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Abstract We study the evolution of isolated self-interacting dark matter (SIDM) halos that undergo gravothermal collapse and are driven deep into the short-mean-free-path regime.We assume spherical Navarro-Frenk-White (NFW) halos as initial conditions and allow for elastic dark matter self-interactions.We discuss the structure of the halo core deep in the core-collapsed regime and how it depends on the particle physics properties of dark matter, in particular, the velocity dependence of the self-interaction cross section. We find an approximate universality deep in this regime that allows us to connect the evolution in the short- and long-mean-free-path regimes, and approximately map the velocity-dependent self-interaction cross sections to constant ones for the full gravothermal evolution. We provide a semi-analytic prescription based on our numerical results for halo evolution deep in the core-collapsed regime.Our results are essential for estimating the masses of the black holes that are likely to be left in the core of SIDM halos. 

ABSTRACT We study the evolution of isolated self-interacting dark matter halos using spherically symmetric gravothermal equations allowing for the scattering cross-section to be velocity dependent. We focus our attention on the large class of models where the core is in the long mean free path regime for a substantial time. We find that the temporal evolution exhibits an approximate universality that allows velocity-dependent models to be mapped onto velocity-independent models in a well-defined way using the scattering time-scale computed when the halo achieves its minimum central density. We show how this time-scale depends on the halo parameters and an average cross-section computed at the central velocity dispersion when the central density is minimum. The predicted collapse time is fully defined by the scattering time-scale, with negligible variation due to the velocity dependence of the cross-section. We derive new self-similar solutions that provide an analytic understanding of the numerical results.