Silicon carbide grains of type C provide evidence for the production of the unstable isotope $^{32}$Si in supernovae

Carbon-rich grains are observed to condense in the ejecta of recent core-collapse supernovae, within a year after the explosion. Silicon carbide grains of type X are C-rich grains with isotpic signatures of explosive supernova nucleosynthesis have been found in primitive meteorites. Much rarer silicon carbide grains of type C are a special sub-group of SiC grains from supernovae. They show peculiar abundance signatures for Si and S, isotopically heavy Si and isotopically light S, which appear to to be in disagreement with model predictions. We propose that C grains are formed mostly from C-rich stellar material exposed to lower SN shock temperatures than the more common type X grains. In this scenario, extreme $^{32}$S enrichments observed in C grains may be explained by the presence of short-lived $^{32}$Si ($\tau$$_{1/2}$ = 153 years) in the ejecta, produced by neutron capture processes starting from the stable Si isotopes. No mixing from deeper Si-rich material and/or fractionation of Si from S due to molecular chemistry is needed to explain the $^{32}$S enrichments. The abundance of $^{32}$Si in the grains can provide constraints on the neutron density reached during the supernova explosion in the C-rich He shell material. The impact of the large uncertainty of the neutron capture cross sections in the $^{32}$Si region is discussed.

mixing from deeper Si-rich material and/or fractionation of Si from S due to molecular chemistry is needed to explain the 32 S enrichments. The abundance of 32 Si in the grains can provide constraints on the neutron density reached during the supernova explosion in the C-rich He shell material. The impact of the large uncertainty of the neutron capture cross sections in the 32 Si region is discussed.

Introduction
Despite recent improvements in simulations of core-collapse supernova (CCSN) explosions (e.g., Janka 2012) the understanding of supernova still has major gaps, and observations of SN and their ejecta still provide many puzzles (e.g., Fryer et al. 2012, and references therein). Of particular importance may be the assymmetric nature of the explosion and the hydrodynamic development of the layers ejected after the explosion (e.g., Kjaer et al. 2010;Isensee et al. 2010;DeLaney et al. 2010).
Several types of pre-solar grains from primitive carbonaceous meteorites that are associated with SN nucleosynthesis due to their isotopic ratios (see e.g., Clayton & Nittler 2004;Zinner 2013) provide constraints on these explosions. Pre-solar grains carry the signatures of their stellar origin, and their interpretation may help to guide CCSN models.
Silicon carbide is one of the types of stardust grains that have been identified in primitive meteorites (e.g., Zinner 2013). While most of these so-called presolar SiC grains originate in Asymptotic Giant Branch stars, there are two rare sub-types of SiC grains that have a CCSN origin. Type X grains (about 1% of all presolar SiC grains), have large excesses in 28 Si. This signature and evidence for the initial presence of 44 Ti in a subset of these grains is proof of their SN origin: both isotopes are predicted to be abundant in the Si/S zone of supernovae (Rauscher et al. 2002). More recently, Pignatari et al. (2013), hereafter P13, showed that 28 Si and 44 Ti may also be produced at the bottom of the He shell exposed to high shock velocities and/or high energies, reproducing several isotopic abundance patterns typical of SiC X grains and graphites from SNe.
Silicon carbide grains of type C are even rarer (about 0.1% of all SiC grains) than SiC X grains. They have a large excess in 29 Si and 30 Si and most of them have been found by automatic searches in the NanoSIMS detection apparatus. Some of these grains contain extinct 44 Ti, similar to SiC-X grains. Just over a dozen of these grains have been identified, and nine have been analyzed for their S isotopic ratios, showing large 32 S excesses, with 32 S/ 33,34 S ratios ranging up to 16 times solar (Amari et al. 1999;Croat et al. 2010;Gyngard et al. 2010;Hoppe et al. 2010Hoppe et al. , 2012Zinner et al. 2010;Orthous-Daunay et al. 2012;Xu et al. 2012). This is puzzling, because in existing SN models the only zone with large 32 S excesses is the Si/S zone (Meyer et al. 1995), which has large 28 Si excesses, whereas zones with 28 Si depletions (i.e., 29,30 Si excesses) are predicted to have also 32 S depletions (e.g., Rauscher et al. 2002). Hoppe et al. (2012) have invoked element fractionation between sulfur and silicon by molecule chemistry in the SN ejecta to explain this result. However, this ad hoc explanation cannot explain all the data, especially the S isotopic composition of one C grain with δ( 33 S/ 32 S) and δ( 34 S/ 32 S) values being as low as -940 (Xu et al. 2012), even more extreme than those of S in the Si/S zone. In this paper we propose that the 32 S excesses in C grains are due to the radioactive decay of short-lived 32 Si (τ 1/2 = 153 years, Ouellet & Balraj 2011). We present models of explosive nucleosynthesis in the inner part of the He/C zone where 29 Si and 30 Si as well as 32 S excesses can be produced while maintaining a C-rich environment.
The paper is organized as follows. In §2 we describe the stellar models and the nucleosynthesis calculations, in §3 we compare theoretical results with measurements for C grains. Finally, in §4 we give our conclusions.

Stellar model calculations and nucleosynthesis
This investigation is based on seven SN explosion models for a 15 M ⊙ , Z = 0.02 star, three of which were introduced in P13. The pre-supernova evolution is calculated with the code GENEC (Eggenberger et al. 2008). The explosion simulations include the fallback prescription by Fryer et al. (2012), and are performed for a case with recommended initial shock velocity and six cases where the latter is reduced by a factor of 2, 4, 5, 10, 20 and 100, respectively (models 15r, 15r2, 15r4, 15r5, 15r10, 15r20 and 15r100). The standard initial shock velocity used beyond fallback is 2 × 10 9 cm s −1 . The kinetic explosion energy for these 15 M ⊙ models ranges from 4 − 5 × 10 51 ergs to less than 10 51 ergs. The post-processing code MPPNP is used to calculate the nucleosynthesis in the star before and during the explosion (see e.g., Bennett et al. 2012). For the present study we focus only on the C-rich explosive He burning layers, including the He/C zone and a small part of the O/C zone.
The abundances of key species and 28−34 Si are reported in Fig. 1 for models 15r and 15r4. Results are similar for the intermediate model 15r2. The bottom of the He/C zone is strongly affected by the explosion. While 12 C is not significantly modified, 16 O is depleted and feeds the production of heavier αisotopes, including 28 Si. This stellar region was defined as the C/Si zone in P13. The main reason for this behavior is the higher α-capture rates starting from the 16 O(α,γ) 20 Ne reaction than that of the 12 C(α,γ) 16 O reaction at explosive He shell temperatures (as explained by P13). Models with lower shock velocities show weaker explosion signatures. In particular, model 15r100 does not show any significant departures from pre-explosive abundances during the explosion in the C-rich region.
Along the Si neutron capture chain, 29−30 Si and heavier unstable Si species are produced efficiently by neutron captures starting from 28 Si. The larger explosion temperatures in model 15r than in model 15r4 are pushing the production peaks of different Si neutron-rich species to larger mass coordinates, not significantly affecting their absolute abundance. Therefore, abundance yields for the Si isotopes in the explosive He shell result from the interplay between α-captures and neutron captures, triggered by activation of the 22 Ne(α,n) 25 Mg neutron source (e.g., Meyer et al. 2000, and references therein). The main abundance features and dominating nucleosynthesis fluxes for two different times of the SN explosion are given in Fig. 2, in the so-called C/Si zone (M ∼ 2.95 M ⊙ , model 15r, see also P13). In the early stages of the explo-sion, depending on the available 22 Ne, the α-capture path starting from 16 O is accompanied by (n,γ)(α,n) sequences, producing the same α-species. An example is 20 Ne(α,γ) 24 Mg and 20 Ne(n,γ) 21 Ne(α,n) 24 Mg. During the later stages of the explosion and/or low 22 Ne abundances, the (α,γ) fluxes become dominant. Note that for explosive He burning conditions the (α,p) fluxes are compensated by their reverse reactions, and proton captures on the abundant α-isotopes do not affect the abundance of their parent species because of the efficient reverse (γ,p) photodisintegrations.
In the present calculations, we use for the (n,γ) reactions on unstable Si species the rates from Hauser-Feshbach (HF) calculations by the NON-SMOKER code (Rauscher & Thielemann 2000), available in JINA REACLIB v1.1 (e.g., Cyburt et al. 2010). The uncertainties of the neutron capture rates in the mass region of 32 Si are very large. Figure 3, upper panel, shows the Maxwellian averaged cross section (MACS) for neutron capture on 32 Si as calculated from the HF codes CoH 3 (Kawano et al. 2004) and TALYS 1.4 (Koning et al. 2008(Koning et al. , 2011, and NON-SMOKER. At a temperature near 90 keV (∼ 10 9 K) we see a difference of almost two orders of magnitude between the highest (from CoH 3 ) and the lowest calculated values (TALYS 1.4). Notice, however, that these theoretical predictions are still consistent within the large uncertainty of the 32 Si(n,γ) 33 Si rate. The large uncertainty is due to the nuclear level density being too low to apply the HF model for neutron-rich isotopes of Si. The model relies on the statistical averaging over levels in the compound nucleus and thus a sufficiently high nuclear level density is required at the compound formation energy (Rauscher et al. 1997). The ENDF/B-VII.1 library of Chadwick et al. (2011) provides the location of neutron capture resonances for even-even nuclei near 32 Si, shown in Fig. 3, lower panel. While no data are available on 32 Si neutron capture resonances, the neighboring even-even nuclei 30 Si and 28 Si give an indication of the number of levels accessible at different incident particle energies. Above an energy of ∼ 600 keV statistical methods become appropriate. For this reason, we considered an uncertainty of a factor of 100 for the 32 Si neutron capture cross section. The impact of this uncertainty is presented in §3.
Where experimental knowledge of the single resonances has been obtained, such as in the case of 28 Si and 30 Si, uncertainties may still arise from the precise location and strength of each resonance. However, uncertainties from experiment are expected to be much lower than those introduced by the use of HF calculations in an inappropriate region.

Comparison with observations
We compare in Fig. 4 the abundances from the C-rich ejecta from our models ( §2) originating from the C/Si zone, the whole He/C zone and the C-rich part of the He/N zone, with isotopic ratios of single SiC X and C grains from the St. Louis Presolar Grains Database (Hynes & Gyngard 2009). No mixing between layers is considered and SiC-X and C grains with 12 C/ 13 C lower than solar are excluded. They are not reproduced by these models that have high C isotopic ratio.
The standard model (15r, upper panel, layer 1 Fig. 4) shows a strong 28 Si and 32 S production and absence of 32 Si in the C/Si zone during the explosion (see also P13). Outward, in the inner part of the He/C zone, the lower explosion temperatures and the neutron burst triggered by the 22 Ne(α,n) 25 Mg (n process, e.g., Meyer et al. 2000) gradually reduce 28 Si-and 32 S-enrichments, whereas 32 Si is synthesized and accumulated according to its neutron capture cross section (as discussed in §2). The outer parts of the He/C zone show mild enrichments of the stable neutron-rich Si and S isotopes due to pre-explosive s-processing.
The 28 Si-excess observed in SiC X grains are reproduced in parts of the C/Si zone for the models 15r and 15r2 (e.g, layer 1 of model 15r, Fig. 4, lower panel). SiC C grains show larger 32 S-excesses than SiC X grains, and positive δ( 30 Si). Such a signature is consistent with abundance predictions from more external zones in the C-rich He shell. In models 15r4-15r20 the shock temperature is not sufficient to reproduce the 28 Si-excess observed in SiC X grains (see also P13). Conversely, the presented models can reproduce the Si and S isotopic ratios in the C grains over a large range in initial shock velocities. Also in case of contamination or mixing with isotopically more normal material (see P13), the grain signatures can be explained since δ( 30 Si) values up to ∼ 15000−20000 (e.g., models 15r, 15r2 and 15r4, zones "2" and "3") are associated with large 32 S enrichments (δ( 34 S) ∼ −1000, Fig. 4, lower panel, outside the plot range). For most of the He shell material the 32 Si signature dominates S isotopic anomalies, assuming an arbitrary Si/S fractionation of 10 4 during grain formation (Fig. 4, lower panel). This assumption expresses the hypothesis that all 32 S observed in C grains originates from the decay of 32 Si (see below for details). Only little S condenses into SiC grains, justifying the assumed elemental fractionation (e.g., Amari et al. 1995).
In Fig. 5, upper panel, we show the 32 Si/ 28 Si isotopic ratios from different models described in §2, comparing them with the ratios inferred for C grains from the radiogenic 32 S. We estimated the ratio of the radioactive 32 Si ( 32 S * ) to 28 Si and thus the original 32 Si/ 28 Si ratio by assuming that all the S (S tot ) in the grains was either 32 S * or isotopically normal S (S norm ) from contamination. The latter assumption is based on the fact that S is volatile and is not likely to condense into SiC. The grains are therefore expected to contain only marginal intrinsic S. Second, the S concentrations are low in the He shell layers with no 28 Si enrichment. Finally, some of the S isotopic images of the C grains measured showed 34 S to be more abundant at the edges of the grains and 32 S excesses to be higher in interior than in border regions. We determined the atomic 32 Si/ 28 Si ratios by applying a S − /Si − sensitivity factor of 3, inferred from measurements of Si and S ion yields on synthetic SiC and Mundrabilla FeS, respectively (Hoppe et al. 2012). Since 32 S tot = 32 S * + 32 S norm and 32 S * = −0.001 × δS×( 32 S * + 32 S norm ), we obtained the 32 S * / 28 Si ratios by multiplying 32 S/ 28 Si with −0.001 × δS. Here 32 S norm is 32 S of the isotopically normal component S norm (assumed to be contamination). For δS we took the average of δ( 33 S/ 32 S) and δ( 34 S/ 32 S). Within errors the latter two values are equal for all measured grains, providing additional evidence that we are dealing just with an excess in 32 Si. In Fig. 5, we show that the observed range of 32 Si/ 28 Si ratios is matched by predictions from stellar models at different energies, in agreement with Fig. 4. Typical conditions required for matching the inferred 32 Si/ 28 Si ratios (e.g., at M = 3.4 M ⊙ for models 15r4 and 15r5) have a peak temperature of ∼ 8 × 10 8 K and a neutron density peak of ∼ 10 18−19 cm −3 , with a 28 Si mass fraction of ∼ 5 × 10 −4 . The models 15r-15r5 with the highest explosion temperatures also fit the observed 32 Si/ 28 Si ratio deeper in the He shell (e.g., at M = 3.05 M ⊙ for model 15r and 15r2), with a 28 Si mass fraction of ∼ 5 × 10 −2 . In these cases, the temperature peak is about 1.6 × 10 9 K, with a neutron density peak of a few 10 22 cm −3 for few 10 −5 sec, dropping quickly to densities more typical of the n process.
Since the grains may contain some normal component (P13), the inferred 32 Si/ 28 Si needs to be considered a lower limit of the original ratio in the He shell material. In Fig. 5, lower panel, we show that increasing the neutron capture cross section of 32 Si by a factor of 100 (see discussion in §2) does not change our results. By reducing the 32 Si Maxwellian-averaged cross section (MACS) of the same factor the 32 Si/ 28 Si ratio increases by less than 10%, since the 32 Si MACS adopted in our models is already lower than 1 mb, behaving as a bottle-neck in the neutron capture flow feeding heavier Si species. Note that at the temperatures of explosive He-burning the half-life of 32 Si can be reduced down to few days (e.g., Oda et al. 1994). However, the timescale of the explosive nucleosynthesis is less than ∼ 0.3 secs, and the impact of the 32 Si half-life in the calculations is negligible.
We have shown that CCSN models can explain the large 32 S-excess measured in SiC C grains by the radioactive decay of the unstable isotope 32 Si after grain formation. Furthermore, in SiC C grains most of the remaining S is coming from contamination. We have identified two typical conditions where the correct 32 Si/ 28 Si ratio can be obtained, depending on the explosion temperature and on the abundance of 28 Si.

Conclusions
We have compared the isotopic signatures in presolar SiC grains of type C with nucleosynthesis predictions for CCSN ejecta exposed to different shock velocities. We propose that the seemingly incompatible Si and S isotopic ratios in these grains are explained by assuming that the 32 S excess observed today originates from radioactive 32 Si that condensed into the forming SiC grains, and decayed into 32 S at later stages. Assuming that all the remaining S is due to contamination, we estimated the 32 Si/ 28 Si ratio in the parent CCSN ejecta, ranging from a few 10 −4 to a few 10 −3 . We propose this ratio to be a lower limit of its original value in the explosive He shell layers, depending on the level of contamination or mixing with more normal material for each C grain. Such ratios can be produced for different shock velocities and/or explosion energies. Two typical conditions reproducing directly the observed 32 Si/ 28 Si ratios are: one with high temperature and large 28 Si abundance (∼ 1.6 × 10 9 K and ∼ 5 × 10 −2 , respectively), and one with temperature ∼ 0.7 − 0.9 × 10 9 K and 28 Si abundance ∼ 5 × 10 −4 . In the first case the neutron density reaches a peak of a few 10 22 cm −3 for few 10 −5 sec, rapidly dropping to values more typical of the n-process neutron-burst. In the second case, the neutron density peak is on the order of 10 18−19 cm −3 .
In conclusion, C grains carry a record of the neutron density reached in the explosive He shell of the CCSN where they formed. We showed that the theoretical nuclear reactions in the 32 Si mass region have large uncertainties, but our results are not significantly affected. We conclude that C grains carry the signature of lower energy ejecta compared to SiC X grains, showing positive δ(Si) values and a significant amount of 32 Si produced by neutron captures.
We thank the Anonymous Referee for the very careful review of the paper, which significantly contributed to improve the quality of the publication. NuGrid acknowledges significant support from NSF grants PHY 02-16783 and PHY 09-22648 (Joint Institute for Nuclear Astrophysics, JINA) and EU MIRG-    Si, calculated by different statistical HF models in the temperature range of interest T = 1 − 2 × 10 9 K (corresponding to ∼ 90 − 170 keV). No experimental data exist for 32 Si, therefore one has to rely on theoretical calculations. Statistical methods are not applicable in the primary energy range of interest for this nucleus, therefore a more appropriate approach is needed to constrain the uncertainty. Lower panel: neutron capture cross-sections for 28 Si and 30 Si from the ENDF/B-VII.1 library. (see end of §2 for discussion). Si/ 28 Si and 34 S/ 32 S isotopic ratios of presolar SiC X and C grains, plotted as δ-values, deviations from the solar ratios in parts per thousand ( ), are compared with predictions of three different models (15r, 15r4 and 15r20) in the mass range shown in the upper panel. We highlight the predicted Si and S isotopic ratios of model 15r at two different mass coordinates, M = 2.95 and 3.7 M ⊙ (see upper panel). The Si isotopic ratios of zones "2" and "3" are located out of the plot range, with δ( 30 Si) ∼ 15000 and δ( 34 S) ∼ −1000. A fractionation factor of 10 4 for Si/S is assumed. Si in the C-rich explosive He shell for models with initial shock velocities varying by a factor of 100 (decreasing from model 15r to 15r100). The blue-shaded area denotes O-rich material. For comparison, the red-shaded area indicates the range of 32 Si/ 28 Si ratios, inferred from S isotopic ratios and S and Si abundances in presolar SiC C grains, under the assumption that the measured 32 S excess derives from 32 Si decay. Lower panel: Impact on the 32 Si/ 28 Si ratio from increasing the 32 Si neutron capture cross section by a factor of 100 for models 15r5 and 15r10.