8.08\times {10}^{-18}$	$4.72\times {10}^{-3}$	265.4	HeI-a	$9.07\times {10}^{-18}$	$1.58\times {10}^{-2}$
SN2009dc	379.8	Pa$\beta$	$8.00\times {10}^{-18}$	$2.72\times {10}^{-4}$	287.2	HeI-a	$1.32\times {10}^{-17}$	$2.91\times {10}^{-3}$
SN2009ig	405.1	H$\alpha$	$1.18\times {10}^{-17}$	$1.10\times {10}^{-4}$	405.1	HeI-a	$1.82\times {10}^{-17}$	$1.87\times {10}^{-4}$
SN2009le	316.5	H$\alpha$	$6.89\times {10}^{-17}$	$2.45\times {10}^{-3}$	316.5	HeI-a	$1.29\times {10}^{-16}$	$6.42\times {10}^{-3}$
SN2010ev	270.2	H$\beta$	$6.34\times {10}^{-17}$	$2.39\times {10}^{-3}$	270.2	HeI-b	$1.70\times {10}^{-17}$	$1.44\times {10}^{-3}$
SN2010gp	276.2	H$\alpha$	$6.51\times {10}^{-18}$	$6.47\times {10}^{-4}$	276.2	HeI-a	$1.14\times {10}^{-17}$	$1.36\times {10}^{-3}$
SN2010hg	203.2	H$\alpha$	$3.55\times {10}^{-16}$	$8.95\times {10}^{-3}$	203.2	HeI-b	$7.22\times {10}^{-17}$	$5.61\times {10}^{-3}$
SN2010lp	264.0	H$\beta$	$2.00\times {10}^{-16}$	$4.88\times {10}^{-3}$	264.0	HeI-a	$1.87\times {10}^{-16}$	$4.70\times {10}^{-3}$
SN2011K	344.2	H$\beta$	$6.35\times {10}^{-17}$	$1.73\times {10}^{-3}$	344.2	HeI-a	$1.11\times {10}^{-16}$	$2.77\times {10}^{-3}$
SNhunt37	306.2	H$\beta$	$1.01\times {10}^{-16}$	$9.84\times {10}^{-4}$	306.2	HeI-a	$1.05\times {10}^{-16}$	$1.03\times {10}^{-3}$
SN2011at	359.1	H$\beta$	$1.54\times {10}^{-16}$	$1.17\times {10}^{-3}$	359.1	HeI-a	$2.87\times {10}^{-16}$	$1.93\times {10}^{-3}$
SN2011by	207.1	H$\alpha$	$2.60\times {10}^{-16}$	$2.33\times {10}^{-3}$	207.1	HeI-b	$1.75\times {10}^{-16}$	$4.28\times {10}^{-3}$
SN2011ek	422.4	H$\alpha$	$4.24\times {10}^{-17}$	$2.06\times {10}^{-4}$	422.4	HeI-a	$8.19\times {10}^{-17}$	$4.19\times {10}^{-4}$
PTF11kly	228.9	H$\alpha$	$3.70\times {10}^{-15}$	$2.63\times {10}^{-3}$	228.9	HeI-a	$8.68\times {10}^{-15}$	$8.74\times {10}^{-3}$
SN2011iy	204.9	H$\alpha$	$8.11\times {10}^{-16}$	$5.19\times {10}^{-3}$	204.9	HeI-b	$7.12\times {10}^{-16}$	$1.38\times {10}^{-2}$
SN2011im	313.3	H$\beta$	$5.13\times {10}^{-17}$	$3.79\times {10}^{-3}$	313.3	HeI-a	$8.73\times {10}^{-17}$	$6.30\times {10}^{-3}$

Table 10. Table 16: New photometry presented in this study. Some data stem from archival images processed by this study for flux calibration purposes.

SN	MJD	Filter	AB Mag
ASASSN-14jg	57183.78	V	$20.49\pm 0.08$
ASASSN-15hx	57396.33	V	$21.33\pm 0.04$
SN2001el	52492.37	I	$19.82\pm 0.07$
SN2001el	52549.24	I	$20.24\pm 0.07$
SN2001el	52552.37	I	$20.23\pm 0.08$
SN2001el	52618.04	I	$22.08\pm 0.15$
SN2001el	52492.36	R	$20.68\pm 0.10$
SN2001el	52549.23	R	$21.47\pm 0.08$
SN2001el	52552.35	R	$21.34\pm 0.08$
SN2001el	52612.04	R	$22.31\pm 0.10$
SN2001el	52617.10	R	$22.16\pm 0.10$
SN2001el	52492.35	V	$19.93\pm 0.09$
SN2001el	52549.22	V	$20.76\pm 0.09$
SN2001el	52552.34	V	$20.55\pm 0.08$
SN2001el	52612.10	V	$21.02\pm 0.15$
SN2007on	54800.23	r	$24.70\pm 0.35$
SN2007on	54772.70	r	$24.15\pm 0.14$
SN2009ig	55484.29	I	$22.39\pm 0.07$
SN2009ig	55484.28	R	$22.53\pm 0.08$
SN2009ig	55484.28	V	$22.09\pm 0.06$
SN2009le	55484.30	V	$21.88\pm 0.18$
SN2009le	55484.31	I	$21.79\pm 0.45$
SN2009le	55484.31	R	$21.47\pm 0.35$
SN2010ev	55655.00	V	$20.41\pm 0.07$
SN2010ev	55655.00	R	$20.58\pm 0.08$
SN2010ev	55655.00	I	$20.65\pm 0.07$
SN2010ev	55655.00	B	$20.22\pm 0.05$
SN2010gp	55682.27	V	$23.19\pm 0.06$
SN2010gp	55682.27	R	$23.09\pm 0.11$
SN2010gp	55682.28	I	$22.76\pm 0.11$
SN2010gp	55682.26	B	$22.16\pm 0.22$
SN2010hg	55654.15	B	$19.15\pm 0.11$
SN2010hg	55654.15	V	$19.35\pm 0.07$
SN2010hg	55654.15	R	$20.05\pm 0.06$
SN2010hg	55654.15	I	$20.06\pm 0.08$
SN2010lp	55834.24	V	$20.66\pm 0.16$
SN2010lp	55834.26	I	$19.50\pm 0.09$
SN2010lp	55834.25	R	$20.09\pm 0.07$
SN2011K	55831.38	I	$21.69\pm 0.06$
SN2011K	55831.37	R	$21.59\pm 0.05$
SN2011K	55831.36	V	$22.41\pm 0.09$
SNhunt37	55932.34	V	$20.98\pm 0.11$
SNhunt37	55932.34	R	$20.25\pm 0.15$
SNhunt37	55932.34	I	$19.89\pm 0.12$
SN2011at	55943.18	I	$20.13\pm 0.06$
SN2011at	55943.18	R	$20.17\pm 0.05$
SN2011at	55943.18	V	$21.02\pm 0.06$
SN2011ek	56210.20	V	$23.07\pm 0.17$
SN2011ek	56210.20	R	$21.95\pm 0.12$
SN2011ek	56210.21	I	$21.62\pm 0.12$
SN2011im	56213.03	I	$21.05\pm 0.07$
SN2011im	56213.02	R	$21.37\pm 0.08$
SN2011im	56206.08	R	$20.77\pm 0.08$
SN2011im	56213.01	V	$22.84\pm 0.11$
SN2011im	56206.08	V	$22.11\pm 0.09$
SN2011iv	56207.29	I	$17.55\pm 0.13$
SN2011iv	56207.29	R	$18.08\pm 0.11$
SN2011iv	56207.29	V	$17.49\pm 0.11$
SN2012cg	56444.99	I	$19.49\pm 0.11$
SN2012cg	56444.99	R	$18.40\pm 0.09$
SN2012cg	56444.99	V	$20.76\pm 0.10$
SNhunt136	56423.19	I	$21.50\pm 0.13$
SNhunt136	56423.19	R	$21.67\pm 0.12$
SNhunt136	56423.18	V	$22.06\pm 0.12$
SN2012ei	56414.88	r	$20.54\pm 0.11$
SN2013gy	56883.41	R	$23.50\pm 0.27$
SN2014bv	57134.16	g	$20.91\pm 0.06$

Table 11. Table 18: Photometry data for each SN Ia studied in this work. N t ​ o ​ t subscript 𝑁 𝑡 𝑜 𝑡 N_{tot} refers to the total number of photometric points for a given SN. Phases are given relative to maximum light. Objects denoted with a ⋆ are used in deriving the NPPR (Appendix A ).

SN	$N_{tot}$	Phases	Filters	Refs.
ASASSN-14jg⋆	113	$5-268$	B, V, g, r, i	ASAS-SN; Graham et al. (2017); This work
ASASSN-15hx	202	$-16-325$	V, g, i, SwiftU, SwiftB, SwiftV	ASAS-SN; This work
PSN J1149	16	$-12-141$	B, V, I	ASAS-SN
SN1972E⋆	468	$-23-359$	U, B, V, R, I	Przybylski (1972); Cousins (1972); Barbon et al. (1972); Ardeberg & de Groot (1973); van Genderen (1975); Osmer et al. (1972); Lee et al. (1972); Frye et al. (1972); Przybylski (1972)
SN1980N⋆	238	$-11-368$	U, B, V, R, I, H	Hamuy et al. (1991); Blanco et al. (1980); Blanco et al. (1980); Olszewski (1982); Elias & Frogel (1983)
SN1981B	281	$-9-136$	U, B, V, R, J, H, K	Busko et al. (1981); Tsvetkov (1982); Buta & Turner (1983); Tsvetkov (1982); Barbon et al. (1982); Vettolani et al. (1981); Elias & Frogel (1983)
SN1981D⋆	30	$-14-274$	B, V, J, H	Cragg et al. (1981); Hamuy et al. (1991); Elias & Frogel (1983)
SN1983W⋆	57	$-7-161$	U, B, V
SN1986G	93	$-7-403$	U, B, V, R, I	Munch et al. (1986); Phillips et al. (1987); Bues et al. (1986); Blanco et al. (1986); Turatto et al. (1990); Schaefer (1987)
SN1989B⋆	350	$-5-263$	U, B, V, R, I, J, H, K	Barbon et al. (1990); Suntzeff et al. (1989); Lavery (1989); Tsvetkov et al. (1990); Wells et al. (1994); Pollas et al. (1989); Volkov (1991); Gaskell et al. (1989)
SN1990N⋆	289	$-12-376$	U, B, V, R, I	Lira et al. (1998)

Equations

$$\log_{10}L(M,t)=\log_{10}L_{200}+0.17M\\ -0.20M^{2}-\Big{(}\frac{t-t_{0}}{200~{}\hbox{days}}-1\Big{)}$$

$$F(10\sigma )\equiv EW(10\sigma )\times C_{\lambda }=10C_{\lambda }\Delta I\sqrt{W_{\mathrm{line}}\Delta X}$$

$$F(10\sigma )=10\Delta f_{\lambda }{\mathcal{F}}^{-1}\sqrt{W_{\mathrm{line}}\Delta X}$$

$$f<1-(1-P{)}^{(N+1{)}^{-1}}$$

$$m_{\lambda ,\mathrm{neb}}(t_p)=m_{\lambda ,\max }+\Delta m_{\lambda }(t_p),$$

$$\Delta m_{\lambda }=A_{\lambda }(\Delta m_{15})\times (t_p-250\mathrm{d})+{\mathrm{B}}_{\lambda }(\mathrm{\Delta }{\mathrm{m}}_{15}),$$

$$A_{\lambda }(\Delta m_{15})=a_{\lambda }(\Delta m_{15}-1.1\mathrm{mag})+{\mathrm{b}}_{\lambda },$$

$$B_{\lambda }(\Delta m_{15})=c_{\lambda }(\Delta m_{15}-1.1\mathrm{mag})+{\mathrm{d}}_{\lambda }.$$

Full text

††pubyear: 2019††pagerange: Nebular Spectra of 111 Type Ia Supernovae Disfavor Single Degenerate Progenitors–b

1 Introduction

Type Ia supernovae (SNe Ia) are utilised across many astronomical disciplines, including the extragalactic distance scale, dark energy studies, and Galactic chemical evolution. Despite their prevalence, the origins of SNe Ia are still unclear even after decades of study. The general consensus is that they are explosions of carbon/oxygen (C/O) white dwarfs (Hoyle & Fowler, 1960) with fairly homogeneous properties. For example, the magnitude of SNe Ia at peak is well constrained ($M_{\rm{max}}\sim-19$, e.g.; Folatelli et al., 2010a), and, after correcting for light curve decline and color, they have an intrinsic scatter of $\sim 0.1$ mag (e.g., Fig. 19, Folatelli et al., 2010a). Many formation mechanisms for SNe Ia have been proposed to reproduce this level of uniformity, which can be grouped into two main categories: the double degenerate (DD) and single degenerate (SD) scenarios (see Maoz et al., 2014; Livio & Mazzali, 2018; Jha et al., 2019, for reviews on SNe Ia and their progenitors).

The DD scenario consists of two degenerate stars, usually C/O white dwarfs, which induce a SNe Ia through accretion, collision, or merger. This can occur due to gravitational wave emission (Tutukov & Yungelson, 1979; Iben & Tutukov, 1984; Webbink, 1984), collision/violent merger due to perturbations by external bodies (Thompson, 2011; Katz & Dong, 2012; Shappee & Thompson, 2013; Pejcha et al., 2013; Antognini et al., 2014), accretion from a low-mass white dwarf onto a smaller, higher-mass white dwarf (Taam, 1980; Livne, 1990; Tutukov & Yungelson, 1996; Pakmor et al., 2012), or a "double detonation" where an accreted helium layer detonates and drives the core to detonate (Woosley & Weaver, 1994; Fink et al., 2010; Kromer et al., 2010). Due to the intrinsic faintness of both components in these systems, observational confirmation of DD systems is exceptionally difficult (e.g., Rebassa-Mansergas et al., 2018). Some progress has been made on this front, such as bimodal emission in the nebular phase (Dong et al., 2015a; Vallely et al., 2019a) and possible hyper-velocity remnants (Shen et al., 2018; Ruffini & Casey, 2019). However, most of the evidence for DD systems comes from the exclusion of SD progenitors (e.g., Shappee et al., 2017).

The SD scenario involves a WD with a nearby non-degenerate companion (Whelan & Iben, 1973; Nomoto, 1982; Yoon & Langer, 2003), usually undergoing Roche Lobe overflow (RLOF). The WD accumulates material until reaching critical mass and then explodes. This critical mass is typically considered the Chandrasekhar mass ($M_{ch}\sim 1.4~{}M_{\odot}$), although sub-$M_{ch}$ explosions, including double detonation scenarios, are also possible (e.g., Livne & Arnett, 1995). There are several predicted observational signatures of the SD degenerate scenario due to the interaction of the ejecta/explosion and the donor star (Wheeler et al., 1975), including effects on the rising SN Ia light curve (Kasen, 2010), soft X-ray emission in the accretion phase (Lanz et al., 2005; Tutukov & Fedorova, 2007; Woods et al., 2018), surviving companions with anomalous characteristics (e.g., Canal et al., 2001; Shappee et al., 2013b), and the amount of 56Ni decay products synthesized in the explosion (e.g., Röpke et al., 2012; Shappee et al., 2017).

One of the most promising signatures of a RLOF companion to an exploding WD are emission lines produced by material stripped/ablated from the non-degenerate companion (e.g., Wheeler et al., 1975; Chugai, 1986; Marietta et al., 2000; Mattila et al., 2005; Pan et al., 2012), observable in nebular-phase spectra once the SN Ia has faded considerably and become optically thin. For example, Boehner et al. (2017) simulated stripping from red giant (RG), main sequence (MS), and sub-giant (SG) stars, finding approximately $0.33$, $0.25$, and $0.17M_{\odot}$, respectively, of stripped mass. Botyánszki et al. (2018) converted these estimates into expected H$\alpha$ luminosities and found that the emitted H$\alpha$ luminosity does not vary linearly with amount of stripped companion mass, which had been the assumption of previous studies (e.g. Leonard, 2007; Shappee et al., 2013a), but instead the relation is closer to logarithmic. Additionally, the H$\alpha$ emission is powered by gamma-ray deposition from the SN Ia ejecta and roughly follows the bolometric luminosity.

In this work we compile a comprehensive sample of SNe Ia nebular spectra spanning $200-500~{}\rm{days}$ after explosion ($181-481~{}\rm{days}$ after maximum assuming a rise time of $\sim 19~{}\rm{days}$ from Firth et al., 2015) to search for the expected emission from stripped/ablated material. We find no such emission in any spectrum in our sample, and place new or updated stripped/ablated mass constraints for each SN Ia. The entirety of similar work in the literature totals 33 SNe Ia (Mattila et al., 2005; Leonard, 2007; Shappee et al., 2013a; Lundqvist et al., 2013, 2015; Maguire et al., 2016; Graham et al., 2017; Shappee et al., 2018; Sand et al., 2018a; Holmbo et al., 2018; Dimitriadis et al., 2019a; Tucker et al., 2018; Sand et al., 2019), a fraction of the sample analyzed in this work. All SNe Ia included in this study are listed in Table 6 and photometric parameters ($t_{max}$, $\Delta m_{15}$, $\mu$, $E(B-V)_{\rm{host}}$) are provided in Table 8.

We outline our data sources and reduction techniques, including absolute flux calibration, in §2. In §3, we discuss our methodology in searching for and placing limits on material stripped from a RLOF companion. Our upper limits on stripped material are provided in §4, and our findings are discussed in the context of SNe Ia formation in §5. Included in §5 are discussions about peculiar SNe Ia and their role in our study including SNe Ia-CSM. Finally, in §6, we summarize our results.

2 Data Sources and Reduction

Our sample of 227 spectra of $111$ SNe Ia comes from the 40 instruments on 29 telescopes listed in Table 1. All spectroscopically peculiar SNe Ia are included except for those exhibiting signatures of circumstellar material (SNe Ia-CSM). These SNe Ia exhibit H$\alpha$ emission, but the velocity and magnitude of the emission is inconsistent with material stripped from a nearby companion; instead, these SN Ia appear to have exploded in a dense circumstellar environment (e.g., SN 2002ic, Wang et al., 2004) and exhibit H$\alpha$ emission before the SN enters the nebular phase (e.g., Silverman et al., 2013). A discussion of SNe Ia-CSM and their role in our results is provided in §5.2. For non-CSM SNe Ia we impose the following criteria when selecting nebular spectra:

• •

Obtained between 200 and 500 days after explosion to maintain consistency with the models of Botyánszki et al. (2018), assuming a typical rise time of $t_{\rm{rise}}\approx 19~{}\rm{days}$ (Firth et al., 2015).

• •

Cover $\pm 1\,000~{}\rm{km}~{}\rm s^{-1}$ of at least one H or He line in Table 2.

• •

Have at least one method of absolute flux calibration, outlined in §2.3.

• •

Published, posted, or observed by our team before the submission date of this article (15 March 2019).

The complete list of new and archival spectra is provided in Table 10. Additionally, we include new and archival photometry to supplement our spectral data and analysis. Early-phase photometry ($\lesssim 50$ days after maximum light) is used in deriving the photometric properties of each SN Ia using the photometric fitting code SNooPy (Burns et al., 2011), including time of maximum ($t_{max}$), the decline rate parameter $\Delta m_{15}$, extinction along line of sight, and the distance modulus. Late- and nebular-phase photometry are used for flux calibrating the nebular spectra and deriving a Nebular Phase Phillips Relation (NPPR). The NPPR approximates the nebular magnitude of a SN Ia given its peak magnitude and decline rate, calibrated to an extensive sample of new and archival SNe Ia photometry. A complete description of the NPPR, its derivation and usage is provided in Appendix A.

2.1 New Spectra and Photometry

We present 14 new nebular-phase spectra of 13 SNe Ia, of which 10 have no prior published nebular spectra. These spectra were acquired in our ongoing study of SNe Ia progenitors, taken with MagE and IMACS on Baade, MUSE on the VLT, and WFCCD on duPont (see Table 1 for telescope and instrument designations). For the new spectra presented here, each spectrum was reduced using telescope and instrument-specific pipelines, if available, otherwise typical IRAF111http://iraf.noao.edu/ tasks were used. The spectra acquired with MagE/Baade were reduced with a pipeline provided by the Carnegie Observatories222http://code.obs.carnegiescience.edu/mage-pipeline (Kelson et al., 2000; Kelson, 2003), with the exception of standard star calibrations and stitching together each echellette spectrum, which was done with custom Python routines. For newly presented MUSE data acquired as part of the AMUSING survey (Galbany et al., 2016), spectra were extracted in a 1" circular aperture at the SN Ia location using the PyMUSE package (Pessa et al., 2018), and corrected for host galaxy contributions using a background annulus extending from 2" to 3". New IMACS/Baade spectra were reduced with typical IRAF procedures including bias subtraction, flat-field correction, arc lamp exposures for wavelength calibration and standard star onbservations to correct for instrument and atmospheric response.

For absolute flux calibrations, we also include nebular photometry for any SNe Ia in our sample. This includes new observations and reproccessed archival images for which we could not find a published magnitude. New photometry includes $V$-band images taken with FORS2, $r$-band images from MODS1, and $BVRI$ images from WFCCD. Archival imaging includes $UBVRI$ imaging from FORS1/2 and $BVRgri$ imaging from EFOSC2 (Table 16). All images are bias subtracted and flat-field corrected before performing aperture photometry with the IRAF apphot task. For targets with $\delta\geq-30^{\circ}$, photometry from the Pan-STARRS Stack Object catalog333http://archive.stsci.edu/panstarrs/stackobject/search.php (Chambers et al., 2016; Flewelling et al., 2016) was used in calibrating the images, otherwise Gaia DR2 photometry (Gaia Collaboration et al., 2016, 2018; Riello et al., 2018) was used. When transforming reported magnitudes to other photometric systems, Tonry et al. (2012) and Evans et al. (2018) were used for Pan-STARRS and Gaia, respectively. The only exceptions to this procedure are the $B$-band FORS2/VLT images, which are calibrated using the reported photometric zeropoints444https://www.eso.org/observing/dfo/quality/FORS2/qc/zeropoints/zeropoints.html.

2.2 Archival Spectra and Photometry

The primary sources of our archival spectra and photometry are the Berkeley SuperNova Ia Program555http://heracles.astro.berkeley.edu/sndb/ (BSNIP, Silverman et al., 2012, 2013), the Center for Astrophysics (CfA) Supernova Data Archive666https://www.cfa.harvard.edu/supernova/SNarchive.html (Riess et al., 1999; Jha et al., 2006; Matheson et al., 2008; Blondin et al., 2012), the Carnegie Supernova Project777http://csp.obs.carnegiescience.edu/ (CSP, Hamuy et al., 2006; Folatelli et al., 2010a; Contreras et al., 2010; Stritzinger et al., 2011; Folatelli et al., 2013; Krisciunas et al., 2017; Phillips et al., 2019), the 100IAs project (Dong et al., 2018a), the ANU WiFeS SuperNovA Program (AWSNAP; Childress et al., 2016), and the All-Sky Automated Survey for SuperNovae (ASAS-SN, Shappee et al., 2014a; Holoien et al., 2017a, b, c, 2019, Vallely et al., Chen et al., in prep). The majority of the publicly available data were retrieved using the Open Supernova Catalog (OSC, Guillochon et al., 2017) and the Weizmann Interactive Supernova data REPository (WISeREP, Yaron & Gal-Yam, 2012). All data provided by these sources are already reduced with the exception of precise spectral flux calibration, which we outline in §2.3. Additionally, we supplement these sources with archival data obtained from telescope databases, including the Keck Observatory Archive888https://koa.ipac.caltech.edu/ (KOA), the ESO Science Archive Facility 999http://archive.eso.org/cms.html (ESO SAF), the Isaac Newton Group Archive101010http://casu.ast.cam.ac.uk/casuadc/ingarch/query and the Gemini Observatory Archive111111https://archive.gemini.edu/ (GOA). Information on all the spectra in this study is presented in Table 10.

Data reduction and calibration was performed as uniformly as possible across all sources of spectra. Data retrieved from public archives were already reduced, with the exception of absolute flux calibration. The reduction of data retrieved from telescope archives was generally less complete. All spectra retrieved from the ESO SAF were already reduced (excluding flux corrections) with the exception of FORS1/2 data. For any ESO SAF data reduction, both spectroscopy and photometry, we used the ESO SAF esorex data reduction pipeline (Freudling et al., 2013).

Spectra obtained from the KOA and GOA were not reduced prior to retrieval and had to be manually reduced. Recent LRIS spectra were reduced using Lpipe121212http://www.astro.caltech.edu/~dperley/programs/lpipe.html, while older LRIS and DEIMOS data were reduced using the LowRedux/XIDL pipeline131313http://www.ucolick.org/~xavier/LowRedux/. Gemini North/South GMOS spectra were reduced with the GMOS Data Reduction Cookbook141414http://ast.noao.edu/sites/default/files/GMOS_Cookbook/.

We manually reduced any unreduced spectra for which no pipeline exists using standard IRAF procedures. Images were flat-fielded and bias-subtracted using archival calibration images taken near the epoch of observation, and wavelength calibrated with arc lamp exposures. Spectrophotometric standard star observations were used to correct for telescope/instrumental artefacts, atmospheric effects, and to place each spectrum on a reliable relative flux scale.

2.3 Accurate Flux Calibration

For our analysis in §3, the spectra must be on a reliable absolute flux scale. While calibrating spectra with spectrophotometric standard stars places these spectra on a dependable relative flux scale, slit losses, atmospheric conditions, and other effects can cause the resulting spectra to deviate from an absolute flux scale. To scale a spectrum to the absolute scale, we employed Eq. 7 from Fukugita et al. (1996) to calculate synthetic photometry from the spectra. The spectra are then scaled so that the synthetic photometry matches the observed photometry. There were several different sources of photometry used to calibrate the spectra. In order of preference and reliability, with accuracy estimates in given parentheses:

For spectra with acquisition images taken at the time of observation, we scale the entire spectrum to match these photometric observations, usually in the $V$ or $r$ filters ($\sim 5-10\%$). 2. 2.

If acquisition images are unavailable, we next tried to use photometry within $\pm 5~{}\rm d$ of the spectral observations. Photometry in all available filters within this temporal limit were used in the flux calibration ($\sim 10-15\%$). 3. 3.

If no photometric data was available within $\pm 5~{}\rm d$, we searched for photometry within $\pm 50~{}\rm d$. If at at least 3 photometric data points fell within this time span, we linearly interpolated to estimate the magnitude at the time of the spectral observation ($\sim 15-20\%$). 4. 4.

If none of these were available, the nebular $BVR$ magnitude was estimated with the NPPR and used to calibrate the spectrum (see Appendix A, $\sim 20\%$).

We required $>90\%$ of the filter’s transmission curve be covered by the observed spectrum for viable calibrations. If only a single filter was available, the entire spectrum was scaled to match the observation. If two filters were available for flux calibration, a simple linear fit was applied to the scale factors. If $>3$ filters were available, we use spline fits with fixed endpoints to ensure a robust flux correction across the entire spectrum. After placing the spectrum on an absolute flux scale, we correct for host galaxy and Milky Way reddening using the $E(B-V)_{\rm{host}}$ derived from the light curve fits. We implement a Fitzpatrick (1999) extinction law and a Schlegel et al. (1998) Milky Way dust map for our reddening corrections. We assume $R_{V}=3.1$ unless stated otherwise (see Appendix B).

2.4 Sample Demographics

After collecting all nebular spectra that meet our temporal and calibration requirements, our sample consists of 111 SNe Ia (Table 6). Due to the comprehensive nature of our search for nebular spectra, our sample is inherently biased towards brighter or peculiar SNe Ia as these objects have a higher likelihood of being observed in the nebular phase. This effect is readily apparent in Fig. 1 where the $\Delta m_{15}$ values of SNe Ia in our sample are compared to a purely photometric sample from the Lick Observatory Supernova Search (LOSS, Li et al., 2000; Ganeshalingam et al., 2010). Similar to the luminosity bias, we are biased to lower redshift SNe Ia with a median redshift of $z_{\rm{med}}\approx 0.015$. We provide the temporal distribution for our set of nebular spectra in Fig. 2, including distributions for the earliest and latest spectra for each SN Ia. As expected, the number of spectra generally decline at later phases due to the supernovae fading from view.

3 Searching for Emission from Stripped Companion Material

Prior to the work of Botyánszki et al. (2018), the majority of unbound mass limits in the literature utilised the work of Mattila et al. (2005) and Leonard (2007) to compute stripped mass limits from comparing observed spectra to expected H$\alpha$ luminosities. Several subsequent studies have adopted these methodologies in their work (e.g., Maguire et al., 2016; Graham et al., 2017) with notable success in ruling out hydrogen-rich companions. Yet the models of Mattila et al. (2005) had several shortcomings in observational implementation. In particular, Leonard (2007) assumed a linear scaling between the amount of unbound companion mass and the corresponding H$\alpha$ luminosity.

Botyánszki et al. (2018), using the MS38 model (a main-sequence star undergoing RLOF) from Boehner et al. (2017), instead found the emitted H$\alpha$ luminosity scales logarithmically with the amount of stripped mass. Additionally, Botyánszki et al. (2018) computed a simplified helium-star model, where all the stripped mass from the MS38 model is replaced with helium instead of Solar abundance material. This is not a true helium-star model, as helium-star companions are expected to have lower amounts of stripped mass than their hydrogen-rich counterparts and a modestly different velocity distribution (e.g. Pan et al., 2012), but it provides a starting point for calculating limits on the amount of unbound helium in a SN Ia spectrum.

While the models of Botyánszki et al. (2018) clarify the mass-luminosity scaling issue and expand to helium emission, they share two other shortcomings with the models of Mattila et al. (2005): the requirement of using H$\alpha$ to constrain the amount of unbound mass, and only calculating the expected H$\alpha$ luminosity at a single epoch (200 days post-explosion for Botyánszki et al., 2018 and 350 days post-maximum for Mattila et al., 2005). In the following subsections we discuss our stripped mass limits given these limitations.

3.1 Expanding on these Models

For SNe Ia with star-forming host galaxies, the region around H$\alpha$ can be contaminated by narrow host galaxy H$\alpha$ and NII emission lines which complicates setting limits on H$\alpha$ emission. However, the unbound material has emission lines besides H$\alpha$, including H$\beta$, H$\gamma$, and the Paschen series. Assuming roughly Solar metallicity, the stripped material will also exhibit prominent HeI lines in the optical and NIR (Botyánszki et al., 2018). We provide the luminosities for each of these lines in Table 2 at $(t-t_{0})=200$ days from explosion for the hydrogen-rich (H-rich) model using the same MS38 model as Botyánszki et al. (2018). Additionally, we supply similar data for the simplified helium star model from Botyánszki et al. (2018), which we refer to as the He-rich model.

Botyánszki et al. (2018) estimated the line luminosity at 200 days as a function of the amount of stripped mass ($M_{st}$). Table 2 provides the expected luminosity $L_{200}(M_{st})$ of various lines for $M_{st}=0.25~{}M_{\odot}$. The dependence on the amount of stripped mass is well approximated by $\log_{10}L_{200}(M)\simeq\log_{10}L_{200}(0.25M_{\odot})+0.17M-0.2M^{2}$, where $M=\log_{10}(M_{st}/M_{\odot})$. Botyánszki et al. (2018) do not provide the time dependence of the line emission specifically, but note that the H$\alpha$ emission is proportional to the FeIII emission over the $200<(t-t_{0})<500$ day period they consider. Utilising the synthetic spectra models from Botyánszki & Kasen (2017), we find the FeIII emission is well fit by an exponential (Fig. 3), which leads to an estimate for the line luminosity of

[TABLE]

provided $M_{st}<2M_{\odot}$. This should hold well for the Balmer lines, and is at least a better approximation for the Paschen and HeI lines than assuming their luminosities are temporally constant.

The models from Botyánszki & Kasen (2017) used to derive the luminosity decay in Fig. 3 are truncated at 400 days after explosion. However, the ratio between FeIII and H$\alpha$ remains roughly constant out to 500 days after explosion (Botyánszki et al., 2018). To incorporate spectra taken between $400-500~{}\rm{days}$ after explosion, we extrapolate the exponential fit to the later epoch. Since the models used to derive the FeIII emission decay are generalized to non-peculiar SNe Ia and independent of any possible H or He emission, we consider this assumption valid. However, we do not extrapolate to earlier epochs for two reasons. The onset of the nebular phase is not clearly defined in the literature (e.g., Black et al., 2016), leading to ambiguities in when stripped material might become visible. Additionally, the luminosities for stripped material given in Table 2 are taken from Botyánszki et al. (2018) who explicitly state that their models are valid in the regime of $200\leq(t-t_{0})\leq 500$ days. If these concerns are mitigated by future work our results can be expanded to include objects with earlier spectra.

3.2 Placing Statistical Limits on Stripped Mass

Once each spectrum is flux calibrated and corrected for the reddening, we place statistical limits on the presence of emission lines listed in Table 2, roughly following the methods of Leonard (2007). Each spectrum is rebinned to the approximate spectral resolution, and the spectral continuum is fit with a 2nd-order Savitsky-Golay polynomial (Press et al., 1992), excluding pixels within $2\times\rm{FWHM}$ of line centers to prevent biasing our continuum fit, as done in previous studies (e.g., Maguire et al., 2016). However, since we are inspecting multiple lines for emission signatures, we apply our continuum model in velocity space instead of wavelength space to incorporate this modification.

No single continuum width adequately fits the continuum for all SNe Ia in our sample, especially considering the spectroscopic and temporal diversity. We tailored the continuum fit width for each spectrum based on the observed SN Ia expansion velocity, measured from the prominent emission lines in the spectrum. Since most of the major emission lines in nebular SNe Ia are blended to some extent (e.g., Mazzali et al., 2015, Fig. 5), we compute the weighted average from the fitted line profiles assuming a Gaussian emission profile + linear continuum. The lines considered for deriving the expansion velocity are the major FeII, FeIII, and CoIII lines indicated by the vertical dashed lines in Fig. 4. If the SNR of the spectrum is too low for the widths of at least 2 lines to be measured confidently, we assume a typical width of $3\,000~{}\rm{km}~{}\rm s^{-1}$. For velocities lower than this value, we risk biasing our continuum fit to include possible weak emission, and implement $3\,000~{}\rm{km}~{}\rm s^{-1}$ as a strict lower bound. Additionally, since SNe Iax are known to have narrow line profiles in the nebular phase compared to typical SNe Ia (Foley et al., 2016), we adopt this lower bound for SNe-Iax as well. Because these velocities are simply a proxy for the width of the continuum fit, this method neglects the intricacies of SNe Ia emission profiles, especially since spectroscopically bi-modal SNe Ia are not uncommon (Dong et al., 2015a; Vallely et al., 2019a). However, these complications are unimportant for our analysis, and we consider these simple velocity approximations adequate.

When applying the continuum fit to each spectrum, we minimize biasing our continuum by using $3\sigma$ clipping to exclude narrow host galaxy lines, telluric absorption, or instrumental artefacts. After fitting the continuum model to the data, we subtract off this continuum and inspect the residuals for emission-line signatures from unbound companion material. For each line in Table 2, we compute $10\sigma$ bounds on the integrated line flux in each region similar to Eq. 4 from Leonard & Filippenko (2001). However, for flux-calibrated spectra,

[TABLE]

where $F(10\sigma)$ is the $10\sigma$ upper limit on the integrated flux, $EW(10\sigma)$ is the corresponding upper limit on the equivalent width, $C_{\lambda}$ is the continuum flux at wavelength $\lambda$, $\Delta I$ is the RMS scatter around a normalised continuum, $W_{\rm{line}}$ is the width of the line profile, and $\Delta X$ is the bin size of the spectrum. We assume $W_{\rm{line}}$ is equal to the FWHM of a $\sim 1\,000~{}\rm{km}~{}\rm s^{-1}$ emission line and provide these values in Table 2. Eq. 2 can be re-written as

[TABLE]

where $\Delta f_{\lambda}$ is the $1\sigma$ RMS scatter of the spectrum around the continuum in flux units (erg s*-1* cm*-2* Å*-1*) and $\mathcal{F}^{-1}$ is the correction term for masked pixels (see §3.3). Our $10\sigma$ statistical limit may seem overly conservative but it does correspond to a line profile that would be visibly obvious (e.g., Fig. 5). Additionally, other studies have run injection-recovery tests to determine the true detection threshold for $\sim 1\,000~{}\rm{km}~{}\rm s^{-1}$ emission lines in SNe Ia nebula spectra and a purely statistical $F(3\sigma)$ is difficult to recover (e.g., Sand et al., 2018a).

$F(10\sigma)$ is then converted into a luminosity via the distance moduli listed in Table 8. Distance moduli computed from the SN Ia light curves are used except where more reliable methods are available, such as Cepheid or Tip of the Red Giant Branch (TRGB) distances. Eq. 1 is inverted to numerically calculate a limit on $M_{st}$, which we consider a conservative upper bound on the amount of mass removed from a non-degenerate companion undergoing RLOF. This is done for each H/He line, retaining the best mass limit for both the H-rich and He-rich models. Note that the strictest mass limit for each model can come from different spectra, as each spectrum will have varying amounts of contamination from host galaxy and telluric lines.

3.3 Mitigating Host Galaxy Emission and Other Contaminants

Due to the comprehensive nature of our sample, some spectra have poor quality, significant host-galaxy emission and/or other contaminants. Pixels affected by host-galaxy emission, telluric absorption, or instrumental artefacts are masked in the ensuing flux limit calculation, ensuring only informative pixels are used in placing our flux upper limit. Masking these pixels also reduces the effective number of pixels used in the non-detection limit calculation and weakens our statistical limit. In Eq. 3 we include the masked pixel correction term $\mathcal{F}^{-1}$ from Tucker et al. (2018) to correct our limit to a more robust estimate. Concisely, the correction term $\mathcal{F}$ is the fraction of unmasked line flux to total line flux ($\mathcal{F}\in[0,1]$). Thus, masked pixels decrease $\mathcal{F}$ and increase $F(10\sigma)$, but the effect is weighted by the location of the masked pixels relative to the line centre. For example, the masked narrow host galaxy H$\alpha$ and H$\beta$ in the bottom panels of Fig. 4 have larger effects on $\mathcal{F}$ than the masked [SII] line at $6713$Å since [SII] is on the outskirts of the HeI-a line profile. Masking is only implemented when the derived $F(10\sigma)$ is not representative of the true flux limit due to contaminated pixels, we leave weak or minor contamination unmasked as it only solidifies our conservative flux limit and does not introduce extra steps in our analysis.

Another difficulty occurs when the expected emission line is blended with the edge of a steep SN spectral feature. This is especially problematic for 91bg-like and Iax SNe which have intrinsically narrow emission line profiles. If the continuum near H/He varies by more than the amplitude of our flux limit over its FWHM, we increase our flux limit to match the continuum level variation. This results in an unambiguous line profile that would be definitively detected and prevents questionable limits from being included in our statistical analysis.

Some spectra in our study have resolutions of order $\sim 500~{}\rm{km}~{}\rm s^{-1}$, which approaches the lower end of the expected stripped mass velocity distribution (e.g., Boehner et al., 2017). If broad, unresolved H emission was present in a spectrum, we confirm the host galaxy source with other typical galaxy emission lines such as [OII] ($3727$Å), [OIII] ($4959$, $5007$Å), [NII] (6548, 6583Å), and [SII] (6713, 6731Å). Any unresolved H$\alpha$ emission with velocity widths $\gtrsim 300~{}\rm{km}~{}\rm s^{-1}$ had at least one other unresolved galaxy emission line in the spectrum, indicating the observed H emission was not from stripped material. Additionally, the recent discovery of broad H$\alpha$ emission in ATLAS18qtd (Prieto et al., 2019) affirms our treatment of galaxy emission lines, as none of the galaxy emission lines discussed previously were present in the discovery spectrum (see §5).

4 Results

We find no evidence of emission from stripped/ablated companion material in any of our nebular phase spectra. Fig. 4 provides an example Baade/MagE spectrum of SN 2015F at +295 days after maximum light, including the observed spectrum, the continuum fit, and the $10\sigma$ flux limits for each line. We provide a random selection of H$\alpha$ flux limit cutouts in Fig. 5 and the spectral cutouts for all H and He lines are provided as supplementary material.

The distribution of stripped mass limits are shown for the H-rich and the He-rich cases in Figs. 6 and 7, respectively, with colour-shaded regions indicating the expected amounts of stripped mass from various studies in the literature. Fig. 8 shows the H-rich results using the methods and models of Mattila et al. (2005) and Leonard (2007) for comparison with previous estimates. Table 14 gives the phases, flux limits, and derived H-rich and He-rich mass limits for each SN Ia in our study.

We include the range of mass estimates from an H-rich RLOF companion in Figs. 6 and 8 as shaded regions for main-sequence (MS, blue), sub-giant (SG, green), and red giant (RG, red) companions taken from Marietta et al. (2000), Pan et al. (2012), and Boehner et al. (2017). We take $0.15~{}M_{\odot}$ as the minimum amount of mass stripped from a companion in the SD scenario, SNe Ia with $M_{st,H}<0.15~{}M_{\odot}$ are considered unlikely to have an H-rich SD progenitor system.

For the He-rich SD channel, only Pan et al. (2012) and Liu et al. (2013a) have published models. We include their expected values for mass stripped from a RLOF helium-star companion in Fig. 7 as the magenta shaded area (Liu et al., 2012) and the cyan line (Pan et al., 2012). However, there are several caveats when considering the He-rich model. The expected line luminosities given in Table 2 are for $0.25~{}M_{\odot}$ of stripped He-rich material, more mass than expected for a true He-donor star. We compare our mass limits to the dedicated He-rich models from Pan et al. (2012), Liu et al. (2013a) and take a limit of $M_{st,He}<0.023~{}M_{\odot}$ as our upper limit for He-rich SD systems.

If we assume SNe Ia with $M_{st,H}<0.15~{}M_{\odot}$ and $M_{st,He}<0.023~{}M_{\odot}$ exclude H-rich and He-rich SD progenitor systems, respectively, we can constrain the observed fraction of SD systems. Based on the non-detections in our sample, we can place observed upper limits on the fraction of SD SNe Ia. For a binomial distribution with $N$ trials and no successes, the upper limit $f$ at a confidence level $P$ can be expressed as

[TABLE]

with the results for our sample provided in Table 3. $f_{1\sigma}$ and $f_{3\sigma}$ correspond to the $1\sigma$ and $3\sigma$ fractional upper limits on SD SNe Ia. For our null detections of unbound mass emission, we place statistical constraints on the fraction of SNe Ia that can form through the classical SD scenario for H-rich and He-rich companions. We do not consider SNe Ia with inadequate limits on $M_{st}$ “successes”, as the spectra do not show any evidence of the expected emission signatures, so these objects are simply omitted from our statistical analysis.

5 Discussion

5.1 Statistical Implications

With our updated modelling and comprehensive sample, we place strict constraints on the fraction of SNe Ia that can form through the classical SD scenario. At most, $\sim 6\%$ of SNe Ia (at $3\sigma$ confidence) can stem from the H-rich formation channel, placing the majority of the production of SNe Ia on the DD channel, unless a modification on the SD scenario can prevent nearly all SNe Ia from exhibiting these expected H and He emission signatures such as the spin-up/spin-down scenario (Justham, 2011; Di Stefano et al., 2011; Meng & Podsiadlowski, 2013). Considering the simplest case of only spectroscopically normal SNe Ia, we place a $1\sigma$ ($3\sigma$) upper limit on SD progenitors of $<1.3\%$ ($<6.6\%$). The full statistical results are provided in Table 3, and we use the Normal+91T+91bg+SC sample as the most representative sample from our survey. Unfortunately, our sample prevents an analysis of under- versus over-luminous SNe Ia, as we are biased towards brighter SNe Ia (Fig. 1). This highlights the importance of volume-limited surveys such as 100IAs (Dong et al., 2015a). Still, these stringent constraints on the observed rate of SD SNe Ia provide strong evidence for the DD channel producing the majority of SNe Ia.

We separately consider spectroscopic sub-classes at the extreme edges of the Phillips Relation. Because these SNe Ia are thought to be on the edges of typical SN Ia formation, we compare the derived stripped mass limits to the same expected stripped mass values as normal SNe Ia. Our sample has $8$ 91bg-like and $5$ 91T-like SNe Ia, for which we place $1\sigma$ ($3\sigma$) upper limits on H-rich SD progenitors at $<12.0\%$ ($<48.2\%$) and $<17.4\%$ ($<62.7\%$), respectively. It is worth mentioning that the stripped mass models assume a normal SN Ia explosion and the effects of under- and over-luminous SNe Ia on the amount of stripped material has yet to be investigated.

For SNe Iax and “Super Chandrasekhar” (SC) SNe Ia, it is worth discussing their characteristics and applicability to our study. The Iax sub-type (Foley et al., 2013) is thought to stem from an entirely different formation mechanism and are not observed to enter a nebular phase but instead have photospheric properties (Foley et al., 2016). Our study includes $4$ such systems: SNe 2002cx, 2005hk, 2008A, and 2012Z. Liu et al. (2013b) investigated the expected values of unbound mass for these systems if in a SD system, finding significantly lower values of $M_{st,H}\approx 0.013-0.016~{}M_{\odot}$ compared to the typical $\sim 0.1-0.5~{}M_{\odot}$ range. All Iax SNe Ia in our sample have $M_{st,H}<0.013~{}M_{\odot}$, so the statistics are unchanged if the more stringent mass limit is employed. However, even if material is unbound from non-degenerate donor stars in these SNe Ia, it is unclear if this material would be visible at late times. For these reasons, our main statistical analysis excludes these objects.

Our sample also includes $4$ “Super Chandrasekhar" (SC) SNe Ia explosions (SNe 2006gz, 2007if, 2009dc, and SNF 20080723-012), where the inferred ejecta mass, $M_{ej}$, is higher than the Chandrasekhar mass of $\approx 1.4~{}M_{\odot}$ (e.g., Howell et al., 2006; Scalzo et al., 2019) although the nomenclature is currently debated (Chen et al., 2019). The preferred formation theory of SC SNe Ia involves a DD merger of two WDs with a combined mass above the Chandrasekhar mass (Tutukov & Yungelson, 1994; Howell, 2001), although SD progenitors have also been proposed (Yoon & Langer, 2005). Because these objects do enter a nebular phase and have possible SD progenitors, we include these SNe Ia in our preferred sample.

For completeness and comparison to the literature, we also derive mass limits using the prior models of Marietta et al. (2000) and Mattila et al. (2005) which are shown in Fig. 8. Considering the same preferred Normal+91T+91bg+SC sample, we still rule out H-rich non-degenerate companions ($M_{st,H}<0.15~{}M_{\odot}$) for $60$ SNe Ia, corresponding to a $1\sigma$ ($3\sigma$) fractional upper limit of $<1.9\%$ ($<9.2\%$). This result differs slightly from the upper limit provided in Table 3 due to the assumed linear scaling between stripped mass and emitted luminosity (e.g., Leonard, 2007).

In addition to the observational limitations discussed in §3, the models used in this work are developed for normal SNe Ia. Over- and under-luminous explosions will likely differ in the amount of stripped material from a companion star due to the differing expansion velocities (e.g., Benetti et al., 2005; Blondin et al., 2012; Folatelli et al., 2013) and amount of ejecta mass (e.g., Cappellaro et al., 1997; Scalzo et al., 2014, 2019). Additionally, the SN luminosity depends on the amount of Ni synthesized in the explosion (e.g., Arnett, 1982; Cappellaro et al., 1997; Stritzinger et al., 2006b), indicating SNe Ia with lower Ni mass will have less gamma-ray production to power the H$\alpha$ emission (i.e., a reduced $L_{\rm H\alpha}$). These effects likely superimpose, as under-luminous SNe Ia will strip less mass and synthesize less Ni, but the magnitude of these effects is currently unexplored in the literature. We encourage the modeling of other SNe Ia sub-types in future works.

5.2 The Exclusion of SNe Ia-CSM

SNe Ia-CSM, which show interaction with a nearby circumstellar environment, are a rare class of thermonuclear explosions for which SN 2002ic is the prototype (Wang et al., 2004). These events preferentially occur in star-forming host galaxies and generally have broad, over-luminous light curves ($M_{R}\sim-20$ mag, Silverman et al., 2013). The observed H$\alpha$ emission in SNe Ia-CSM usually appears near maximum light, has luminosities of $L_{\rm H\alpha}\sim 10^{40-41}~{}\rm{ergs}~{}\rm{s}^{-1}$, and have velocity widths on the order of $\sim 2\,000~{}\rm{km}~{}\rm s^{-1}$. SNe Ia-CSM are broadly thought to stem from SD progenitor systems (e.g., Han & Podsiadlowski, 2006), although DD progenitors have also been proposed (Livio & Riess, 2003).

Even among this rare class of SNe Ia there are peculiar events that do not conform to the “standard” properties. In particular, ASASSN-18tb (Kollmeier et al., 2019; Vallely et al., 2019b) was an under-luminous explosion, occurred in an elliptical host galaxy with little star formation, and had (comparatively) weak H$\alpha$ emission ($L_{\rm{H}\alpha}\sim 10^{38}~{}\rm{ergs}~{}\rm{s}^{-1}$), inconsistent with typical SNe Ia-CSM. Additionally, there are cases where the H$\alpha$ emission does not appear until later in the SN’s evolution, referred to as “delayed-onset” SNe Ia-CSM (e.g., Graham et al., 2019).

H$\alpha$ emission is also expected for material stripped from a companion, therefore differentiating between SNe Ia-CSM and SNe Ia with stripped material emission is an important distinction. Stripped companion material will have significantly lower velocities than the expanding SN ejecta ($v_{\rm{strip}}\sim 10^{3}~{}\rm{km}~{}\rm s^{-1}$ versus $v_{\rm{ej}}\sim 10^{4}~{}\rm{km}~{}\rm{s}^{-1}$), shrouding the H-emitting material with the optically-thick photosphere until the SN enters the nebular phase ($\sim 150-180~{}\rm{days}$ after maximum light). Thus, we exclude all objects with broad H$\alpha$ detected $<100~{}\rm{days}$ after maximum light. The only SN Ia-CSM that passes this criterion is SN 2015cp, a delayed-onset SN Ia-CSM (Graham et al., 2019).

While it is possible that the H$\alpha$ emission observed in SN 2015cp is from material stripped from a companion, we find this scenario unlikely. The classification spectrum taken by PESSTO (Smartt et al., 2015b) at $\sim 45~{}\rm{days}$ after maximum excludes the presence of PTF11kx-like H$\alpha$ emission at $10\sigma$ (Graham et al., 2019). The next spectrum was acquired at $\sim 700$ days after maximum light and exhibited broad H$\alpha$ emission with $v_{\rm{FWHM}}\approx 2\,400~{}\rm{km}~{}\rm{s}^{-1}$ and $L_{\rm H\alpha}\approx 10^{38}~{}\rm{ergs}~{}\rm{s}^{-1}$. This measured $L_{\rm{H}\alpha}$ is an order of magnitude higher than the H$\alpha$ luminosity extrapolated from Eq. 1 at $\sim 710$ days after explosion, although the models have not been tested at these epochs. Additionally, the H$\alpha$ flux decreases sharply at $\sim 730~{}\rm{days}$ after peak by a factor of $\approx 3$ over the span of $\sim 90~{}\rm{days}$, inconsistent with H$\alpha$ emission powered by radioactively-decaying SN ejecta which would roughly follow the SN bolometric luminosity. These properties are consistent with CSM interaction, attributing the abrupt flux decrement to the shock passing through the CSM material. For these reasons we consider SN 2015cp a likely SN Ia-CSM and exclude it from our analysis, although further modeling is encouraged to definitively determine mass estimates.

5.3 Time-Variable and Blue-Shifted Sodium Absorption

Another subset of SNe Ia with interesting properties are objects with time-varying and blue-shifted NaID absorption, for which SN 2006X is the prototype (Patat et al., 2007). The NaID absorption is thought to stem from NaID material near the explosion that photo-ionizes during the early phases of the explosion and produces the absorption lines as the NaID material cools and recombines (e.g., Simon et al., 2009). However, the origin of the NaID material is unclear and proposed sources include wind from a SD progenitor system (e.g., Patat et al., 2007), circumstellar debris from a DD merger (e.g., Raskin & Kasen, 2013), or even nearby gas clouds within the host galaxy (Chugai, 2008).

Sternberg et al. (2011) analyzed a set of 35 SNe Ia and found 22 exhibit some form of NaID absorption profiles, with 12 having blue-shifted (relative the host-galaxy velocity) NaID profiles. However, comparing their SNe Ia sample to a sample of core collapse (CC) SNe could not statistically confirm the two sets come from different parent populations (i.e., the source for SNe Ia and CC SNe NaID absorption could be the same). Additionally, the blue-shifted NaID profiles are preferentially observed in spiral galaxies, indicating age or host-galaxy environment may play a role in the NaID interpretation.

Another prediction for NaID absorption associated with the SN Ia progenitor system is a time-variable NaID equivalent width, as the NaID material will recombine at different times depending on the distance from the explosion. Sternberg et al. (2014) searched for time-varying NaID absorption in a sample of 14 objects and found 3 SNe Ia that meet this criterion (PTF11kx, SNe 2006X and 2007le). With these detections, Sternberg et al. (2014) found $18\pm 11$% of SNe Ia have variable NaID profiles and thus could be produced by a SD progenitor system, in conflict with the results presented here. One of these objects is a known SNe Ia-CSM that we exclude from the sample (PTF11kx, Dilday et al., 2012), but SNe 2006X and 2007le are both in our nebular sample and have strict constraints on stripped companion material ($M_{st}<4\times 10^{-5}~{}M_{\odot}$ for SN 2006X and $M_{st}<3\times 10^{-3}~{}M_{\odot}$ for SN 2007le). We discuss these discrepancies further in §5.4.

5.4 The Lack of a Consistent Theory for SNe Ia Progenitors

Besides this work, there are several other studies which place quantitative or qualitative limits on the fraction of SD progenitor systems using a range of wavelengths and techniques (e.g., Gilfanov & Bogdán, 2010; Hayden et al., 2010; Bianco et al., 2011; Brown et al., 2012; Chomiuk et al., 2016). Most of these studies focus on WD+RG systems, as these are the easiest to observationally detect. Each study individually does not definitively rule out SD SNe Ia progenitors, however, when considered as a whole it is clear that most SNe Ia cannot form through the classical SD scenario. Thus, the DD scenario likely account for the majority of normal SNe Ia. However, detecting and characterising double WD binaries is exceptionally difficult (e.g., Rebassa-Mansergas et al., 2018).

Reconciling limits on SD progenitors with SD-favored SNe (i.e., SNe Ia-CSM and SNe Ia with variable NaID) has long been a difficulty for the community. Especially interesting are the systems with conflicting interpretations, such as SN 2007le and ASASSN-18bt. SN 2007le exhibits time-variable, blue-shifted NaID absorption (Sternberg et al., 2014) but has stringent limits on stripped material emission (this work, Table 14). Similarly, ASASSN-18bt showed a two-component rising light curve (Shappee et al., 2019; Dimitriadis et al., 2019b), a potential signature for SN ejecta impacting a nearby companion (Kasen, 2010). However, nebular spectra rule out any stripped material emission with strict upper limits (Tucker et al., 2018; Dimitriadis et al., 2019a, this work). While the discrepancies for both SNe Ia can also be explained with alternative theories (e.g., Ni56 mixing for the two-component rise in ASASSN-18bt and DD merger debris for the NaID absorption in SN 2007le), these objects highlight the uncertainties that still surround SN Ia progenitors.

Recently, ATLAS18qtd (SN 2018cqj) was discovered to exhibit time-variable H$\alpha$ emission in the nebular phase (Prieto et al., 2019). The spectra were posted after the submission of this manuscript, however, it warrants a brief discussion here. The classification spectrum taken at $19$ days after maximum has no evidence for H emission, and the next spectrum was not acquired until $\sim 190$ days after maximum. The measured H$\alpha$ luminosity declines contemporaneously with the SN Ia luminosity, a key expectation for material stripped from a SD progenitor. However, there are only two measurements of the H$\alpha$ emission and the inferred mass of the stripped material ($M_{st}\approx 10^{-3}~{}M_{\odot}$) is far lower than expected ($\sim 0.1-0.5M_{\odot}$). ATLAS18qtd is an under-luminous explosion, so it is possible the stripped material will be lower than expected from simulations in the literature, but the extent of these effects is still unexplored. Late-time observations of this unique object may yet further constrain the evolution of the H$\alpha$ emission and help elucidate its origin. If we assume ATLAS18qtd is indeed a SD progenitor system, this discovery highlights the inherent rarity of such events compared to the typical SN Ia population.

There is also the possibility that stripped material does exist in our sample but is invisible due to observational factors. The radioactively-decaying SN Ia ejecta provides a power source for the stripped material, namely gamma-ray deposition. Since we only analyze spectra that are in the nebular phase we are probing the innermost regions of the explosion. SNe Ia at these epochs essentially have no photosphere, and thus have no way of shrouding the H$\alpha$-emitting material. No such mechanism or process has been proposed to suppress the expected H$\alpha$ emission, so we consider this possibility unlikely. We conclude most SNe Ia cannot have formed from a classical SD progenitor system based on this work.

6 Conclusion

We present a large, comprehensive search for emission expected from stripped companion material in the SD formation scenario of SNe Ia. Using 227 spectra of $111$ SNe Ia from a variety of telescopes and instruments, we find no evidence for any stripped material emission in our sample. Using these null detections, we place statistical constraints on the fraction of SNe Ia that can form through the classical RLOF SD scenario, finding $<5.5\%$ and $<6.4\%$ of SNe Ia can form through the H-rich and He-rich channels, respectively, at $3\sigma$ confidence. The lack of emission is difficult to reconcile with the classical SD formation scenario for SNe Ia, and provides unique constraints on the production mechanism of these phenomena.

Thus far, there has not been a proposed formation mechanism that adequately reproduces all aspects of SN Ia properties. There seems to be contributions from both SD and DD progenitors to the total SN Ia rate (e.g., Sec. 4.1 from Maoz et al., 2014), yet the exact distribution is widely debated. Reconciling seemingly conflicting results (e.g., this work versus Sternberg et al., 2014) has long been a difficulty. Any unifying theory for SNe Ia formation must account for all the observed characteristics of these phenomena and the seemingly conflicting results across various methodologies. If the SD channel does produce a significant fraction of SNe Ia, there must be an unincorporated physical process in previous modeling efforts to explain our non-detections of stripped material. Alternatively, most SNe Ia must form from DD systems to match the results presented here.

Facilities: duPont, Magellan, Very Large Telescope

Software: Python2.7, astropy (The Astropy Collaboration et al., 2018), astroquery (Ginsburg et al., 2019) numpy, scipy, PyMUSE (Pessa et al., 2018), SpectRes (Carnall, 2017), extinction151515https://github.com/kbarbary/extinction, SExtractor (Bertin & Arnouts, 1996), Montage161616http://montage.ipac.caltech.edu/, Lpipe, IDL8.6, LowRedux, IRAF, SNooPy (Burns et al., 2011)

Acknowledgements

We thank K. Maguire, K. Graham, K. Motohara, K. Maeda, S. Taubenberger, T. Diamond, G. Dimitriadis, C. Ashall, and D. Sand for supplying nebular spectra. We thank A. Laity for assisting with the KOA data search and retrieval. Additionally, we thank C. Auge, G. Anand, A. Payne, and O. Graur for useful conversations about the project. We thank P. Chen from providing several SNe Ia light curves prior to publication. Also, many thanks to Bev Wills for her help tracking down the information regarding the nebular spectrum of SN 1981B.

M.A.T. acknowledges support from the United States Department of Energy through the Computational Sciences Graduate Fellowship (DOE CSGF) through grant DE-SC0019323. B.J.S is supported by NSF grants AST-1908952, AST-1920392, and AST-1911074. M.D.S. is supported in part by a generous grant (13261) from VILLUM FONDEN and a project grant from the Independent Research Fund Denmark. Support for J.L.P. is provided in part by FONDECYT through the grant 1191038 and by the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics, MAS. P.J.V. is supported by the National Science Foundation Graduate Research Fellowship Program Under Grant No. DGE-1343012. C.S.K. is supported by NSF grants AST-1515876, AST-1515927 and AST-181440. C.S.K. is also supported by a fellowship from the Radcliffe Institute for Advanced Studies at Harvard University.

This work is Based on (in part) observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere under ESO programmes 0100.D-0191(A), 0101.D-0173(A), 0102.D-0287(A), and 096.D-0296(A). This paper includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile. The CSP has been supported by the National Science Foundation under grants AST0306969, AST0607438, AST1008343, AST1613426, and AST1613472.

This paper made use of the modsIDL spectral data reduction reduction pipeline developed in part with funds provided by NSF Grant AST-1108693.

This research made use of Montage. It is funded by the National Science Foundation under Grant Number ACI-1440620, and was previously funded by the National Aeronautics and Space Administration’s Earth Science Technology Office, Computation Technologies Project, under Cooperative Agreement Number NCC5-626 between NASA and the California Institute of Technology.

This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been made possible through contributions by the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the University of Edinburgh, the Queen’s University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation Grant No. AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.

Based on observations obtained at the Gemini Observatory acquired through the Gemini Observatory Archive and processed with the Gemini PyRAF package, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina), and Ministério da Ciência, Tecnologia e Inovação (Brazil).

This paper makes use of data obtained from the Isaac Newton Group of Telescopes Archive which is maintained as part of the CASU Astronomical Data Centre at the Institute of Astronomy, Cambridge.

The LBT is an international collaboration among institutions in the United States, Italy and Germany. LBT Corporation partners are: The University of Arizona on behalf of the Arizona Board of Regents; Istituto Nazionale di Astrofisica, Italy; LBT Beteiligungsgesellschaft, Germany, representing the Max-Planck Society, The Leibniz Institute for Astrophysics Potsdam, and Heidelberg University; The Ohio State University, and The Research Corporation, on behalf of The University of Notre Dame, University of Minnesota and University of Virginia.

Appendix A A Nebular Phase Phillip’s Relation