What happens to a white dwarf past the Chandrasekhar limit? This is a multiple choice question I had trouble with on an exam.

Will a white dwarf that has had too much mass piled on top of it

a) undergo a thermonuclear flash and explode in a type IA supernova

b) collapse to form a black hole

c) collapse to form a neutron star in a core collapse (type II) supernova
It's not completely clear what you are asking, but if this is a multi-choice quiz, then the only option that could be correct is (a).

(b) Is not correct, because a white dwarf that just passes the Chandrasekhar mass is comfortably below the maximum mass that is supportable by a neutron star. So neutronisation followed by neutron degeneracy pressure and the strongly repulsive nuclear force between neutrons at small separations ought to be capable of preventing black hole formation.

(c) Is not correct because by definition, type II supernovae result from the collapse of massive stars. Observationally, they are distinguished by hydrogen absorption in their spectra, but since a white dwarf will contain little if any hydrogen, then this is not possible.

(a) Might happen. As mass is added to the white dwarf it will become smaller and denser. It is possible that nuclear reactions (carbon fusion) might begin. Because the white dwarf is supported by temperature-independent electron degeneracy pressure, then the nuclear reactions take off at constant density, but the increasing temperature leads to runaway nuclear reactions that detonate the star as a type Ia supernova.