PRODUCTION OF CARBON-RICH PRESOLAR GRAINS FROM MASSIVE STARS

Massive stars (M ≳ 8 M_☉) are among the major contributors to the chemical enrichment of the galaxy through both their winds and core-collapse supernova (CCSN). In carbonaceous meteorites several types of C-rich presolar grains condensed in CCSN ejecta have been identified through association of the measured isotopic abundance patterns with signatures of such events (see, e.g., Zinner 2003; Clayton & Nittler 2004). Among those, C-rich grains like Type X silicon carbides (SiC-X) and graphites are assumed to require a C-rich environment to form (C/O > 1, e.g., Travaglio et al. 1999).

Standard massive star models predict that C-rich ejecta originate in explosive He shell burning, characterized by partial pre-explosive He-burning products (e.g., Woosley & Weaver 1995). The heavy species abundances show a mild s-process signature from pre-explosive convective He-shell burning (triggered by the ²²Ne(α, n)²⁵Mg reaction; e.g., Rauscher et al. 2002), and by the explosive neutron burst triggered again by the ²²Ne(α, n)²⁵Mg reaction (namely the n-process, with n_n ∼ 10¹⁸ cm⁻³; e.g., Blake & Schramm 1976; Meyer et al. 2000).

SiC-X grains show a ²⁸Si excess compared to ^{29, 30}Si, and most of these grains have a ¹²C and ¹⁵N excess while some show a ¹³C and ¹⁵N excess. The ²⁶Mg and ⁴⁴Ca excess compared to solar has been explained by the condensation of unstable ²⁶Al and ⁴⁴Ti into the grains (e.g., Amari et al. 1992; Nittler & Alexander 2002; Besmehn & Hoppe 2003). Graphite grains (with low density, LD group; Amari et al. 1995) show a large range of ¹²C/¹³C ratio, possibly correlated with ¹⁸O excess. Both an excess and deficit of ²⁸Si with respect to ^{29, 30}Si can be observed. Indication of ²⁶Mg and ⁴⁴Ca excess is also found for several of those grains. Finally, their measured ¹⁴N/¹⁵N ratio with few exceptions is quite normal, pointing to a contamination from solar nitrogen (e.g., Zinner 2003 and references therein).

To explain these abundance signatures, Travaglio et al. (1999) and Yoshida (2006) assume mixing of He-shell matter with Si/S zone material (see Meyer et al. 1995) deeper in the supernova without any mixing contribution from the O-rich layers in between. The main constraint is that the material out of which the grains form needs to be C-rich to have free carbon to condense in SiC and graphites after CO formation. Clayton (2013) and references therein suggests instead that since SN ejecta are not in thermodynamic equilibrium, C-rich grains may condense in O-rich and ²⁸Si-rich ejecta.

More recently, Marhas et al. (2008) found a deficit or normal ⁵⁴Fe compared to ⁵⁶Fe abundance in SiC-X grains, in disagreement with nucleosynthesis predictions for the ²⁸Si-rich Si/S zone to be ⁵⁴Fe-rich (e.g., Thielemann et al. 1996). Possible fractionation between Si and Fe proposed by Marhas et al. (2008) is unlikely to be sufficient, since Fe-rich subgrains in the SiC-X grains also show a normal ⁵⁴Fe/⁵⁶Fe ratio.

In this Letter we propose a new nucleosynthesis scenario, where the observational signatures of C-rich presolar grains can be obtained without mixing from the C-rich material in CCSN that experience a strong shock. The Letter is organized as follows. In Section 2 we describe stellar models and the nucleosynthesis calculations, in Section 3 we compare theoretical results with measurements for SiC X grains and graphite grains. Finally, in Section 4 results are summarized.

In this study, we consider three SN explosion models for a 15 M_☉, Z = 0.02 star. (M. Pignatari et al. 2013, in preparation). The pre-supernova evolution is computed with the stellar code GENEC (for more details see Bennett et al. 2012, model 15ST in their Figure 6). The explosion simulations include the fallback prescription by Fryer et al. (2012), using the recommended initial shock velocity and reduced by a factor of two and four, respectively (models 15r, 15r2 and 15r4). The standard initial shock velocity used beyond fallback is 2 × 10⁹ cm s⁻¹. For a 15 M_☉ star simulation by Fryer et al. (2012), a 2 × 10⁹ cm s⁻¹ shock velocity corresponds to a 3–5 × 10⁵¹ erg explosion, a 1 × 10⁹ cm s⁻¹ shock velocity corresponds to a 1–2 × 10⁵¹ erg explosion, and the 5 × 10⁸ cm s⁻¹ shock velocity corresponds to a weak explosion below 10⁵¹ erg.

The full nucleosynthesis is calculated using the post-processing code MPPNP (see, e.g., Bennett et al. 2012). Here we focus only on C-rich explosive He burning ejecta which include the He/C zone and a small part of the O/C zone (Meyer et al. 1995).

Compared to standard symmetric CCSN models with explosion energy of 10⁵¹ erg (e.g., Woosley & Weaver 1995), our models show that depending on the explosion energy ¹⁶O is depleted and ²⁸Si is accumulated at the bottom of the He/C zone and at the top of the C/O zone, where ¹²C is not significantly modified (see Figure 2 for the details of models 15r and 15r4 with the largest and smallest shock). Such ²⁸Si-enrichment is also obtained in the intermediate model 15r2. Similar nucleosynthesis signatures and high temperature conditions are also predicted in high energy ejecta of aspherical SN and in hypernovae (e.g., Nomoto et al. 2009).

At temperatures above ∼3.5 × 10⁸ K the (α, γ)-rates of ¹⁶O and ²⁰Ne exceed the ¹²C(α, γ)-rate (Figure 1). The reaction rate is directly correlated with the S-factor. The rate is obtained by integrating the S-factor over the Gamow window, the energy range of stellar burning at a certain temperature as defined by Caughlan et al. (1985). The S-factor curve of ¹²C(α, γ)¹⁶O is characterized by non-resonant reaction components: they primarily consist of interfering E1 transitions from tails of broad high energy 1⁻ resonances and the 1⁻ sub-threshold state, and a E2 direct capture component interfering with low energy tails of 2⁺ resonances and the subthreshold state (Buchmann & Barnes 2006). While at low temperatures the reaction rate is lower than ¹⁶O(α, γ)²⁰Ne, it declines toward higher temperatures because of the decline of the S-factor by two orders of magnitude. The ¹⁶O(α, γ)²⁰Ne reaction rate, on the other hand, is determined by a constant non-resonant S-factor term and by the narrow 3⁻ and 1⁻ resonances at 1.1 MeV and 1.3 MeV, respectively, which dominate the reaction rate above temperatures of T ∼ 10⁹ K (Costantini et al. 2010). Concerning the reaction rates of the subsequent α-capture reactions ²⁰Ne(α, γ)²⁴Mg (Schmalbrock et al. 1983) and ²⁴Mg(α, γ)²⁸ Si (Strandberg et al. 2008), the non-resonant S-factor terms are larger and the critical energy range above 0.3 MeV is characterized by narrow resonances which cause a further enhancement in the reaction rate, as demonstrated for ²⁰Ne(α, γ)²⁴Mg in Figure 1. This is also true but for larger energies and to a smaller extent for the production of ³²S, ³⁶Ar, ⁴⁰Ca, and ⁴⁴Ti.

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In parts of the He/C and C/O zones, ¹⁶O is thus depleted and feeds the production of ²⁸Si. This zone is C- and Si-rich, and therefore we call this zone the C/Si zone. A fundamental condition required to form the C/Si zone is that sufficient ⁴He fuel is available while high enough temperatures are reached in the explosive burning.

For model 15r, ¹⁶O and ²⁰Ne are depleted, whereas ²⁸Si and ³²S are produced up to a mass fraction of ∼20% in the C/Si zone due to reactions along the α-capture chain (Figure 1). As shown in Figure 2, the α-capture chain is efficient up to ⁴⁴Ti. At the bottom of the He/C zone results are similar, but since the pre-explosive ¹⁶O abundance is lower the production of ²⁸Si and ³²S is less efficient. In this zone ⁴⁰Ca is depleted via neutron captures, and unstable ⁴⁴Ti is not produced. In model 15r4 the most produced species in the C/Si zone are ²⁰Ne, ²⁴Mg and ²⁸Si. In comparison with the pre-explosive abundances, the species above ³²S and along the α-chain are not produced efficiently. A similar but milder signature is obtained again at the bottom of the He/C zone. Note that the rapid decrease of α-particles in the O/C zones causes a weaker O-depletion (and ²⁸Si excess). Before the SN explosion such a zone is radiative, and still carries the signature of the pre-explosive convective He-burning core. The He profile under the He shell depends on uncertain physics assumptions in the models. Furthermore, ⁴He may be mixed into the O/C zone from the bottom of the He shell by extra-mixing triggered by processes that have not been considered in our pre-SN model, such as rotation (e.g., Meynet et al. 2006) or convective boundary mixing (e.g., Meakin & Arnett 2007). In that case larger fractions of the O/C zone would be converted into the C/Si zone compared to our model.

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In summary, in the CCSN ejecta exposed to strong shocks the upper part of the C/O zone and an extended region of the He/C zone are ¹⁶O-depleted and ²⁸Si-rich, and ²⁸Si will be present in C-rich material when grains will start to condense.

In this section, the nucleosynthesis predictions described in Section 2 are compared with observations for single SiC-X and graphite grains from the St. Louis Presolar Grains Database (Hynes & Gyngard 2009). We compare only the abundances from the C-rich region in the He shell (namely, the C/Si zone and the He/C zone). Mildly C-rich regions in the He/N zone (H-burning layer) will be discussed in a future work.

In Figure 3, left panel, C and N isotopic ratios for SiC-X grains are shown compared to the abundances in C-rich material from our models. Not included in the figure, LD graphites show a similar ¹²C/¹³C spread compared to SiC-X grains. The C/Si zone and the bottom of the He/C zone show high ¹²C/¹³C and low ¹⁴N/¹⁵N. The carbon isotopic ratio is at least 3 orders of magnitude larger than that of the grains due to lack of ¹³C (area labeled as "Si-rich" in the plot). Grains data are located in between our predictions and the solar ratios. Some mixture with a normal component and/or with material from the external part of the He shell is required to fit the observations in this scenario. Indeed, in the most external part of the He/C zone (the part that is not O-depleted) the C ratio evolves to normal values, but with a N ratio larger than solar. Note that in Figure 3 there is a group of SiC-X grains showing ¹²C/¹³C lower than solar. We will discuss them in a future work, where SN ejecta affected by H burning are considered. In Figure 3, we report the comparison with LD graphites for ¹⁶O/¹⁸O, and again ¹²C/¹³C. The largest measured ¹⁸O excess is observed for few graphites with ¹²C/¹³C larger than solar, in agreement with the abundance signature in the external part of the He/C zone. In the C/Si zone and at the bottom of the He/C zone the ¹⁶O/¹⁸O becomes up to 7–8 orders of magnitude larger than solar. However, such a large ratio can be reduced to a ratio ∼ solar with minor mixing with normal material, since there is negligible amount of oxygen left in these layers (see, e.g., Figure 2).

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In Figure 4, right panels, the Si isotopic ratio of stellar models and SiC-X grains are compared. The same is done for LD graphites in the bottom left panel. In the upper left panel, the pre-explosive and post-explosive isotopic Si abundances are reported for model 15r. During the explosion, in the C/O zone with low α-fuel available, ²⁸Si is marginally produced via α-capture, and ^{29, 30}Si are strongly produced via neutron capture. The C/Si zone shows a strong ²⁸Si production. In particular, in zone 1 (M = 2.95 M_☉) the pre-explosive temperature and density are 3.1 × 10⁸ K and 1.34 × 10³ cm⁻³, rising up to 2.0 × 10⁹ K and 7.58 × 10³ cm⁻³, respectively, during the explosion. Moving outward in the deepest part of the He/C zone, the n-process (e.g., Meyer et al. 2000) gradually changes the ²⁸Si-enrichment to strong ^{29, 30}Si-enrichments. Less extreme Si isotopic ratios with a mild ^{29, 30}Si excess are seen in the external He/C zone due to the pre-explosive s-processing. The ²⁸Si excess is reproduced in part of the C/Si zone for models 15r and 15r2 (see, e.g., zone 1 in model 15r, Figure 4, upper left panel and right bottom panel). Also in this case, the grains data shows δ-values closer to the solar ratio, corresponding again to some mixing with unprocessed material, or with more external C-rich stellar layers. On the other hand, in model 15r4 the shock temperature is not sufficient to reproduce the ²⁸Si excess observed in SiC-X grains. The combined nucleosynthesis contribution from α-captures and neutron captures cause a milder ²⁸Si/³⁰Si-enrichment compared to ²⁸Si/²⁹Si moving outward in the ²⁸Si-rich regions, and an earlier positive δ(³⁰Si) with decreasing temperature compared to δ(²⁹Si). This trend is consistent with a subset of SiC-X grains, whereas most of the SiC-X grains belong to the group X1 (Lin et al. 2002).

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Finally, in Figure 4, left bottom panel, LD graphites show a relevant amount of grains with ²⁸Si excess, but with many scattered around the solar ratios, and few with positive Si δ ratios. This different behavior between SiC-X grains and graphites is qualitatively explained looking at the profile of Si isotopes in model 15r (Figure 4, left upper panel). The efficiency of graphite condensation depends on the C enrichment only, whereas SiC-X grains depend on both the C and Si inventory. Therefore, SiC-X condensation will be more efficient in the C/Si zone than in the He/C zone, whereas constraints for graphites are less severe. We may also expect that the condensation of SiC-X and graphites will be less efficient in the external part of the He/C zone, compared to the C-rich and O-depleted regions. Indeed, in these stellar layers there is less free C and Si available. Simulations of the condensation processes using present abundance predictions are required to better quantify this analysis.

The initial ⁴⁴Ti and ²⁶Al enrichment are distinctive signatures for a significant fraction of SiC-X grains and LD graphites (e.g., Clayton & Nittler 2004). Their initial amount that condenses into the grains is usually estimated assuming that the ⁴⁴Ca/⁴⁰Ca and ²⁶Mg/²⁴Mg ratios are solar. This is not the case in our calculations (see, e.g., ⁴⁰Ca abundance profile in Figure 2). Furthermore, Al and Ti condense more efficiently than Mg and Ca, respectively (e.g., Amari et al. 1995; Besmehn & Hoppe 2003). For model 15r, the thermodynamic conditions allow to produce ⁴⁰Ca and ⁴⁴Ti at the same time, with ⁴⁴Ti/⁴⁰Ca ∼ 10⁻² (Figure 2). The largest measured ⁴⁴Ca/⁴⁰Ca ratio in SiC-X grains of ∼2–3 (Hynes & Gyngard 2009) would be satisfied with a fractionation Ti/Ca ∼ 100 without considering also direct ⁴⁴Ca production. In the He/C zone, the neutron captures deplete the pre-explosive ⁴⁰Ca by orders of magnitude, eventually leading to high ⁴⁴Ca/⁴⁰Ca and high ⁴⁸Ca/⁴⁰Ca. ⁴⁸Ti is depleted in this case. We note that in measurements by, e.g., Besmehn & Hoppe (2003) ⁴⁸Ca and ⁴⁸Ti were not possible to distinguish. For model 15r4, the abundances in the C/Si zone are less extreme than model 15r, with a nucleosynthesis more similar to the He/C zone.

One of the main puzzles for the previous ad-hoc mixing scenarios for SiC-X grains is the non-enhancement of ⁵⁴Fe compared to ⁵⁶Fe, since in standard CCSN models ²⁸Si-rich zones are also ⁵⁴Fe-rich. In the C/Si zone of our models Fe species are destroyed by neutron captures and grain signatures with low ⁵⁴Fe are predicted. The isotopes ^{57, 58}Fe can also be produced outward in the He/C zone.

We have compared the abundance signature in presolar SiC-X grains and LD graphites with nucleosynthesis predictions from CCSN ejecta exposed to high shock velocities. Due to basic nuclear properties, an α-capture chain starts from ¹⁶O feeding heavier species including ²⁸Si, without affecting the pre-explosive abundance of ¹²C and creating a new C/Si zone. The amount and distribution of α-isotopes mainly depend on the abundance of the seed ¹⁶O, on the explosion shock velocity and on the amount of α-particles available. The interplay between the α-captures and the n-process regulates the relative abundances of ^{28, 29, 30}Si in the He/C zone.

The typical isotopic trends for C, N, and O of LD graphites and SiC-X grains can be reproduced using the C-rich ejecta, with the exception of grains with low ¹²C/¹³C. The observed ²⁸Si excess is explained qualitatively from the signature in the C/Si zone, where ¹⁶O has been depleted by following α-captures to build ²⁸Si and other heavier species. Since production of graphites depends only on the C abundance, and SiC-X on both C and Si, this may explain why the ²⁸Si excess is not observed in all LD graphites. Therefore, the C/Si zone is an ideal environment to condense SiC-X and LD graphites. Such abundance signatures triggered by high temperatures can be also obtained in parts of asymmetric CCSN ejecta exposed to high shock velocities, or in hypernovae ejecta.

We reconsidered the ⁴⁴Ti excess extrapolated from a sample of C-rich presolar grains. In the C/Si zone the ⁴⁴Ca/⁴⁰Ca is not solar, affecting the results of such extrapolation. The Ca and Ti condensation efficiency is uncertain, leading to their elemental fractionation. For the model with the largest explosion energy (model 15r) both ⁴⁰Ca and ⁴⁴Ti (and ⁴⁸Ti) are produced in the C/Si zone (with ⁴⁰Ca/⁴⁴Ti ∼ 100). Neutron captures destroy ⁴⁰Ca in the He/C zone. The isotope ⁴⁴Ca (and ⁴⁸Ca) instead is produced by neutron captures in all the O-depleted and C-rich ejecta. For weaker shocks (see, e.g., model 15r4) neutron captures dominate the Ca nucleosynthesis, ⁴⁰Ca is depleted and ⁴⁴Ca produced. In both cases, a comparison needs to be made grain-by-grain, where correlations with, e.g., Ti species and ²⁸Si excess (e.g., Clayton & Nittler 2004) are considered. A similar discussion can be derived for ²⁶Al enrichment.

Finally, the present results provide support for the existence of different energy components in the ejecta of the same CCSN. Asymmetries during the SN explosion of, e.g., SN1987A and CasA are confirmed by observations. In SN1987A the emission Si i and Fe i–ii from core material are correlated with He i emission, possibly indicating the signature of α-rich freezout during high-energy-SN explosion in at least part of the ejecta (Kjær et al. 2010). In CasA, DeLaney et al. (2010) reported two major velocity components for Si ii in the ejecta. We suggest that they may be the signature of the Si/S-Si/O and C/Si zones, respectively. This scenario would also explain the non-correlation between Ne ii and O iv emission in CasA (Isensee et al. 2010). Indeed, Ne (together with Mg, S, Ar and Ca) could be produced also in the C/Si zone, whereas for standard CCSN O and Ne are produced in the same regions.

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. also thanks support from EuroGENESIS. NuGrid data is served by Canfar/CADC. We thank the anonymous reviewer for detailed comments and suggestions that greatly improved the manuscript.