The gravitational collapse of ONe electron-degenerate cores and white   dwarfs: the role of $^{24}$Mg and $^{12}$C revisited
  The final stages of the evolution of electron--degenerate ONe cores, resulting from carbon burning in ``heavy weight'' intermediate--mass stars ($8 M_{\sun}\la M \la 11 M_{\sun}$) and growing in mass, either from carbon burning in a shell or from accretion of matter in a close binary system, are examined in the light of their detailed chemical composition. In particular, we have modelled the evolution taking into account the abundances of the following minor nuclear species, which result from the previous evolutionary history: $^{12}$C, $^{23}$Na, $^{24}$Mg, and $^{25}$Mg. Both $^{23}$Na and $^{25}$Mg give rise to Urca processes, which are found to be unimportant for the final outcome of the evolution. $^{24}$Mg was formerly considered a major component of ONe cores (hence called ONeMg cores), but updated evolutionary calculations in this mass range have severely reduced its abundance. Nevertheless, we have parameterized it and we have found that the minimum amount of $^{24}$Mg required to produce NeO burning at moderate densities is $\sim 23%$, a value exceedingly high in the light of recent evolutionary models. Finally, we have determined that models with relatively small abundances of unburnt carbon ($X(^{12}$C)$\sim 0.015$) could be a channel to explosion at low to moderate density ($\sim 1\times 10^9$ g cm$^{-3}$). This is clearly below the current estimate for the explosion/collapse threshold and would have interesting consequences. 
J. L. Gutierrez, R. Canal, E. Garcia-Berro