How does the Chandrasekhar limit relate to the ignition of carbon in white dwarf stars?

Question

Why carbon in white dwarfs ignites (deflagrate, detonate) at the Chandrasekhar limit? The limit relates stability of the star made of degenerate electron Fermi gas to the white dwarf mass without a word about chemical identity of the atomic nuclei. How is that carbon ignites at (or around) the limit?

Answer 1

The carbon ignites if the densities become high enough to initiate pycnonuclear reactions.

These fusion reactions occur, even in thermally cold, crystalline carbon if the zeropoint oscillations are sufficient to overcome the Coulomb barrier between the positively charged nuclei. This zeropoint energy increases with density. The reaction rate can then become supercharged because the star is supported by degeneracy pressure which is not greatly increased because most of the heat gets dumped into the non-degenerate nuclei.

The ignition may occur close to the Chandrasekhar mass because the central density of a white dwarf climbs rapidly as the limiting Chandrasekhar mass is approached. The critical density is likely to be a few $\times 10^{13}$ kg/m$^3$, which occurs in white dwarfs more massive than about $1.35M_\odot$.

An alternative ignition source would be in (accreted) helium in the white dwarf envelope. Although the density threshold for He pycnonuclear reactions, it stil takes a white dwarf close to the Chandrasekhar limit to have the necessary high density in its envelope.