We use a semianalytic approach that is calibrated to N-body simulations to study the evolution of self-interacting dark matter cores in galaxies. We demarcate the regime where the temporal evolution of the core density follows a well-defined track set by the initial halo parameters and the cross section. Along this track, the central density reaches a minimum value set by the initial halo density. Further evolution leads to an outward heat transfer, inducing gravothermal core collapse such that the core shrinks as its density increases. We show that the time scale for the core collapse is highly sensitive to the outer radial density profile. Satellite galaxies with significant mass loss due to tidal stripping should have larger central densities and significantly faster core collapse compared to isolated halos. Such a scenario could explain the dense and compact cores of dwarf galaxies in the Local Group like Tucana (isolated from the Milky Way), the classical Milky Way satellite Draco, and some of the ultrafaint satellites. If the ultimate fate of core collapse is black hole formation, then the accelerated time scale provides a new mechanism for creating intermediate mass black holes.
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