The surprising accuracy of isothermal Jeans modelling of
  self-interacting dark matter density profiles
  Recent claims of observational evidence for self-interacting dark matter
(SIDM) have relied on a semi-analytic method for predicting the density
profiles of galaxies and galaxy clusters containing SIDM. We present a thorough
description of this method, known as isothermal Jeans modelling, and then test
it with a large ensemble of haloes taken from cosmological simulations. Our
simulations were run with cold and collisionless dark matter (CDM) as well as
two different SIDM models, all with dark matter only variants as well as
versions including baryons and relevant galaxy formation physics. Using a mix
of different box sizes and resolutions, we study haloes with masses ranging
from 3e10 to 3e15 Msun. Overall, we find that the isothermal Jeans model
provides as accurate a description of simulated SIDM density profiles as the
Navarro-Frenk-White profile does of CDM halos. We can use the model
predictions, compared with the simulated density profiles, to determine the
input DM-DM scattering cross-sections used to run the simulations. This works
especially well for large cross-sections, while with CDM our results tend to
favour non-zero (albeit fairly small) cross-sections, driven by a bias against
small cross-sections inherent to our adopted method of sampling the model
parameter space. The model works across the whole halo mass range we study,
although including baryons leads to DM profiles of intermediate-mass (10^12 -
10^13 Msun) haloes that do not depend strongly on the SIDM cross-section. The
tightest constraints will therefore come from lower and higher mass haloes:
dwarf galaxies and galaxy clusters.
