Gravothermal Evolution of Self-Interacting Dark Matter Halos across Knudsen Numbers

Abstract

If the dark matter self-interacts elastically via a light mediator, then at relative velocities above a scale $w$ dictated by particle physics parameters, the cross section scales as $σ\propto v^{-4}$. Depending on the value of $w$, the self-interaction cross section in low-mass halos could be (much) larger than has been previously studied extensively. We perform kinetic simulations of isolated self-interacting dark matter halos using the code KiSS-SIDM for a wide range of halo masses, concentrations, and cross sections from $50 \,\mathrm{cm}^2 \, \mathrm{g}^{-1}$ to $250{,}000 \, \mathrm{cm}^2 \, \mathrm{g}^{-1}$, including several velocity-dependent and fully differential (anisotropic) cross sections. We demonstrate that for idealized NFW halos the collapse time can be predicted from the Knudsen number at the scale radius of the halo. We perform similar calculations for halos extracted from cosmological simulations using either $N$-body (collisionless) or SPH (strongly collisional) dynamics, and then evolve cutouts with KiSS-SIDM. For these halos, the collapse times differ from the idealized NFW simulations by up to a factor of a few. Further, we calibrate a hydrostatic fluid model to these results, which solves the structure equations as a boundary value problem via two-point shooting. The fluid calculation predicts that for velocity-independent cross sections, a convective region of the halo develops late in the collapse. The collapse times agree well between the kinetic simulations and the fluid code, especially in the velocity-independent case. The density profiles agree well in some cases, which include all of the velocity-dependent cross section runs.