Analytic Approximation of Carbon Condensation Issues in Type Ii Supernovae

Abstract

I present analytic approximations for some issues related to condensation of graphite, TiC, and silicon carbide in oxygen-rich cores of supernovae of Type II. Increased understanding, which mathematical analysis can support, renders researchers more receptive to condensation in O-rich supernova gases. Taking SN 1987A as typical, my first analysis shows why the abundance of CO molecules reaches an early maximum in which free carbon remains more abundant than CO. This analysis clarifies why O-rich gas cannot oxidize C if 56 Co radioactivity is as strong as in SN 1987A. My next analysis shows that the CO abundance could be regarded as being in chemical equilibrium if the CO molecule is given an effective binding energy rather than its laboratory dissociation energy. The effective binding energy makes the thermal dissociation rate of CO equal to its radioactive dissociation rate. This preserves possible relevance for the concept of chemical equilibrium. My next analysis shows that the observed abundances of CO and SiO molecules in SN 1987A rule out frequent suggestions that equilibrium condensation of SUNOCONs has occurred following atomic mixing of the He-burning shell with more central zones in such a way as to reproduce roughly the observed spectrum of isotopes in SUNOCONs while preserving C/O > 1. He atoms admixed along with the excess carbon would destroy CO and SiO molecules, leaving their observed abundances unexplained. The final analysis argues that a chemical quasiequilibrium among grains (but not gas) may exist approximately during condensation, so that its computational use is partially justified as a guide to which mineral phases would be stable against reactions with gas. I illustrate this point with quasiequilibrium calculations by Ebel & Grossman that have shown that graphite is stable even when O/C >1 if prominent molecules are justifiably excluded from the calculation of chemical equilibrium.

Late formation of silicon carbide in type II supernovae

“…Both ungrouped grains lie along a 1:1 line in the plot of d 49 Ti versus d 50 Ti, indicating approximately equal production of 49 Ti and 50 Ti in the He/C zones of their parent SNe. The inferred production ratio for 49 Ti/ 50 Ti of 1.04 (the solar ratio) is further supported by the Ti isotopic signature of a previously reported (38) presolar graphite grain with large 29 Si and 30 Si excesses that also originated in the SN He/C zone (39). On the basis of these observations, we adopted the production ratio of 1.04 in the He/C zones of SNe in the calculations that follow ( Fig.…”

“…It is also noteworthy to point out the following two aspects: (i) Selective mixing of materials from the inner Si/S zone and the outer C-rich zones, as suggested by the isotopic signatures of presolar X grains, may be supported by the observation of Rayleigh-Taylor instabilities in three-dimensional simulations of core-collapse SNe [for example, (28)]. (ii) Electrons arising from 56 Co decay could dissociate the stable CO molecule, allowing carbonaceous grains to grow even in O-rich conditions [for example, (29)]. However, quasi-equilibrium calculations (30) show that, although graphite could be stable in O-dominated SN zones, SiC is not stable under such O-rich conditions.…”

Formulation of Non-Steady-State Dust Formation Process in Astrophysical Environments

“…However, in the ejecta of SNe, some of CO molecules might be destroyed by the collisions with energetic electrons and charge transfer reactions with the ionized inert gas (Liu & Dalgarno 1994Clayton et al 1999Clayton et al , 2001Clayton 2013). Here, we do not consider the formation and destruction processes of CO molecules, since we treat the initial abundance of carbon atoms available for dust formation as a parameter.…”

Radiative shocks create environments for dust formation in classical novae

“…Carbon nucleation can occur even in an oxygen rich environment if free carbon is made available by CO destruction, as can occur due to neutral reactions in a shielded region (Pontefract & Rawlings 2004) or due to dissociation by energetic electrons (e.g. Todini & Ferrara 2001;Clayton 2013;Lazzati & Heger 2016). In core collapse supernovae, energetic electrons are produced by the radioactive decay of 56 Ni.…”