Nucleosynthesis in the Innermost Ejecta of Neutrino-Drive Supernova Explosions in Two Dimensions

TL;DR

This study investigates nucleosynthesis in the innermost ejecta of two-dimensional supernova models across various progenitor masses, revealing significant production of light trans-iron elements and isotopes like $^{48}$Ca and $^{60}$Fe, with implications for galactic chemical enrichment.

Contribution

It provides the first detailed 2D nucleosynthesis analysis of innermost supernova ejecta across a range of progenitor masses, highlighting their role in galactic element production.

Findings

Low-mass models produce high levels of light trans-iron elements.

E8.8 and Z9.6 models yield similar nucleosynthesis outcomes.

Massive models mainly produce $^{92}$Mo, with limited galactic contribution.

Abstract

We examine the nucleosynthesis in the innermost, neutrino-processed ejecta (a few $10^{-3}\,M_\odot$) of self-consistent, two-dimensional explosion models of core-collapse supernovae for six progenitor stars with different initial masses. Three models have initial masses near the low-mass end of the supernova range, $8.8\,M_\odot$ (e8.8; electron-capture supernova), $9.6\,M_\odot$ (z9.6), and $8.1\,M_\odot$ (u8.1), with initial metallicities of 1, 0, and $10^{-4}$ times the solar metallicity, respectively. The other three are solar-metallicity models with initial masses of $11.2\,M_\odot$ (s11), $15\,M_\odot$ (s15), and $27\,M_\odot$ (s27). The low-mass models e8.8, z9.6, and u8.1 exhibit high production factors (nucleosynthetic abundances relative to the solar ones) of 100--200 for light trans-iron elements from Zn to Zr. This is associated with appreciable ejection of neutron-rich matter in these models. Remarkably, the nucleosynthetic outcomes for progenitors e8.8 and z9.6 are almost identical, including interesting productions of $^{48}$Ca and $^{60}$Fe, irrespective of their quite different (O-Ne-Mg and Fe) cores prior to collapse. In the more massive models s11, s15, and s27, several proton-rich isotopes of light trans-iron elements, including the $p$-isotope $^{92}$Mo (for s27) are made, up to production factors of $\sim$30. Both electron-capture and core-collapse supernovae near the low-mass end can therefore be dominant contributors to the Galactic inventory of light trans-iron elements from Zn to Zr and probably $^{48}$Ca and live $^{60}$Fe. The innermost ejecta of more massive supernovae may have only sub-dominant contributions to the chemical enrichment of the Galaxy except for $^{92}$Mo.

Tables

Table 1. Table 1: Parameters of Supernova Explosion Models

Model	$M_{\mathrm{prog}}$aaProgenitor mass at the zero-age main sequence.	$Z_{\mathrm{prog}}$bbMetallicity at the zero-age main sequence.	$M_{\mathrm{CO}}$cc CO core mass at collapse.	$M_{\mathrm{He}}$dd He core mass at collapse.	$\Delta \theta$eeAngular resolution.	$t_{\mathrm{expl}}$ffPost-bounce time of explosion, defined as the point in time when the average shock radius $⟨r_{\mathrm{sh}}⟩$ reaches $400\mathrm{km}$.	$t_{\mathrm{fin}}$ggFinal post-bounce time reached in simulation.	$m_{\mathrm{fin}}$hhMass coordinate corresponding to the average shock radius at the end of the simulation.	$E_{\mathrm{diag}}$iiDiagnostic explosion energy at the end of simulation.
	($M_{\odot }$)	($Z_{\odot }$)	($M_{\odot }$)	($M_{\odot }$)	deg	(ms)	(ms)	($M_{\odot }$)	(${10}^{50}\mathrm{erg}$)
e8.8	8.8	1	1.377	1.377	1.4	92	362	$>1.377$jj Note that an artificial envelope with $\rho \propto r^{-3}$ was used in Wanajo et al. (2011a) outside the He core. It is therefore not appropriate to give a more precise mass coordinate for final position of the shock in the hydrogen shell.	0.9
z9.6	9.6	0	1.371	1.69	1.4	125	1420	$>1.373$kkBy the end of the simulation, the shock has crossed the outer grid boundary at a mass coordinate of $1.373M_{\odot }$ in model z9.6.	0.6
u8.1	8.1	${10}^{-4}$	1.385	1.92	1.4	177	335	1.373	0.4
s11llSame as model s11.2 in Woosley et al. (2002) and Müller et al. (2012a).	11.2	1	1.89	2.84	2.8	213	922	1.39	0.4
s15mmSame as model s15s7b2 in Woosley & Weaver (1995) and Müller et al. (2012a).	15	1	2.5	4.5	2.8	569	779	1.45	1.3
s27nnSame as model s27.0 in Woosley et al. (2002) and Müller et al. (2012b).	27	1	7.2	9.2	1.4	209	790	1.74	1.9

Table 2. Table 2: Properties of Innermost SN Ejecta

Model	Type	$M_{\mathrm{PNS}}$ccBaryonic mass of the proto-neutron star at the end of simulation.	$M_{\mathrm{ej}}$ddTotal mass in the innermost ejecta.	$M_{\mathrm{ej},n}$eeEjecta mass with .	$Y_{e,\min }$ffMinimal $Y_e$ evaluated at $T_9=10$ (see text).	$Y_{e,\max }$ggMaximal $Y_e$ evaluated at $T_9=10$ (see text).	$S_{\min }$hhMinimal asymptotic entropy (at the end of simulation).	$S_{\max }$iiMaximal asymptotic entropy (at the end of simulation).
		($M_{\odot }$)	(${10}^{-3}{M}_{\odot }$)	(${10}^{-3}{M}_{\odot }$)			($k_B{\mathrm{nuc}}^{-1}$)	($k_B{\mathrm{nuc}}^{-1}$)
e8.8	ECSN	1.36	11.4	5.83	0.398	0.555	9.80	383
z9.6	CCSN	1.36	12.4	4.94	0.373	0.603	12.6	27.8
u8.1	CCSN	1.36	7.69	3.24	0.399	0.612	9.83	29.9
s11	CCSN	1.36	14.1	0.133	0.474	0.551	6.64	34.7
s15	CCSN	1.58	15.9	0.592	0.464	0.598	6.78	36.7
s27	CCSN	1.65	27.3	0.759	0.387	0.601	5.19	44.0

Table 3. Table 3: Top 5 Production Factors

Model	1		2		3		4		5
e8.8	86Kr	354	87Rb	260	82Se	252	74Se	222	88Sr	210
z9.6	82Se	168	88Sr	166	90Zr	123	74Se	110	87Rb	102
u8.1	74Se	149	90Zr	82.6	70Ge	47.9	78Kr	38.9	64Zn	33.8
s11	64Zn	1.48	45Sc	1.01	60Ni	0.857	32S	0.743	40Ca	0.632
s15	74Se	24.8	90Zr	15.4	78Kr	6.97	64Zn	6.10	70Ge	5.36
s27	74Se	43.1	78Kr	35.4	92Mo	30.7	90Zr	17.2	84Sr	12.5

Table 4. Table 4: Masses of Radioactive Isotopes in the Innermost Ejecta ( M ⊙ subscript 𝑀 direct-product M_{\odot} )

Model	26Al	41Ca	44Ti	53Mn	60Fe	56Ni	57Ni
e8.8	4.39E$-$08	1.96E$-$07	2.06E$-$06	1.11E$-$06	3.61E$-$05	2.93E$-$03	1.01E$-$04
z9.6	1.29E$-$07	1.16E$-$07	2.41E$-$06	1.61E$-$06	3.14E$-$05	2.51E$-$03	9.15E$-$05
u8.1	4.77E$-$08	5.77E$-$08	1.97E$-$06	1.45E$-$06	6.65E$-$07	1.60E$-$03	7.33E$-$05
s11aaValues for these models should be taken as lower limits (see text).	1.22E$-$09	1.50E$-$07	1.19E$-$06	2.53E$-$06	1.96E$-$20	3.86E$-$03	8.75E$-$05
s15aaValues for these models should be taken as lower limits (see text).	1.07E$-$08	2.25E$-$07	1.71E$-$06	4.46E$-$06	2.44E$-$18	6.05E$-$03	1.16E$-$04
s27aaValues for these models should be taken as lower limits (see text).	2.53E$-$08	4.56E$-$07	3.31E$-$06	5.89E$-$06	1.14E$-$06	5.57E$-$03	1.49E$-$04

Equations

$$\rho (t)=c_1(t-t_1{)}^{-2}(t>t_{\mathrm{fin}}),$$

$$T(t)=c_2(t-t_1{)}^{-2/3}(t>t_{\mathrm{fin}})$$

$$\frac{f_{z9.6}}{1-f_{z9.6}}=\frac{X_{\odot }{(}^{82}\mathrm{Se})/X_{\odot }{(}^{16}\mathrm{O})}{M_{z9.6}{(}^{82}\mathrm{Se})/⟨M{(}^{16}\mathrm{O})⟩}=0.164,$$

Full text

nuclear reactions, nucleosynthesis, abundances — stars: abundances — stars: neutron — supernovae: general

1 Introduction

Core-collapse supernovae (CCSNe), the deaths of stars with initial masses heavier than about $8M_{\odot}$, have long been suggested to be important astrophysical sources of trans-iron species as well as of intermediate-mass and iron-group elements. Traditionally, studies of CCSN nucleosynthesis were based on artificial one-dimensional (1D) explosion models with free parameters such as the mass-cut (location of ejecta-remnant interface), the electron fraction ($Y_{\mathrm{e}}$; number of protons per nucleon) of the ejecta, and the explosion energy (e.g., Woosley & Weaver, 1995; Thielemann, 1996; Rauscher et al., 2002; Limongi & Chieffi, 2006; Tominaga, 2007; Heger & Woosley, 2010; Nomoto et al., 2013). Nucleosynthetic abundances made near the mass-cut in the innermost ejecta are, however, highly dependent on such free parameters.

The approach of replacing the complex multi-dimensional dynamics of a neutrino-driven supernova (SN) with a piston or thermal bomb as an artificial explosion engine is likely to be problematic when it comes to studying the innermost ejecta. These parameterized models face two serious problems in modelling the innermost ejecta: Most importantly, they fail to reproduce the thermodynamic history of the neutrino-driven ejecta, i.e., of material that makes its way deep into the gain region, is then heated by neutrinos and ejected in buoyant high-entropy bubbles. In these ejecta, any memory of the initial composition is lost as charged-current neutrino interactions completely reset the electron fraction $Y_{\mathrm{e}}$ and entropy $s$. The final $Y_{\mathrm{e}}$ and $s$ in the ejecta are determined by the interplay of the neutrino reactions and the expansion of the ejecta (see Pruet et al. 2005, 2006; Fröhlich et al. 2006; Wanajo et al. 2011a and in particular Section 2.2.1 of Müller 2016). It is therefore impossible to reproduce this ejecta component if one assumes that the only effect of the supernova engine on the ejecta is to provide shock heating as in simpler models of the engine. Moreover, even for the explosive burning of material that is immediately ejected after being shocked, the simple engine models are problematic for material close to the “mass cut”: For ejecta that are shock-heated while the supernova engine is still feeding energy into the incipient explosion (which can take seconds; Müller, 2015; Bruenn et al., 2016; Müller et al., 2017), the shock heating is sensitive to the nature of the engine, and it is therefore not sufficient to merely tune an artificial engine to produce plausible final explosion energies and nickel masses to capture the nucleosynthesis in this ejecta component. This makes it difficult to predict nucleosynthesis of some iron-group and trans-iron (Zn and heavier) elements based on such parameterized models in these two ejecta components, which we term the “innermost ejecta”. It is therefore imperative to complement extant studies of the detailed explosive and hydrostatic nucleosynthesis with nucleosynthesis calculations based on more consistent models of the supernova engine.

Recent work by Sukhbold et al. (2016) has advanced the 1D approach by adopting parameterized neutrino-powered explosion models, which is a first step towards addressing these problems. In their models the boundary conditions (e.g., proto-neutron star contraction and core luminosity) are set deep inside the proto-neutron star and the physical conditions of the innermost ejecta are obtained as a result of hydrodynamical computations (see also Fröhlich et al., 2006; Perego et al., 2015, for comparable approaches beyond piston and thermal bomb models in 1D). Similar to previous works, they found production of elements from B to Cu in reasonable agreement with the solar ratio (except for some elements that had other contributors such as low-mass stars and SNe Ia). They reported, however, a severe deficiency of light trans-iron elements from Zn to Zr, which had been explained in part by the weak $s$-process in previous studies (e.g., Woosley & Heger, 2007). In addition, astrophysical sources of 48Ca (neutron-rich isotope of Ca), 64Zn (main isotope of Zn), and 92Mo ($p$-isotope) still remain unresolved, for which a rare class of SNe Ia (Meyer et al., 1996; Woosley, 1997), hypernovae (Umeda & Nomoto, 2002; Tominaga, 2007) and neutron-rich nuclear equilibrium (Hoffman et al., 1996; Wanajo, 2006), respectively, have been proposed as possible explanations. Note, however, that Sukhbold et al. (2016) did not include neutrino-heated (but just shock-heated) ejecta in their analysis.

One of the fundamental problems in such 1D models is obviously the limitation of dimensionality. Among other things, they do not account for the spatial variations in electron fraction $Y_{\mathrm{e}}$, entropy $S$, and ejection velocity that is seen in multi-dimensional CCSN models. Two-dimensional (2D) simulations with sophisticated neutrino transport therefore provide a much better basis for studying the nucleosynthesis in the innermost CCSN ejecta. Pruet et al. (2005, 2006) used the hydrodynamical trajectories of a $15M_{\odot}$ CCSN (Buras et al., 2006) for nucleosynthesis and showed that interesting amounts of Sc, Zn, and light $p$-nuclei were formed in the innermost proton-rich ejecta (see also Fujimoto et al., 2011), while the contribution of neutron-rich ejecta appeared to be subdominant (Hoffman et al., 2007). This was an important step beyond previous CCSN nucleosynthesis studies, but the explosion, though neutrino-driven, was still induced artificially like the piston-induced or thermal-bomb explosions of the previous 1D approaches, i.e., the 2D explosion was not obtained in a fully self-consistent manner. Moreover, based on the superior treatment of the neutrino transport in our present models we can re-investigate the question of nucleosynthesis in the neutron-rich ejecta, in which light trans-iron species could be abundantly produced (e.g., Hoffman et al., 1996).

To our knowledge, the only extant study of nucleosynthesis based on a self-consistent multi-dimensional explosion model is the one by Wanajo et al. (2011a, 2013a, 2013b), which is based on a 2D simulation of an $8.8M_{\odot}$ electron-capture SN (ECSN; a sub-class of CCSNe arising from collapsing O-Ne-Mg cores, Nomoto, 1987; Janka et al., 2008). They found appreciable production of trans-iron elements from Zn to Zr, 48Ca, and 60Fe (radioactive nuclei) in the innermost neutron-rich ejecta, a very different result from nucleosynthesis studies (Hoffman et al., 2008; Wanajo et al., 2009) based on the corresponding 1D models (Kitaura et al., 2006; Janka et al., 2008). This demonstrates the importance of self-consistent multi-D models for reliable nucleosynthesis predictions.

2D explosion models only provide a first glimpse at the role of multi-D effects in supernova nucleosynthesis, however. Recent three-dimensional (3D) core-collapse simulations have shown qualitative and quantitative differences to 2D (see, e.g., Janka et al., 2016, for a recent review) concerning shock revival (with a trend towards delayed or missing explosions) and also concerning the multi-D flow dynamics and energetics during the first phase of the explosion (Melson et al., 2015; Müller, 2015). Thus, nucleosynthesis studies based on 3D models will eventually be needed, but are, of course, computationally much more demanding.

This paper aims at extending the 2D studies of Wanajo et al. (2011a, 2013a, 2013b) to examine the nucleosynthesis in the innermost ejecta of CCSNe arising from iron-core progenitors. This will be an important step toward future nucleosynthesis studies from self-consistent 3D explosion models. In addition to the ECSN model studied by Wanajo et al. (2011a, 2013a, 2013b), we consider five CCSN models with zero-age main sequence progenitor masses of $9.6\,M_{\odot}$ (initial metallicity of $Z=0\,Z_{\odot}$), $8.1\,M_{\odot}$ ($10^{-4}\,Z_{\odot}$), and $11.2\,M_{\odot}$, $15\,M_{\odot}$, and $27M_{\odot}$ ($1\,Z_{\odot}$) (§ 2). By including the $8.1M_{\odot}$ and $9.6M_{\odot}$ progenitors side-by-side with an ECSN model, our study retains a strong focus on the low-mass end of the progenitor spectrum. With the uncertainties surrounding the ECSN channel (Poelarends et al., 2008; Jones et al., 2013, 2014; Doherty et al., 2015; Jones et al., 2016), one particular question that we seek to answer is whether ECSN-like nucleosynthesis can also be obtained for slightly different progenitor channels close to the iron core formation limit.

All these SN explosions were obtained self-consistently, i.e., with no free parameters, in 2D axisymmetric simulations adopting an elaborate neutrino transport scheme (Müller et al., 2012a, b; Janka et al., 2012). Nucleosynthetic abundances are calculated by applying an up-to-date reaction network code to hydrodynamic trajectories in a post-processing step (§ 3). Some details of the nucleosynthesis mechanisms operating in the innermost ejecta are described by taking the result of the metal-free $9.6\,M_{\odot}$ star as representative of our models. The mass-integrated nucleosynthetic yields are compared to the solar abundances to test if the innermost ejecta of these SNe can be major sources of light trans-iron elements and some other species in the Galaxy (§ 4). Our conclusions follow (§ 5).

2 SN models

2.1 Numerical methods and progenitor models

All the SN hydrodynamical trajectories have been computed from 2D general relativistic simulations with energy-dependent ray-by-ray-plus neutrino transport based on a variable Eddington factor technique as implemented in the supernova code Vertex (Rampp & Janka, 2002; Buras et al., 2006; Müller et al., 2010). Except for the pseudo-relativistic ECSN model of Wanajo et al. (2011a), general relativity is treated in the extended conformal flatness approximation (Cordero-Carrión et al., 2009). A modern set of neutrino interaction rates (the “full rates” set of Müller et al. 2012a) has been used for the simulations. The explosions were obtained self-consistently and thus the models contained no free parameters.

The initial pre-SN models were adopted from Nomoto (1987, $8.8\,M_{\odot}$ star with an O-Ne-Mg core with solar metallicity), A. Heger (unpublished111Extension of Heger & Woosley (2010)., $9.6\,M_{\odot}$ and $8.1\,M_{\odot}$ models222Both the $9.6\,M_{\odot}$ of zero metallicity and the $8.1\,M_{\odot}$ model of $10^{-4}\,Z_{\odot}$ were at the low-mass ends of CCSN progenitors for their respective metallicities in the KEPLER calculations. See also Ibeling & Heger (2013) for general metallicity dependence of the CCSN lower mass limit. with metallicities $Z=0$ and $Z=10^{-4}\,Z_{\odot}$, respectively), Woosley et al. (2002, $11.2\,M_{\odot}$ solar metallicity model, s11.2 in their paper), Woosley & Weaver (1995, $15\,M_{\odot}$ solar metallicity model, s15s7b2 in their paper), Woosley et al. (2002, $27\,M_{\odot}$ solar metallicity model, s27.0 in their paper). The corresponding explosion models are labeled as e8.8, z9.6, u8.1, s11, s15, and s27 hereafter. Relevant model parameters are summarized in Table 1. For more details on the individual explosion models, we refer the reader to the original publications on e8.8 (Wanajo et al., 2011a), z9.6 (Janka et al., 2012), u8.1 (Müller et al., 2012b), s11, s15s7b2 (Müller et al., 2012a), and s27 (Müller et al., 2012b).

Note that although we include two models of subsolar metallicity, the limited number of models does not permit us to discuss the dependency on metallicity in this paper.

2.2 Explosion dynamics

Snapshots of the electron fraction, $Y_{\mathrm{e}}$, and the entropy per nucleon, $S$, in these simulations at late times are shown in Figure 1. One can see roughly spherical structures for e8.8 and z9.6 (top panels) and more strongly asymmetric features with a dipolar or quadrupolar geometry for the other models (middle and bottom panels). The different explosion dynamics reflects the core structures of pre-SN stars with steeper to shallower density gradients in the order of e8.8, z9.6, u8.1, s11, s15, and s27 (see Fig. 8 in Janka et al., 2012). The ECSN progenitor for e8.8 is a super-asymptotic giant branch (SAGB) star with an O-Ne-Mg core surrounded by a very dilute H-He envelope, while those of CCSNe are iron cores embedded by dense oxygen-silicon shells. For e8.8, therefore, the explosion sets in very early at a post-bounce time of $t_{\mathrm{pb}}\sim 80$ ms before vigorous convection can develop. Overturn driven by the Rayleigh-Taylor instability only occurs when the explosion is underway, but the plumes do not have sufficient time to merge into large structures so that no global asymmetry emerges. For the CCSN cases (except for z9.6), by contrast, the explosions gradually start after multi-dimensional effects, i.e., convection or the standing-accretion-shock instability (SASI, Blondin et al., 2003), have reached the non-linear regime (the onset of the explosion occurs at $t_{\mathrm{pb}}\sim 500$ ms for s15 and $t_{\mathrm{pb}}\sim 150\ldots 200$ ms for the others, Table 1 and Fig. 14 in Janka et al. (2012)). Moreover, due to the presence of a relatively dense and massive oxygen shell, shock expansion is slow enough for a dominant unipolar or bipolar asymmetry to emerge after shock revival.

Models z9.6 and u8.1 stand apart from the more massive CCSN models s11, s15, and s27, since stars close to the iron core formation limit exhibit evolutionary and structural similarities to ECSN progenitors (Jones et al., 2013, 2014; Woosley & Heger, 2015). Specifically, these progenitors have very thin O and C shells between the core and the low-density He and H envelope. Because of these peculiarities, model z9.6 (and to some degree u8.1) is a case on the borderline to ECSN-like explosion behavior (Müller, 2016). Its progenitor exhibits the steepest core-density gradient near the core-envelope interface among the CCSN cases, resulting in a similarly rapid expansion of the neutrino-heated ejecta and hence in $Y_{\mathrm{e}}$ and $s$ structures rather similar to those of e8.8. The progenitor of u8.1 has a slightly shallower core-density gradient than that of z9.6 so that the propagation of the shock is slightly slower than for z9.6, but still faster than for typical iron-core progenitors. Since the width of the ECSN channel is subject to considerable uncertainties (see Poelarends et al., 2008; Jones et al., 2013, 2014; Doherty et al., 2015; Jones et al., 2016, and references therein), CCSNe from this mass range are particularly interesting as a possible alternative source for “ECSN-like” nucleosynthesis (i.e., the characteristic nucleosynthesis in neutron-rich neutrino-heated ejecta with moderate entropy as discussed in Wanajo et al. 2011a, 2013a, 2013b).

As in Wanajo et al. (2011a) and similar to Wongwathanarat et al. (2016), we compute the trajectories for our nucleosynthesis calculations from the 2D data files (with a time spacing of $0.25\,\mathrm{ms}$) instead of co-evolving tracer particles during the simulation. In order not to follow the tracers during multiple convective overturns with the risk of accumulating discretization errors, we integrate the tracer trajectories backwards in time from an appropriate point during the simulation (i.e., starting either from the end of the simulation, or from a time when the bulk of the ejecta have cooled sufficiently as in the case of z9.6). This procedure greatly reduces the number of required trajectories to adequately sample the ejecta: Selecting the final locations of the tracer particles only within the region of interest reduces the total mass of ejecta that must be covered (less than $0.03M_{\odot}$) and makes it easy to use higher mass resolution where it is most needed, i.e., in the neutrino-processed ejecta. For a more general overview of the problems in extracting tracer trajectories from multi-D simulations, we refer the reader to Harris et al. (2017).

2.3 Nucleosynthesis conditions in the ejecta

Some nucleosynthesis-relevant properties for all SN models are summarized in Table 2. It is important to note that we only calculate the nucleosynthesis for the “early ejecta”, i.e., consider only the material that has been ejected in neutrino-driven outflows or undergone explosive burning in the shock by the end of the simulations. The contributions of the outer shells (i.e., the H-He envelopes of e8.8, z9.6, and u8.1 and material outside the middle of the O burning shell in s11, s15, and s27) and later neutrino-driven ejecta to the total yields are neglected. For the massive CCSNe (s11, s15, s27), the nucleosynthetic contribution for the outer part of the O shell therefore remains uncertain, and long-term simulations to several seconds (Müller, 2015; Müller et al., 2017) will be necessary to determine it. As the shock has only traversed part of the O shell in these models, we also miss part of the contribution of hydrostatic and explosive burning to heavy element production from O/C/He shells so that our yields can only be understood as lower limits for some species (among them ${}^{26}\mathrm{Al}$ and ${}^{60}\mathrm{Fe}$). We also disregard the possibility of late-time fallback of the initial ejecta, but this may not be a major uncertainty since the most advanced parameterised 1D models of neutrino-driven explosions suggest that this plays a minor role (Ertl et al., 2016) for the progenitor mass range considered here.

For models e8.8, z9.6, and u8.1, explosive burning is already complete at the end of the simulations: The outer shell (composed of H and He) will not add significant yields of heavy elements, and no more explosive nucleosynthesis is taking place as the shock propagates to the stellar envelope after the end of the simulations. We still miss small amounts of ejected material from the neutrino-driven wind (Duncan et al., 1986) in these progenitors, however. This material may undergo weak $r$- or $\nu p$-process nucleosynthesis, though the most recent calculations of wind nucleosynthesis for e8.8 suggest only a relatively unspectacular production of iron group elements and some $\nu p$-process nuclides with small production factors (Pllumbi et al., 2015), which turn out to be insignificant compared to the contribution from the early ejecta that we investigate here. For e8.8, z9.6, and u8.1, the yields presented here thus cover essentially the complete nucleosynthesis of heavy elements in these progenitors.

The case is different for s11, s15, and s27, where the shock has progressed only to the middle of the O/Si shell. For these models, substantial amounts of ashes from O, Ne, C, and He burning thus remain to be ejected and will contribute significantly to the total production factors. The post-shock temperatures at the end of our simulations also remain sufficiently high for some additional explosive O burning to take place. Moreover, strong accretion downflows still persist in these models. This keeps the neutrino luminosities high and allows the ejection of neutrino-heated matter to continue well beyond $1\,\mathrm{s}$ after the onset of the explosion (Müller, 2015; Bruenn et al., 2016). Our nucleosynthesis calculations therefore place only a lower bound on the production of iron-group and trans-iron group elements in the supernova core of these models. It is noteworthy that this may partly contribute to the unexpectedly small mass of 56Ni obtained for these models, which remains significantly smaller than expected for “ordinary” supernovae (e.g., $0.07\,M_{\odot}$ for SN 1987A, Bouchet et al., 1991).

Aside from the limitation of our analysis to the nucleosynthesis during the first few hundred milliseconds after shock revival, the nucleosynthesis in our models remains subject to to other uncertainties: The simulations were conducted assuming axisymmetry (2D), and the explosion energies at the end of simulations are only (0.3–$1.5)\times 10^{50}$ erg (see Fig. 15 in Janka et al., 2012), which are either less energetic than typical observed events (several $10^{50}$ erg, e.g., Kasen & Woosley, 2009; Nomoto et al., 2013) or still in a phase of steep rise, i.e., not converged to their final values. We discuss the possible repercussions of this in § 4.8 and § 5.

Figure 2 shows the $Y_{\mathrm{e}}$ distributions in the ejecta for all models evaluated at $T_{9}=10$, where $T_{9}$ is the temperature in units of $10^{9}$ K. For a trajectory with the maximum temperature of $T_{\mathrm{9,max}}<10$, we show $Y_{\mathrm{e}}$ at $T_{9}=T_{\mathrm{9,max}}$ instead. $\Delta M_{\mathrm{ej}}$ is the ejecta mass in each $Y_{\mathrm{e}}$ bin with an interval of $\Delta Y_{\mathrm{e}}=0.005$. The minimum and maximum values of $Y_{\mathrm{e}}$ for all models are given in Table 2 (8th and 9th columns, respectively). The $Y_{\mathrm{e}}$ distributions shown here are similar to those inferred from the hydro data at late times except for small (up to a few %) shifts toward $Y_{\mathrm{e}}\approx 0.5$ as a result of some numerical diffusion and mixing (clipping of extrema) that suppresses the tails of the $Y_{\mathrm{e}}$ distribution in the hydro at late times333In practice, we find this effect to be small up to the point where the ejecta reach a radius of around $1000\,\mathrm{km}$ and the radial computational grid becomes coarser.. We find that low-mass models (e8.8, z9.6, and u8.1) have appreciable amounts of neutron-rich ejecta (40–50%; 7th column in Table 2). This is due to the faster growth of the shock radii for these low-mass cases: As a result of the higher ejecta speed, less time is available to increase the $Y_{\mathrm{e}}$ by neutrino processing as material is ejected from the neutron-rich environment near the gain radius, where conditions close to equilibrium between neutrino absorption and electron (and to some extent positron) captures are maintained and lead to a low $Y_{\mathrm{e}}$. By contrast, the bulk of the ejecta are proton-rich (96–99%; Table 2) in massive models (s11, s15, and s27). Here the ejecta expand more slowly, allowing neutrino absorption to reset the $Y_{\mathrm{e}}$ to an equilibrium value determined by the competition of electron neutrino and antineutrino absorption (Qian & Woosley, 1996; Fröhlich et al., 2006). With similar electron neutrino and antineutrino mean energies the equilibrium value tends to lie above $Y_{\mathrm{e}}=0.5$ because of the proton-neutron mass difference.

Figure 3 illustrates the distributions of ejecta masses as functions of $Y_{\mathrm{e}}$ and asymptotic entropy per nucleon, $S$ (in units of Boltzmann’s constant $k_{\mathrm{B}}$). All SN models show spikes of $Y_{\mathrm{e}}\approx 0.50$ components as leftovers of the initial composition of shocked material that never undergoes strong neutrino processing, and a positive correlation of $S$ with $Y_{\mathrm{e}}$ in the neutrino-processed ejecta. The latter fact is reasonable because neutrino-heating raises both $Y_{\mathrm{e}}$ and $S$. We find, however, a larger scatter of the entropies at a given $Y_{\mathrm{e}}$ for massive SN models (s11, s15, and s27). This reflects the more vigorous motions arising from convective instability and SASI for more massive cases as well as stronger temporal and spatial variations in the neutrino irradiation.

Note that the very high entropies at $Y_{\mathrm{e}}\approx 0.5$ for e8.8 (up to $S_{\mathrm{max}}=383k_{\mathrm{B}}$; last column in Table 2) stem from shock heating of outgoing material colliding with the dilute SAGB envelope. However, a sizable post-shock entropy, $S>100k_{\mathrm{B}}$, is reached only in shells which never reach nuclear equilibrium ($T_{9}<3$, Janka et al., 2008; Kuroda et al., 2008) so that these shells do not contribute to the production of heavy elements (such as an $r$-process suggested by Ning et al., 2007). Except for this component of shock-heated ejecta with low temperatures, e8.8 has a maximum entropy of nucleosynthesis-relevant material of $\approx 25k_{\mathrm{B}}$, and more massive models have larger values ($S_{\mathrm{max}}$; last column in Table 2).

The core-collapse simulations were stopped at $t=t_{\mathrm{fin}}$ for our models, where $t_{\mathrm{fin}}=0.423$ s, 0.605 s, 0.474 s, 0.767 s, 0.947 s, and 1.13 s after core bounce for e8.8, z9.6, u8.1, s11, s15, and s27, respectively. At these times, the temperatures in the ejecta were still high, in particular for massive models, so that nucleosynthesis would be still active. The temperature ($T$) and density ($\rho$) thus need to be extrapolated for nucleosynthesis calculations. It is known that the late-time evolution of the density is well approximated by $\rho\propto t^{-2}$ (e.g., Arcones et al., 2007). We thus assume

[TABLE]

where the constants $c_{1}$ and $t_{1}$ are determined to get a smooth connection of the density at $t=t_{\mathrm{fin}}$. The expansion of the ejecta is almost adiabatic at this stage (i.e., $T^{3}/\rho\approx\mathrm{constant}$)444Entropy generation due to electron-positron annihilation after the freezeout from nuclear statistical equilibrium (NSE) is not taken into account for deriving Equation (2). We expect, however, that its effect is minor because of the strong dependencies of nucleosynthetic abundances on $Y_{\mathrm{e}}$ rather than entropy or expansion timescale., and thus the temperature is extrapolated such as

[TABLE]

with $t_{1}$ from Equation (1) and $c_{2}$ determined so that the temperature matches the value at $t=t_{\mathrm{fin}}$. The radius $r$ for $t>t_{\mathrm{fin}}$, which is needed to calculate the rates of neutrino interactions, is obtained from Equation (1) with the assumption of steady-state conditions, i.e., $r^{2}\rho v_{r}=\mathrm{constant}$ (Panov & Janka, 2009; Wanajo et al., 2011b), where $v_{r}$ is the radial component of velocity at $t=t_{\mathrm{fin}}$ and constant afterwards. Selected temporal evolutions of density and temperature are shown in Figures 4 and 5, respectively, where the extrapolations are indicated by red curves. The evolutions for e8.8 and z9.6 appear to be nearly self-similar as expected from their almost spherical expansions (Fig. 1). For more massive models, in particular s11, s15, and s27, a variety of evolutions can be seen because of highly asymmetric, vigorous convective and SASI motions.

3 Nucleosynthesis

The nucleosynthesis yields in each SN trajectory are computed in a post-processing step by solving an extensive nuclear reaction network (Wanajo et al., 2001) with the temperature and density histories described in § 2. The numbers of processed trajectories are 2343 (e8.8), 6310 (z9.6), 4672 (u8.1), 2739 (s11), 2565 (s15), and 2312 (s27). The up-to-date network consists of 7435 isotopes between the proton- and neutron-drip lines from single neutrons and protons up to isotopes with $Z=110$. All the reaction rates are taken from REACLIB V2.0555https://groups.nscl.msu.edu/jina/reaclib/db/. (Cyburt et al., 2010) making use of experimental data when available. As we will see later, the nucleosynthetic abundances are mostly determined in nuclear equilibrium in the regions relatively close to $\beta$-stability where experimental masses are available. Uncertainties arising from nuclear data are thus expected to be small. Rates for electron capture (Langanke & Martinez-Pinedo, 2001) as well as for neutrino interactions on free nucleons (McLaughlin et al., 1996) and $\alpha$-particles (Woosley et al., 1990) are also included. The radiation field computed in the supernova simulations is used as input for computing the neutrino interactions in our nucleosynthesis calculations. We retain the full dependence of the radiation field on radius, latitude, and time as computed in our ray-by-ray-plus approximation, i.e., we use the local neutrino energy density, number density, and energy moments of the distribution function at the current position of each tracer particle as input for the network calculations.

Each nucleosynthesis calculation is initiated when the temperature decreases to $T_{9}=10$ with initial mass fractions of $Y_{\mathrm{n}}=1-Y_{\mathrm{e}}$ for free neutrons and $Y_{\mathrm{p}}=Y_{\mathrm{e}}$ for free protons, respectively666At such high temperature (and density), the matter immediately attains nuclear statistical equilibrium (NSE) and thus any initial composition with the total charge of $Y_{\mathrm{e}}$ is available.. For the trajectories with $T_{\mathrm{9,max}}<10$, the initial compositions adopted from our hydrodynamical simulations are utilized.

3.1 Types of nucleosynthesis

We first analyze the nucleosynthesis in detail for z9.6, since this model covers the widest range in $Y_{\mathrm{e}}$ ($Y_{\mathrm{e}}$=0.373–0.603; Fig. 2). Figure 6 shows the neutron-, proton-, and $\alpha$-to-seed abundance ratios ($Y_{\mathrm{n}}/Y_{\mathrm{h}}$, $Y_{\mathrm{p}}/Y_{\mathrm{h}}$, and $Y_{\alpha}/Y_{\mathrm{h}}$) at a point when the temperatures decrease to $T_{9}=3$ for all the trajectories of model z9.6. We consider this temperature as it approximately corresponds to the end of nuclear equilibrium: This temperature is close to the conventional critical temperature for the termination of quasi-nuclear equilibrium (QSE; $T_{9}=4$, Meyer et al., 1998b), to the beginning of a $\nu p$-process ($T_{9}=3$, Fröhlich et al., 2006), and the beginning of an $r$-process ($T_{9}=2.5$, Woosley et al., 1994). Here, the seed abundance $Y_{\mathrm{h}}$ is defined as the total abundance of all nuclei heavier than helium. The other SN models show similar dependencies of $Y_{\mathrm{n}}/Y_{\mathrm{h}}$, $Y_{\mathrm{p}}/Y_{\mathrm{h}}$, and $Y_{\alpha}/Y_{\mathrm{h}}$ on $Y_{\mathrm{e}}$ (not shown here), indicating that $Y_{\mathrm{e}}$ (rather than entropy and expansion timescale) is most crucial for the nucleosynthesis in our case. For this reason, we describe our nucleosynthetic results for model z9.6 in terms of $Y_{\mathrm{e}}$. According to Figure 6, we can distinguish the following types of nucleosynthesis regimes in our supernova models: Among the (strongly) neutrino-processed ejecta, we find a nuclear statistical equilibrium (NSE) regime for $Y_{\mathrm{e}}<0.43$, a quasi-nuclear equilibrium (QSE) regime for $0.43\leq Y_{\mathrm{e}}<0.5$, and nucleosynthesis by charged-particle capture processes for $Y_{\mathrm{e}}\geq 0.5$. No $r$-process is expected in our models because of neutron-to-seed ratios far below unity over the entire range of $Y_{\mathrm{e}}$ (Fig. 6). We note that in all of these regimes (and different from “classical” explosive nucleosynthesis), the neutrino-processed material is initially in NSE and the QSE/charged-particle capture regime is reached after an NSE phase as the temperatures decreases during the expansion of the ejcecta.

In addition to these three regimes, there is a fourth regime of material with $Y_{\mathrm{e}}\approx 0.5$ and lower entropy; this comprises the ejecta that immediately expand after being shocked and undergo “classical” explosive nucleosynthesis. The nucleosynthesis in this regime is not the primary subject of this paper; for models e8.8, z9.6, and u8.1 it is unimportant in terms of yields, and for s11, s15, and s27, we merely cover the explosive burning of a part of the O shell, so that there is no basis for an extensive analysis of this regime. Moreover, the physical principles of classical explosive nucleosynthesis are well known in the literature (Arnett, 1996).

It is worth noting that although the regimes of NSE/QSE are also encountered in classical explosive nucleosynthesis, the conditions for the realization of these regimes are very different: For classical explosive burning, the nucleosynthesis is determined by the peak temperature (which depends on the explosion energy and the mass-radius profile of the progenitor) and, in the NSE/QSE regime, on the $Y_{\mathrm{e}}$ in the progenitor. In the case of the neutrino-processed ejecta, the initial temperature is always high enough for NSE to obtain, and the interplay of multi-dimensional fluid flow and weak interactions of neutrinos, electrons and positions determines the conditions at freeze-out from NSE/QSE, i.e., $Y_{\mathrm{e}}$, entropy, and expansion time scale.

3.1.1 NSE

For $Y_{\mathrm{e}}<0.43$, all the ratios $Y_{\mathrm{n}}/Y_{\mathrm{h}}$, $Y_{\mathrm{p}}/Y_{\mathrm{h}}$, and $Y_{\alpha}/Y_{\mathrm{h}}$ are considerably smaller than unity ($<0.01$) at $T_{9}=3$ (Fig. 6). The global distribution of final nucleosynthetic abundances is thus mostly determined in NSE at high temperature ($T_{9}>5$)777In this paper, we use the term “NSE” even for the case of $\alpha$-deficient QSE (Meyer et al., 1996; Wanajo et al., 2013a), in which NSE serves as a reasonable guideline for abundance determinations.. The subsequent QSE does not substantially change the abundance distribution because of the small amounts of free nucleons and $\alpha$ particles. This is due to relatively small entropies ($S\sim 14\,k_{\mathrm{B}}/\mathrm{nuc}$; Fig. 3) for these neutron-rich ejecta and the neutron-richness itself. Under such conditions the three-body process $\alpha(\alpha n,\gamma)^{9}$Be (followed by 9Be$(\alpha,\gamma)^{12}$C), rather than triple-$\alpha$, is fast enough to form the NSE cluster by assembling free nucleons and $\alpha$ particles. Such neutron-rich conditions also disfavor $\alpha$ emission (i.e., to avoid to be more neutron-rich). In NSE, the resulting abundance distribution is independent of specific reactions. What determines the abundance distribution are the binding energies per nucleon ($B/A$; shown in Figure 7, left). As the $Y_{\mathrm{e}}$ of nuclides (indicated by white lines) decreases from $\sim 0.50$ to $\sim 0.40$, the nuclides with the maximal $B/A$ shift from 56Ni ($Z=N=28$) to 48Ca ($Z=20$ and $N=28$) and 84Se ($Z=34$ and $N=50$, see Hartmann et al., 1985).

We find such NSE-like nucleosynthesis features in Figure 8, which shows the abundance distribution in selected trajectories of model z9.6 when the temperatures decrease to $T_{9}=5$, 4, and 3 as well as the abundances at the end of calculations. The top three panels correspond to the trajectories with NSE-like conditions of $Y_{\mathrm{e}}<0.43$ and relatively low entropies ($\sim 14\,k_{\mathrm{B}}/\mathrm{nuc}$). Major abundance peaks are already formed at $T_{9}=5$ (red lines). The abundance patterns are almost frozen when the temperature decreases to $T_{9}=4$ (defined as the end of NSE) and do not change significantly during the subsequent evolution.

3.1.2 QSE

For $0.43\leq Y_{\mathrm{e}}<0.50$, the $\alpha$ concentration becomes important ($Y_{\alpha}/Y_{\mathrm{h}}\sim 0.01$–10) but $Y_{\mathrm{p}}/Y_{\mathrm{h}}$ is less than unity at $T_{9}=3$. In this case, the final abundances are mainly determined in QSE, a subsequent stage after the $\alpha$-rich freeze-out from NSE (Woosley & Hoffman, 1992; Meyer et al., 1998b). At the end of NSE ($T_{9}\sim 5$), the single NSE cluster splits into two QSE clusters with one consisting of free nucleons and $\alpha$ particles and the other consisting of heavy nuclei. In the latter QSE cluster, the heavy nuclei are absorbed in the “$\alpha$-bath” and its distribution is determined by the $\alpha$ separation energies (shown in the right panel of Figure 7), independent of specific nuclear reactions. With a modest neutron-richness of $Y_{\mathrm{e}}\sim 0.43$–0.49 (values are indicated by white lines in Fig. 7), the nuclides near $N=28$ and 50 such as 64Zn, 88Sr, 89Y, 90Zr, and 92Mo are preferentially formed in QSE owing to their greater $\alpha$ separation energies (see also Hoffman et al., 1996; Wanajo, 2006).

We find in the left-middle and middle panels of Figure 8 ($Y_{\mathrm{e}}=0.450$ and 0.475, respectively) that the abundance distributions substantially change during QSE ($T_{9}\sim 5$ to 4). The abundance patterns are determined roughly when the temperature decreases to $T_{9}=3$, and further evolution are unimportant (although an enhancement of nuclei with $A=10$–50 can be seen as a result of $\alpha$-particle capture).

3.1.3 Charged-particle capture process

For $Y_{\mathrm{e}}\geq 0.50$, 56Ni dominates in the heavy QSE cluster, and the $\alpha$-rich freeze-out from QSE ($T_{9}\sim 4$) leads to an $\alpha$-process (Woosley & Hoffman, 1992). This greatly enhances the abundances of $\alpha$-elements with $A\sim 12$–40 (with multiples of 4) as can be seen in the right-middle panel of Figure 8 (for $Y_{\mathrm{e}}=0.500$). For $Y_{\mathrm{e}}>0.51$, both $Y_{\alpha}/Y_{\mathrm{h}}$ and $Y_{\mathrm{p}}/Y_{\mathrm{h}}$ are greater than unity at $T_{9}=3$ (Fig. 6). The freeze-out is thus followed by $\alpha$-capture and proton-capture processes. We find in the bottom three panels of Figure 8 ($Y_{\mathrm{e}}=0.525$, 0.550, and 0.603) that nuclei in a wide range of $A\sim 10$–70, including odd-$Z$ elements, are substantially enhanced by these charged-particle capture processes after the temperature drops below $T_{9}=3$.

Figure 9 compares the final abundances with (blue) and without (cyan) neutrino reactions for the trajectory that has the highest $Y_{\mathrm{e}}=0.603$ in model z9.6 (same as that in the right-bottom panel of Fig. 8). This indicates that the enhancement of nuclei with $A=60$–70 is due to a $\nu p$-process, in which the faster $(n,p)$ and $(n,\gamma)$ reactions with the free neutrons supplied by $\bar{\nu}_{e}$ capture on free protons replace the slower $\beta^{+}$-decays (Fröhlich et al., 2006; Pruet et al., 2006; Wanajo, 2006). Note that the $\nu p$-process in our result is very weak and only the nuclei up to $A\sim 70$ are produced despite its substantial proton-richness (up to $Y_{\mathrm{e}}=0.603$). By contrast, Wanajo et al. (2011b) have shown that the $\nu p$-process in neutrino-driven wind with similar proton-richness can produce nuclei up to $A\sim 120$ (see also Pruet et al., 2006; Arcones et al., 2012). This discrepancy is due to the lower entropies and longer expansion timescales in the early dynamical ejecta, which reduces $Y_{\mathrm{p}}/Y_{\mathrm{h}}$ at the beginning of a $\nu p$-process ($T_{9}\sim 3$), than those in the late-time neutrino-driven wind.

3.2 Dependencies of isotope productions on $Y_{\mathrm{e}}$

In § 3.1 we found that the iron-group (from Ca to Cu) and light trans-iron (from Zn to Mo) species can be produced in the innermost ejecta of z9.6, the model with the widest range in $Y_{\mathrm{e}}$ in the ejecta . No heavier elements are produced in any of our six models. In Figures 10 and 11, the final mass fractions of stable isotopes from K to Mo are presented as functions of $Y_{\mathrm{e}}$ for all the trajectories of model z9.6. The mass fractions of selected radioactive isotopes (before decay) are also shown in the right-bottom panel of Figure 11. We find from these figures that few isotopes exhibit maximum abundances near $Y_{\mathrm{e}}=0.5$, in particular the light trans-iron species (from Zn to Mo). Overall, Ni and light trans-iron species are predominantly formed in neutron-rich ejecta, although the weak $\nu p$-process in proton-rich ejecta plays a sub-dominant role for those up to Ge. Several isotopes such as 48Ca, 50Ti, 54Cr, and radioactive nuclide 60Fe are made only in very neutron-rich ejecta with $Y_{\mathrm{e}}\sim 0.40$–0.43 (Wanajo et al., 2013a, b). This sensitivity clearly demonstrates the importance of nucleosynthesis studies based on multi-dimensional SN simulations with detailed multi-group neutrino transport, which are indispensable for accurately determining the $Y_{\mathrm{e}}$-distribution in the ejecta.

4 Possible Contribution to the Solar Abundance Distribution

For each SN model, we calculate mass-integrated abundances from the nucleosynthetic outcomes of all trajectories. In the following subsections, we discuss the possible contribution of products from the innermost ejecta of SNe with different explosion dynamics during the first second after collapse to the Galaxy by comparing our nucleosynthesis yields to the solar values. In particular, we focus on the production of several key species such as 48Ca, Zn isotopes, light trans-iron elements, $p$-nuclide 92Mo, and the radioactive isotopes 56Ni and 60Fe. It is important to stress that our goal here is not to predict the full core-collapse supernova nucleosynthesis across the whole range of progenitors, which would require both longer simulations and a larger grid of models at different metallicities. Even with our small set of models, we can, however, already establish whether the innermost ejecta can provide an important contribution to the solar inventory for plausible rates of the different explosion behaviours exemplified by our six models. It is particularly noteworthy that focusing on the neutrino-processed ejecta allows us to neglect the influence of the progenitor metallicity on the yields, since any memory of the progenitor composition is erased in this ejecta component; i.e., the production of heavy elements in the neutrino-heated ejecta is always a primary process.

4.1 Comparison with the elemental solar abundance

For all SN models, the mass-integrated yields are compared to the solar abundance (Lodders, 2003). Figure 12 shows the elemental mass fractions in the total ejecta with respect to their solar values (not to the initial compositions of progenitors), i.e., “production factors”, for these models. The total ejecta mass from each SN is taken to be the sum of the ejected mass from the core and the outer envelope, that is, $M_{\mathrm{prog}}-M_{\mathrm{PNS}}$ in Tables 1 and 2. Here, the outer envelope is assumed to be metal-free (i.e., H and He only), which is reasonable for the models near the low-mass end of the SN range, e8.8, z9.6, and u8.1: The part of the H and He shells that were not included in our nucleosynthesis calculations would not contribute substantially to the yields for the range of nuclei considered here ($Z\geq 19$) regardless of progenitor metallicity. For the more massive models s11, s15, and s27, one should bear in mind that there is an important additional contribution to heavy elements (those heavier than helium) from the outer envelope (see Woosley et al., 2002; Woosley & Heger, 2007, and references therein).

In each panel of Figure 12, we show a “normalization band” in yellow, which covers the range within $1\,\mathrm{dex}$ of the maximum production factor and one-tenth of that. The elements that reside in this band can be (at least in part) originate from SNe represented by each model, provided that their production factors are greater than $\sim 10$ (e.g., Woosley & Heger, 2007). As an order-of-magnitude estimate, the production factors of $\sim 40$ for light trans-iron elements from Zn to Zr in our representative model z9.6 suggest that such low-mass CCSNe can be the major sources of these elements if these events account for a few 10% of all CCSNe and would still contribute sizable amounts if they make up $\mathord{\sim}10\%$ of all CCSNe. This suggests that SNe at the low-mass end of the progenitor spectrum as represented by models e8.8, z9.6, and u8.1 could be an important source of light trans-iron elements (§ 4.6).

Note that there is a remarkable agreement of the nucleosynthesis of z9.6 with that of e8.8, which is a consequence of the similarity of their pre-SN core structures with a steep density gradient outside the core and a very dilute outer envelope. In both cases, the resulting fast explosion lead to the ejection of appreciable amounts of neutron-rich material. Model u8.1 with a core structure very similar to (but with a slightly shallower density gradient than) that of z9.6 results in, however, a different nucleosynthetic trend with deficiencies of several elements between Zn and Zr. This indicates that only a slight difference of pre-SN core-density structures can lead to substantially different nucleosynthesis outcomes.

For more massive models, the production factors are smaller than $\sim 10$ for all elements, despite their greater ejecta masses compared to low-mass models ($M_{\mathrm{ej}}$ in Table 2). The maximum production factor of $\sim 1$ for s11 gives no element to be responsible for the Galactic chemical evolution. For s15 and s27, only Zr with the production factor $\sim 10$ is the elements that can be originated from these types of CCSNe. These SNe can be, however, possible contributors of some isotopes as discussed in § 4.2. Moreover, the non-neutrino processed “outer ejecta” from these stars, which are not fully included in our study, contribute significantly to the chemical enrichment of the Galaxy as discussed before.

4.2 Comparison with the isotopic solar abundance

Figure 13 compares the isotopic abundances with the solar values for all SN models. The maximum isotopic production factor for each model is generally greater than that of elements (§ 4.1), and therefore places tighter constraints on the contribution of relevant SNe to the Galaxy. In Table 3, we list the 5 largest production factors for each model. Note that most of the isotopes listed here are made in nuclear equilibrium, and thus uncertainties in individual nuclear reaction rates are irrelevant. Models e8.8 and z9.6 exhibit appreciable production factors of 354 (86Kr) and 168 (82Se), respectively. This implies that such low-mass SNe account for $\sim 10\%$ of all CCSN events (according to the reason described in § 4.1), supposing that these trans-iron elements originate solely from this class of events. A similar contribution of u8.1-like events can be expected with its largest production factor of 149 (74Se). The maximum production factor of 1.48 for s11 indicates that no species are dominantly produced in the innermost ejecta of such SNe. For s15 and s27, the largest production factors are 24.8 and 43.1 (74Se), respectively, which are sizably greater than those of elements ($\sim 10$, Fig. 13). This indicates that such intermediate-mass and massive CCSNe can be important sources of several species listed in Table 3.

To be more quantitative, we consider 82Se with the largest production factor for model z9.6 as representative. By assuming $f_{\mathrm{z9.6}}$ to be the fraction of z9.6-like events to all CCSNe, we have (Wanajo et al., 2011a)

[TABLE]

where $X_{\odot}(^{82}\mathrm{Se})=1.38\times 10^{-8}$ and $X_{\odot}(^{16}\mathrm{O})=6.60\times 10^{-3}$ are the mass fractions in the solar system (Lodders, 2003), $M_{\mathrm{z9.6}}(^{82}\mathrm{Se})=1.91\times 10^{-5}\,M_{\odot}$ is the ejecta mass of 82Se for z9.6, and $\langle M(^{16}\mathrm{O})\rangle=1.5\,M_{\odot}$ is the production of 16O by massive CCSNe averaged over the stellar initial mass function between $13\,M_{\odot}$ and $40\,M_{\odot}$ (see Wanajo et al., 2009). Equation (3) gives $f_{\mathrm{z9.6}}=0.14$, which corresponds to a mass window $\Delta M_{\mathrm{prog}}\sim 1\,M_{\odot}$ near the low-mass end of the SN progenitor spectrum, $M_{\mathrm{prog}}\sim 9\,M_{\odot}$. It is currently uncertain whether this mass window for z9.6-like progenitors is reasonable or not, as only a slight difference of core-density structure leads to a very different nucleosynthetic result of u8.1. If we apply Equation (3) to model e8.8 by replacing 82Se with 86Kr (Table 3), we get $f_{\mathrm{e8.8}}=0.085$. This corresponds to a mass window of $\Delta M_{\mathrm{prog}}\sim 0.5\,M_{\odot}$, which is in reasonable agreement with the prediction from synthetic SAGB models at solar metallicity (Poelarends et al., 2008). If other production channels were to contribute significantly to these elements, the allowed rate of ECSNe or z9.6-like explosion would, of course, be lower.

It is thus well conceivable that a combination (or either) of ECSNe and low-mass CCSNe accounts for the production of light trans-iron species in the Galaxy. For the more massive models s11, s15, and s27, a lack of self-consistent nucleosynthesis yields in the outer envelopes precludes a quantitative estimate of their contributions.

.

4.3 Neutron-rich vs. proton-rich ejecta

Our results described in § 4.1 and 4.2 shows that SNe near the low-mass end produce appreciable amounts of trans-iron species despite their small ejecta masses (compared to those of massive models; $M_{\mathrm{ej}}$ in Table 2). The reason can be found in Figure 14, which shows the fraction of the ejecta that originates in neutron-rich matter ($Y_{\mathrm{e}}<0.4975$, $M_{\mathrm{ej,n}}$ in Table 2) for a given species. For low-mass models e8.8, z9.6, and u8.1, the light trans-iron isotopes of $A=64$–90 are almost exclusively produced in neutron-rich ejecta, whereas proton-rich matter plays a minor role (see also Figs. 10 and 11). The subdominant roles of SNe from massive progenitors (represented by s11, s15, and s27) to production of these species can be understood as a result of the small mass of neutron-rich ejecta for these stars ($M_{\mathrm{ej,n}}$ in Table 2 and Fig. 2).

Among massive models, s27 has a relatively larger amount of neutron-rich ejecta compared to the two others, with $Y_{\mathrm{e}}$ down to $\sim 0.4$. This is a consequence of the fact that model s27 exhibits an earlier explosion with a rapidly increasing shock radius because of prominent SASI activity that is absent in other models. These neutron-rich ejecta lead to a relatively flat trend of production factors in this model, similar to what we found for e8.8 and z9.6 (Figs. 12 and 13). The bottom-panel of Figure 13 indicates, however, that about a half of species between $A=64$ and 90 originate from neutron-rich and proton-rich ejecta. In fact, 43% of 64Zn in s27 comes from the proton-rich ejecta. As described in 3.1.3, a weak $\nu p$-process is responsible for the production of these isotopes in the proton-rich ejecta. Greater entropies of the ejecta (Fig. 3), slower expansion compared to those for low-mass models, and higher neutrino luminosities and mean energies also enhance the efficiency of the $\nu p$-process.

4.4 48Ca

Models e8.8 and z9.6 exhibit appreciable production factors of 48Ca (18.9 and 18.6, respectively), which is made in neutron-rich NSE (or $\alpha$-deficient QSE, Meyer et al., 1996; Wanajo et al., 2013a) as can be seen in Figures 8 and 10 (middle-top panels, $Y_{\mathrm{e}}\sim 0.4$). The amounts are still not large enough to regard these low-mass SNe as the main contributors of 48Ca, although a reduction of the entropies by about 30% would lift the values to a satisfactory level (Wanajo et al., 2013a). A rare class of high-density SNe Ia, in which similar physical conditions are expected, has also been suggested as a possible source of 48Ca (Woosley, 1997).

4.5 Zn isotopes

One of the outstanding features of our nucleosynthesis result is production of all the stable isotopes of Zn ($A=64$, 66, 67, 68, and 70), an element whose origin remains a mystery. Among our explored models, the low-mass models e8.8 and z9.6 exhibit nearly flat production factors over $A=64$–70. This fact implies that the element Zn, or all their stable isotopes, could originate from ECSNe or low-mass CCSNe as represented by e8.8 and z9.6, respectively. As can be seen in the right-bottom panel of Figure 10, Zn isotopes are predominantly made in neutron-rich ejecta with $Y_{\mathrm{e}}\sim 0.4$–0.5; and models e8.8 and z9.6 produce a sufficient amount of ejecta in this range to contribute most of the solar inventory of Zn. There is still a discrepancy of a factor of ten between the largest (66Zn) and smallest (67Zn) production factors, which might be cured if the $Y_{\mathrm{e}}$ distributions for these models were slightly modified. Alternatively, some of the neutron-rich Zn isotopes may originate from hydrostatic neutron-capture processes in massive stars (Woosley & Weaver, 1995; Nomoto et al., 2013). CCSNe represented by u8.1 cannot be the single source of all Zn isotopes because of the descending trend of production factors (Fig. 15). Model s27, which shows a flat trend of production factors, cannot be representative of Zn contributors either because of the small production factors (1.2–5.2).

To date, only hypernova models (Umeda & Nomoto, 2002; Tominaga, 2007; Nomoto et al., 2013) have been proposed as sources of 64Zn (except for an ECSN model in Wanajo et al., 2011a) , the dominant isotope of Zn in the solar system. In their hypernova models high entropies of ejecta lead to strong $\alpha$-rich freeze-out from nuclear equilibrium, resulting in an appreciable production of 64Zn. This mechanism, however, does not co-produce the other isotopes and requires additional contributors such as hydrostatic neutron captures in massive stars. As described in § 3.1.3, the $\nu p$-process also produces 64Zn only, and therefore cannot be the main mechanism responsible for making Zn.

4.6 Light trans-iron elements

The nearly flat production factors over wide range of $A=64$–90 (except for Ga and As; Fig. 13) in e8.8 and z9.6 also suggest that such low-mass SNe are the dominant sources of light trans-iron elements from Zn to Zr as suggested by Wanajo et al. (2011a) if their mass window is $\Delta M_{\mathrm{prog}}\sim 0.5$–1. This is a consequence of the fact that the abundant neutron-rich ejecta for these models (Fig. 2) cover the range of $Y_{\mathrm{e}}$ (down to $\sim 0.40$) where the productions of these species become maximal (Figs. 10 and 11). By contrast, the results for model u8.1 (with a similar pre-SN core structure to that of z9.6) imply that such SNe can only be a source of the proton-rich isotopes of these trans-iron elements. This is due to the small amount of neutron-rich ejecta with $Y_{\mathrm{e}}\sim 0.40$–0.45.

In previous studies, the production of such light trans-iron species has often been attributed to the weak $s$-process (e.g. Käppeler et al., 2011). Woosley & Heger (2007) showed that the $s$-process in massive stars produces appreciable amounts of light trans-iron isotopes but only between $A=65$–85 with a descending trend of production factors. It also has been claimed that significant production of these elements can occur in stars above $25\,M_{\odot}$ via the weak s-process (Pignatari et al., 2010). Sukhbold et al. (2016) pointed out , however, that such light trans-iron species (in particular those above As) were sizably underproduced in their work because a large number of stars formed black holes instead of exploding and therefore did not contribute to weak $s$-process nuclides. A major contribution of the weak s-process from stars above $25\,M_{\odot}$ is also unlikely considering observational evidence against successful explosions of stars in this mass range (Smartt, 2015). It should be noted that Chieffi & Limongi (2013) find that sufficient rotation-induced mixing in massive stars appreciably increases the amount of weak $s$-process elements. We speculate that the weak $s$-process in massive stars might still be responsible for several trans-iron elements, in particular such as Ga and As, which are underproduced in our models e8.8 and z9.6 (Figs. 12 and 13).

4.7 92Mo

It is interesting to note that model s27 gives abundant 92Mo (with the third largest production factor, 30.7, in Table 3), an important $p$-nuclide whose astrophysical origin has been a long-lasting problem. In our case 92Mo is made in slightly neutron-rich ejecta ($Y_{\mathrm{e}}\sim 0.47$, see middle panel of Fig. 8 and middle-bottom panel of Fig. 11) during nuclear equilibrium (as suggested by Hoffman et al., 1996; Wanajo, 2006). With a production factor of $\sim 30$, such a type of CCSNe, i.e., relatively early explosions with dense outer envelopes, s27-like explosions would need to account for $\sim 30\%$ of all CCSNe to explain the solar abundance of 92Mo. A potential problem is that the other $p$-isotope 94Mo cannot be made in neutron-rich nuclear equilibrium (Hoffman et al., 1996; Wanajo, 2006). The $\nu p$-process in the neutrino-driven wind may, however, add these isotopes with a high 94Mo/92Mo ratio (Pruet et al., 2006; Wanajo, 2006; Wanajo et al., 2011b). Note that we do not find large production factors for the $p$-isotopes of Ru and Pd as in Pruet et al. (2006). This is due to the fact that these isotopes were made by the $\nu p$-process (§ 3.1.3) in their late-time ($\gtrsim 1$ s) wind ejecta with high entropies ($S\sim 70\,k_{\mathrm{B}}$), while the hydrodynamical simulations of models s15 and s27 stopped at $\sim 0.8$ s after core bounce with entropies still below $S=50\,k_{\mathrm{B}}$.

4.8 56Ni

The masses of 56Ni ejected from all models are listed in Table 4 (7th column), along with those of 57Ni (last column). These values, ranging from $\sim 0.002$–$0.006\,M_{\odot}$, are about one order of magnitude smaller than typical observed values (e.g., $0.07\,M_{\odot}$ for SN 1987A Bouchet et al., 1991). The 56Ni masses in our study should be taken, however, as lower limits for the massive models s11, s15, and s27, for which we omitted the outer envelopes including large parts of the Si/O layer. We therefore likely underestimate the amount of 56Ni produced by explosive nucleosynthesis in the supernova shock. Moreover, 2D models face a generic difficulty in determining the amount of 56Ni made by explosive burning in the shock, since the shocked material is funneled around the neutrino-driven outflows onto the proto-neutron star with little mixing by the Kelvin-Helmholtz instability into the neutrino-driven ejecta (Müller, 2015). The production of 56Ni by explosive burning also depends on the post-shock temperatures, and could be related to the slow rise of the explosion energy to only (0.3–$1.5)\times 10^{50}$ erg at the end of the simulations.

In addition, the core-collapse simulations of s15 and s27 stopped at a time when accretion was still ongoing and the mass ejection rate in the neutrino-driven outflows was still high, so that we may miss some late-time contribution to 56Ni in the neutrino-driven ejecta (see, e.g., Wongwathanarat et al., 2016). In fact, the late-time ejecta of s15 and s27 are mostly proton-rich and are dominated by 56Ni and $\alpha$-particles (Fig. 6 and the right-bottom panel of Fig. 11).

For the low-mass models e8.8, z9.6, and u8.1, the listed values can be regarded as the final ones; the 56Ni mass is definitely very small ($\sim 0.002$–$0.003\,M_{\odot}$) for these cases. It has already been argued before for e8.8 (Kitaura et al., 2006; Wanajo et al., 2011a; Wanajo, 2013), that the small 56Ni may be consistent with the value estimated for some observed low-luminosity supernovae (e.g., Hendry et al., 2005; Pastorello et al., 2007) with small ejecta masses. The 56Ni mass and the other explosion properties of the three low-mass models are also consistent with the remnant composition and reconstructed light curve of the Crab supernova SN 1054 (Smith, 2013; Tominaga, 2013; Moriya et al., 2014). From the nucleosynthetic point of view, low-mass iron core supernovae thus appear an equally viable explanation for these events compared to ECSNe.

4.9 60Fe and other radioactive isotopes

The low-mass models e8.8 and z9.6 produce appreciable amounts of 60Fe, $3.61\times 10^{-5}\,M_{\odot}$ and $3.14\times 10^{-5}\,M_{\odot}$, respectively (6th column in Table 4), which is comparable to the IMF-averaged ejection mass from CCSNe, (2.70–$3.20)\times 10^{-5}\,M_{\odot}$ in Sukhbold et al. (2016). Note that, in massive stars, 60Fe is produced by successive neutron captures from iron isotopes (Timmes et al., 1995; Limongi & Chieffi, 2006) in the outer envelope, which is not included in our analysis of the massive models s11, s15, and s27. In e8.8 and z9.6 60Fe forms in neutron-rich NSE ($Y_{\mathrm{e}}\sim 0.42$–0.43, right-bottom panel of Fig. 11) as suggested by Wanajo et al. (2013b). This indicates that ECSNe or low-mass CCSNe account for at least $\sim 10\%$ (see $f_{\mathrm{e8.8}}$ and $f_{\mathrm{z9.6}}$ in § 4.2) of live 60Fe in the Galaxy. Models other than e8.8 and z9.6 produce little 60Fe in their innermost ejecta because of their small masses of neutron-rich ejecta.

Table 4 also lists the masses of other important radioactive isotopes 26Al, 41Ca, 44Ti, and 53Mn, which are, however, negligibly small compared to the contribution from the outer envelopes of massive stars (and from neutrino-driven wind for 44Ti, Wongwathanarat et al., 2016). Recent work by Sukhbold et al. (2016) suggested the IMF-averaged amount of 26Al from massive stars to be (2.80–$3.63)\times 10^{-5}\,M_{\odot}$. Their resultant mass ratio of 60Fe to 26Al, $\sim 1$ (although a factor of 2 smaller than previous estimates, e.g., Woosley & Heger, 2007), conflicts with the mass ratio $\sim 0.34$ inferred from gamma-ray observation ( flux ratio $0.148\pm 0.06$, Wang et al., 2007). Taking the observational value as a constraint, this would suggest that Sukhbold et al. (2016) overestimated the 60Fe mass about a factor of 3. The reason for this can be attributed to uncertainties in the relevant reaction rates (Woosley & Heger, 2007; Tur et al., 2010), while for our cases 60Fe forms in nuclear equilibrium and thus individual reactions are irrelevant. If this is the case, ECSNe or low-mass SNe can contribute to live 60Fe up to $\sim 30\%$ of the amount in the Galaxy.

5 Conclusions

We have examined the nucleosynthesis in the innermost ejecta (0.01–$0.03\,M_{\odot}$) of CCSNe, including ECSNe, by adopting thermodynamic trajectories obtained from self-consistent (general-relativistic with one exception) 2D core-collapse supernova explosion models with multi-group neutrino transport. We explored the six models e8.8 ($8.8\,M_{\odot}$ ECSN, $1\,Z_{\odot}$), z9.6 ($9.6\,M_{\odot}$, $0\,Z_{\odot}$), u8.1 ($8.1\,M_{\odot}$, $10^{-4}\,Z_{\odot}$), s11 ($11.2\,M_{\odot}$, $1\,Z_{\odot}$), s15 ($15.0\,M_{\odot}$, $1\,Z_{\odot}$), and s27 ($27.0\,M_{\odot}$, $1\,Z_{\odot}$), with a progressively shallower core-density gradient in that order (Fig. 8 in Janka et al., 2012). In this paper, we focused on the effects of these differences in the pre-SN core-density structure on the nucleosynthesis, and did not attempt to address the exact dependence of the nucleosynthesis on mass or metallicity (owing to the limited number of available models). Our results indicate, however, that “low-mass” progenitors close to the iron core formation limit (which are characterized by off-center ignition of oxygen burning) stand apart from “massive stars” due to shared structural and evolutionary features: The low-mass models e8.8, z9.6, and u8.1 (near the low-mass end of SN progenitors) have abundant neutron-rich matter (40–50%) in their ejecta because of fast shock expansion after the onset of the explosion. By contrast, proton-rich matter dominates the ejecta of the more massive models s11, s15, and s27 by far, because slower shock expansion allows neutrino interactions to efficiently raise $Y_{\mathrm{e}}$.

For this reason, our nucleosynthesis calculations in post-processing steps resulted in remarkably different outcomes between the low-mass (e8.8, z9.6, and u8.1) and massive (s11, s15, and s27) models. We determined that low-mass SNe, in particular those represented by e8.8 (ECSN) and z9.6, could be the dominant source of light trans-iron elements from Zn to Zr (except for Ga and As), if these events account for $\sim 8$–14% (or a mass window of $\Delta M_{\mathrm{prog}}=0.5$–$1\,M_{\odot}$) of all CCSNe (including ECSNe). These species are made predominantly in neutron-rich ejecta during nuclear-equilibrium phases. Good agreement of the nucleosynthetic yields with the solar-abundance pattern over a wide range of isotopes with $A=64$–90 strongly supports our conclusion, which sets this candidate site apart from other previously suggested astrophysical sites, e.g., hypernovae (as origin of Zn, Umeda & Nomoto, 2002; Tominaga, 2007; Nomoto et al., 2013) and the weak $s$-process in massive stars (as origin of light trans-iron elements, Woosley & Heger, 2007; Käppeler et al., 2011). These SNe (e8.8 and z9.6) could also be important sources of the neutron-rich isotope 48Ca and the live radioactive species 60Fe in the Galaxy, and supplement the chemogalactic contribution of other sites such as rare SNe Ia (Woosley, 1997) with high ignition densities and massive stars (e.g., Sukhbold et al., 2016). Model u8.1, however, was found to have contributions of proton-rich isotopes of light trans-iron elements only, despite its similar (but slightly shallower) core-density gradient compared to that of z9.6.

We found that the innermost ejecta of massive SNe make little contributions to the chemical inventory of the Galaxy, except for proton-rich isotopes of light trans-iron elements (in s15 and s27). The most massive model s27 exhibited an interesting production of $p$-nucleus 92Mo, which could explain the solar amount of 92Mo if such s27-like events accounted for $\sim 30\%$ of all CCSNe. This was traced back to a sizable amount of slightly neutron-rich ejecta ($Y_{\mathrm{e}}\sim 0.47$) with moderately high entropies ($\sim 30\,k_{\mathrm{B}}/\mathrm{nuc}$), in which 92Mo is made in nuclear equilibrium (Hoffman et al., 1996; Wanajo, 2006). Note that our calculations did not include the outer envelopes, from which iron-group and lighter elements would be ejected in these massive SNe. Instead, we focused mostly on the neutrino-processed ejecta during the first few hundreds of milliseconds after shock revival. This implies that our results on the production of iron-group and trans-iron elements in the more massive models (s11, s15, s27) are only indicative of the overall nucleosynthesis and may miss important contributions. For the ECSN progenitor e8.8 and the ECSN-like models z9.6 and u8.1, the nucleosynthesis in this range is essentially complete, barring minor contributions from the neutrino-driven wind that follows after our simulations were terminated.

Aside from the fact that the nucleosynthesis in s11, s15, and s27 is not yet complete, some further caveats should be added to our conclusions here. Although nucleosynthesis calculations based on self-consistent 2D core-collapse supernova models represent a fundamental improvement over previous 1D studies (which mostly excluded neutrino-processed ejecta), the explosion dynamics in 3D has emerged as noticeably different from 2D (see Janka et al., 2016; Müller, 2016, for recent reviews). The interaction between buoyant, neutrino-heated ejecta and accretion downflows tends to brake both outflows and downflows (Melson et al., 2015; Müller, 2015) and could therefore modify the final $S$ and $Y_{\mathrm{e}}$ in the neutrino-driven ejecta. So far, model z9.6 offers the only opportunity for a direct comparison of the nucleosynthesis conditions. For this progenitor, 3D effects only moderately affect the explosion dynamics (Melson et al., 2015) and may only slightly raise the minimum $Y_{\mathrm{e}}$ in the ejecta without fundamentally changing the neutron-rich nucleosynthesis in this progenitor (Müller, 2016). The situation for other low-mass iron core-collapse supernovae and ECSNe is likely similar.

For more massive progenitors, larger systematic effects on the nucleosynthesis conditions in 3D cannot be excluded. The results of Müller (2015) for an $11.2M_{\odot}$ model suggest that the outflow velocities (which affect the $Y_{\mathrm{e}}$) and the terminal entropies in 3D can be considerably lower, but these results have yet to be borne out for a broader range of progenitors. The mixing of shocked material into the neutrino-heated ejecta is likely more efficient in 3D, and will affect the contribution of explosive nucleosynthesis in the shock to the total ejecta, because this matter is swept outward instead of being accreted onto the new-born neutron star. Along with the low explosion energies of the massive 2D models, this may explain the unusually small mass of 56Ni found in our calculations.

Effects that may change the final $Y_{\mathrm{e}}$ in the neutrino-processed ejecta by altering the neutrino emission also warrant further exploration. Aside from uncertainties in the neutrino microphysics, the impact of the genuinely three-dimensional LESA (lepton-number emission self-sustained asymmetry) instability (Tamborra et al., 2014; Janka et al., 2016) on the nucleosynthesis conditions deserves investigation. As LESA produces a global asymmetry in the flux difference between electron neutrinos and antineutrinos, it will contribute to a spread in the $Y_{\mathrm{e}}$-distribution in the ejecta. A detailed analysis of LESA effect in z9.6 is currently underway; the neutron-rich bubbles in the early ejecta remain a robust feature for this progenitor also in the presence of LESA (Melson et al., in preparation).

In summary, while our conclusions for low-mass SNe might be robust, those for massive models should only be taken as suggestive. Eventually, successful explosion models of such massive SNe in 3D are required for drawing firmer conclusions. It is, however, also important to scan the low-mass end of the progenitor range with a finer resolution in progenitor mass. While Wanajo et al. (2011a, 2013a, 2013b) suggested that ECSNe could be important contributors of light trans-iron elements (including Zn), 48Ca, and 60Fe, our results show that CCSNe near the low-mass end with iron-cores (z9.6) have almost the same nucleosynthetic outcomes. A model (u8.1) with only a slightly shallower core-density gradient resulted in, however, a substantially different result. Stellar evolution models and core-collapse supernova simulations therefore need to better address over which mass range the progenitors possess core-density profiles that are sufficiently steep to produce ECSN-like nucleosynthesis near the low-mass end of the progenitor-mass spectrum.

It should also be noted that we neglect late-time ejecta in the neutrino-driven wind in the present study. These could also contribute to the enrichment of trans-iron species to the Galaxy by a weak $r$-process (e.g., Wanajo, 2013) and a $\nu p$-process (Fröhlich et al., 2006; Pruet et al., 2006; Wanajo, 2006). Finally, our result should be tested by a study of Galactic chemical evolution to reproduce the observational signatures of light trans-iron elements in the Galaxy.

S.W. thanks N. Prantzos and M. Limongi for discussions about the weak s-process in massive stars. This work was supported by the RIKEN iTHES Project (SW), by the JSPS Grants-in-Aid for Scientific Research (26400232, 26400237; SW), by JSPS and CNRS under the Japan-France Research Cooperative Program (SW), by the Deutsche Forschungsgemeinschaft through the Excellence Cluster Universe EXC 153 (TJ), and by the European Research Council through grant ERC-AdG No. 341157-COCO2CASA (TJ). We also acknowledge partial support by the Australian Research Council through a Discovery Early Career Researcher Award DE150101145 (BM) and ARC Future Fellowships FT120100363 (AH) and FT160100035 (BM) and partial support by the US National Science Foundation under Grant No. PHY-1430152 (JINA Center for the Evolution of the Elements). This research was undertaken with the assistance of resources from the Max Planck Computing and Data Facility (using the hydra cluster), the Minnesota Supercomputing Institute, the National Computational Infrastructure (NCI), which is supported by the Australian Government, and the Pawsey Supercomputing Centre with funding from the Australian Government and the Government of Western Australia.