  Dark matter (DM) which sufficiently heats a local region in a white dwarf
will trigger runaway fusion, igniting a type Ia supernova (SN). In a companion
paper, this instability was used to constrain DM heavier than $10^{16}$ GeV
which ignites SN through the violent interaction of one or two individual DM
particles with the stellar medium. Here we study the ignition of supernovae by
the formation and self-gravitational collapse of a DM core containing many DM
particles. For non-annihilating DM, such a core collapse may lead to a mini
black hole that can ignite SN through the emission of Hawking radiation, or
possibly as a by-product of accretion. For annihilating DM, core collapse leads
to an increasing annihilation rate and can ignite SN through a large number of
rapid annihilations. These processes extend the previously derived constraints
on DM to masses as low as $10^{5}$ GeV.

High Energy Physics - Phenomenology;High Energy Astrophysical Phenomena