SILICON CARBIDE GRAINS OF TYPE C PROVIDE EVIDENCE FOR THE PRODUCTION OF THE UNSTABLE ISOTOPE ³²Si IN SUPERNOVAE

Despite recent improvements in simulations of core-collapse supernova (CCSN) explosions (e.g., Janka 2012), the understanding of supernova (SN) 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 asymmetric nature of the explosion and the hydrodynamic development of the layers ejected after the explosion (e.g., Kjær et al. 2010; Isensee et al. 2010; DeLaney et al. 2010).

Several types of presolar grains from primitive carbonaceous meteorites that are associated with SN nucleosynthesis due to their isotopic ratios (see, e.g., Clayton & Nittler 2004; Zinner 2007) provide constraints on these explosions. Presolar 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 2007). 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 ²⁸Si. This signature and evidence for the initial presence of ⁴⁴Ti 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 SNe (Rauscher et al. 2002). More recently, Pignatari et al. (2013, hereafter P13), showed that ²⁸Si and ⁴⁴Ti 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 ²⁹Si and ³⁰Si and most of them have been found by automatic searches in the NanoSIMS detection apparatus. Some of these grains contain extinct ⁴⁴Ti, similar to SiC X grains. Just over a dozen of these grains have been identified, and 9 have been analyzed for their S isotopic ratios, showing large ³²S excesses, with ³²S/^{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. 2010, 2012; Zinner 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 ³²S excesses is the Si/S zone (Meyer et al. 1995), which has large ²⁸Si excesses, whereas zones with ²⁸Si depletions (i.e., ^{29, 30}Si excesses) are predicted to have also ³²S 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(³³S/³²S) and δ(³⁴S/³²S) values being as low as −940‰ (Xu et al. 2012), even more extreme than those of S in the Si/S zone. In this Letter, we propose that the ³²S excesses in C grains are due to the radioactive decay of short-lived ³²Si (τ_1/2 = 153 yr; Ouellet & Balraj 2011). We present models of explosive nucleosynthesis in the inner part of the He/C zone, where ²⁹Si and ³⁰Si as well as ³²S excesses can be produced while maintaining a C-rich environment.

The Letter is organized as follows. In Section 2 we describe the stellar models and the nucleosynthesis calculations, in Section 3 we compare theoretical results with measurements for C grains. Finally, in Section 4 we give our conclusions.

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-SN 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 × 10⁹ cm s⁻¹. The kinetic explosion energy for these 15 M_☉ models ranges from 4 to 5 × 10⁵¹ erg to less than 10⁵¹ erg. 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). In 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 ^28–34Si are reported in Figure 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 ¹²C is not significantly modified, ¹⁶O is depleted and feeds the production of heavier α-isotopes, including ²⁸Si. 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 ¹⁶O(α,γ)²⁰Ne reaction than that of the ¹²C(α,γ)¹⁶O 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.

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Along the Si neutron capture chain, ^29–30Si and heavier unstable Si species are produced efficiently by neutron captures starting from ²⁸Si. 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 ²²Ne(α, n)²⁵Mg 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 Figure 2, in the so-called C/Si zone (M ∼ 2.95 M_☉, model 15r; see also P13). In the early stages of the explosion, depending on the available ²²Ne, the α-capture path starting from ¹⁶O is accompanied by (n, γ)(α, n) sequences, producing the same α-species. An example is ²⁰Ne(α,γ)²⁴Mg and ²⁰Ne(n, γ)²¹Ne(α, n)²⁴Mg. During the later stages of the explosion and/or low ²²Ne 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.

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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 version 1.1 (e.g., Cyburt et al. 2010). The uncertainties of the neutron capture rates in the mass region of ³²Si are very large. Figure 3, upper panel, shows the Maxwellian-averaged cross section (MACS) for neutron capture on ³²Si as calculated from the HF codes CoH₃ (Kawano et al. 2004) and TALYS 1.4 (Koning et al. 2008, 2011), and NON-SMOKER. At a temperature near 90 keV (∼10⁹ K), we see a difference of almost two orders of magnitude between the highest (from CoH₃) and the lowest calculated values (TALYS 1.4). Note, however, that these theoretical predictions are still consistent within the large uncertainty of the ³²Si(n, γ)³³Si 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 ³²Si, as shown in Figure 3, lower panel. While no data are available on ³²Si neutron capture resonances, the neighboring even–even nuclei ³⁰Si and ²⁸Si 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 ³²Si neutron capture cross section. The impact of this uncertainty is presented in Section 3.

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Where experimental knowledge of the single resonances has been obtained, such as in the case of ²⁸Si and ³⁰Si, 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.

We compare in Figure 4 the abundances from the C-rich ejecta from our models (Section 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 ¹²C/¹³C lower than solar are excluded. They are not reproduced by these models that have high C isotopic ratio.

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The standard model (15r, upper panel, layer 1 Figure 4) shows a strong ²⁸Si and ³²S production and the absence of ³²Si 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 ²²Ne(α, n)²⁵Mg (n process; e.g., Meyer et al. 2000) gradually reduce ²⁸Si and ³²S enrichments, whereas ³²Si is synthesized and accumulated according to its neutron capture cross section (as discussed in Section 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 ²⁸Si 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, Figure 4, lower panel). SiC C grains show larger ³²S excesses than SiC X grains, and positive δ(³⁰Si). 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 ²⁸Si 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 the case of contamination or mixing with isotopically more normal material (see P13), the grain signatures can be explained since δ(³⁰Si) values up to ∼15,000–20,000 (e.g., models 15r, 15r2, and 15r4, zones "2" and "3") are associated with large ³²S enrichments (δ(³⁴S) ∼ −1000, Figure 4, lower panel, outside the plot range). For most of the He shell material, the ³²Si signature dominates S isotopic anomalies, assuming an arbitrary Si/S fractionation of 10⁴ during grain formation (Figure 4, lower panel). This assumption expresses the hypothesis that all ³²S observed in C grains originates from the decay of ³²Si (see below for details). Only little S condenses into SiC grains, justifying the assumed elemental fractionation (e.g., Amari et al. 1995).

In Figure 5, upper panel, we show the ³²Si/²⁸Si isotopic ratios from different models described in Section 2, comparing them with the ratios inferred for C grains from the radiogenic ³²S. We estimated the ratio of the radioactive ³²Si (³²S*) to ²⁸Si and thus the original ³²Si/²⁸Si ratio by assuming that all the S (S_tot) in the grains was either ³²S* 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 ²⁸Si enrichment. Finally, some of the S isotopic images of the C grains measured showed ³⁴S to be more abundant at the edges of the grains and ³²S excesses to be higher in interior than in border regions. We determined the atomic ³²Si/²⁸Si ratios by applying an S⁻/Si⁻ sensitivity factor of three, inferred from measurements of Si and S ion yields on synthetic SiC and Mundrabilla FeS, respectively (Hoppe et al. 2012). Since ³²S_tot = ³²S* + ³²S_norm and ³²S* = −0.001 × δS × (³²S* + ³²S_norm), we obtained the ³²S*/²⁸Si ratios by multiplying ³²S/²⁸Si with −0.001 × δS. Here, ³²S_norm is ³²S of the isotopically normal component S_norm (assumed to be contamination). For δS, we took the average of δ(³³S/³²S) and δ(³⁴S/³²S). Within errors the latter two values are equal for all measured grains, providing additional evidence that we are dealing just with an excess in ³²Si. In Figure 5, we show that the observed range of ³²Si/²⁸Si ratios is matched by predictions from stellar models at different energies, in agreement with Figure 4. Typical conditions required for matching the inferred ³²Si/²⁸Si ratios (e.g., at M = 3.4 M_☉ for models 15r4 and 15r5) have a peak temperature of ∼8 × 10⁸ K and a neutron density peak of ∼10^18–19 cm⁻³, with a ²⁸Si mass fraction of ∼5 × 10⁻⁴. The models 15r–15r5 with the highest explosion temperatures also fit the observed ³²Si/²⁸Si ratio deeper in the He shell (e.g., at M = 3.05 M_☉ for models 15r and 15r2), with a ²⁸Si mass fraction of ∼5 × 10⁻². In these cases, the temperature peak is about 1.6 × 10⁹ K, with a neutron density peak of a few 10²² cm⁻³ for few 10⁻⁵ s, dropping quickly to densities more typical of the n process.

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Since the grains may contain some normal component (P13), the inferred ³²Si/²⁸Si needs to be considered a lower limit of the original ratio in the He shell material. In Figure 5, lower panel, we show that increasing the neutron capture cross section of ³²Si by a factor of 100 (see discussion in Section 2) does not change our results. By reducing the ³²Si MACS of the same factor the ³²Si/²⁸Si ratio increases by less than 10%, since the ³²Si MACS adopted in our models is already lower than 1 mb, behaving as a bottleneck in the neutron capture flow feeding heavier Si species. Note that at the temperatures of explosive He burning the half-life of ³²Si 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 s, and the impact of the ³²Si half-life in the calculations is negligible.

We have shown that CCSN models can explain the large ³²S excess measured in SiC C grains by the radioactive decay of the unstable isotope ³²Si 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 ³²Si/²⁸Si ratio can be obtained, depending on the explosion temperature and on the abundance of ²⁸Si.

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 ³²S excess observed today originates from radioactive ³²Si that condensed into the forming SiC grains, and decayed into ³²S at later stages. Assuming that all the remaining S is due to contamination, we estimated the ³²Si/²⁸Si 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 ³²Si/²⁸Si ratios are: one with high temperature and large ²⁸Si abundance (∼1.6 × 10⁹ K and ∼5 × 10⁻², respectively), and the other with temperature ∼0.7–0.9 × 10⁹ K and ²⁸Si abundance ∼5 × 10⁻⁴. In the first case, the neutron density reaches a peak of a few 10²² cm⁻³ for few 10⁻⁵ s, 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 ³²Si 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 ³²Si produced by neutron captures.

We thank the anonymous referee for the very careful review of this Letter, which significantly contributed to improving 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-CT-2006-046520. The continued work on codes and in disseminating data is made possible through funding from STFC and EU-FP7-ERC-2012-St Grant 306901 (R.H., UK), and NSERC Discovery grant (F.H., Canada), and an Ambizione grant of the SNSF (M.P., Switzerland). M.P., T.R., R.H., and F.K.T. also thank for support from EuroGENESIS. NuGrid data are served by Canfar/CADC. E.Z. was supported by NASA grant NNX11AH14G. M.G.B.'s research was carried out under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396. P.H. thanks Ramanath Cowsik for his hospitality at the McDonnell Center for the Space Sciences at Washington University. T.R. also acknowledges the support from the THEXO Collaboration within the EU Seventh Framework Program, the European Research Council, and the Swiss NSF. R.H. also acknowledges support from the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan, and from European Research Council under the European Union's Seventh Framework Program (FP/2007–2013)/ERC Grant Agreement No. 306901.