Gravothermal evolution of dark matter halos with differential elastic
  scattering
  We study gravothermal evolution of dark matter halos in the presence of
differential self-scattering that has strong velocity and angular dependencies.
We design controlled N-body simulations to model Rutherford and \Moller
scatterings in the halo, and follow its evolution in both core-expansion and
-collapse phases. The simulations show the commonly-used transfer cross section
underestimates the effects of dark matter self-interactions, but the viscosity
cross section provides a good approximation for modeling angular-dependent dark
matter scattering. We investigate thermodynamic properties of the halo, and
find that the three moments of the Boltzmann equation under the fluid
approximation are satisfied. We further propose a constant effective cross
section, which integrates over the halo's characteristic velocity dispersion
with weighting kernels motivated by kinetic theory of heat conduction. The
effective cross section provides an approximation to differential
self-scattering for most of the halo evolution. However, it can significantly
underestimate the growth rate of the central density at late stages of the
collapse phase. This indicates that constant and velocity-dependent dark matter
self-interactions are fundamentally different, as for the latter the cross
section evolves with the halo dynamically, boosting the collapse. This feature
may help test different self-interacting dark matter models.
