Testing the predictions of axisymmetric distribution functions of
  galactic dark matter with hydrodynamical simulations
  Signal predictions for galactic dark matter (DM) searches often rely on
assumptions on the DM phase-space distribution function (DF) in halos. This
applies to both particle (e.g. $p$-wave suppressed or Sommerfeld-enhanced
annihilation, scattering off atoms, etc.) and macroscopic DM candidates (e.g.
microlensing of primordial black holes). As experiments and observations
improve in precision, better assessing theoretical uncertainties becomes
pressing in the prospect of deriving reliable constraints on DM candidates or
trustworthy hints for detection. Most reliable predictions of DFs in halos are
based on solving the steady-state collisionless Boltzmann equation (e.g.
Eddington-like inversions, action-angle methods, etc.) consistently with
observational constraints. One can do so starting from maximal symmetries and a
minimal set of degrees of freedom, and then increasing complexity. Key issues
are then whether adding complexity, which is computationally costy, improves
predictions, and if so where to stop. Clues can be obtained by making
predictions for zoomed-in hydrodynamical cosmological simulations in which one
can access the true (coarse-grained) phase-space information. Here, we test an
axisymmetric extension of the Eddington inversion to predict the full DM DF
from its density profile and the total gravitational potential of the system.
This permits to go beyond spherical symmetry, and is a priori well suited for
spiral galaxies. We show that axisymmetry does not necessarily improve over
spherical symmetry because the (observationally unconstrained) angular momentum
of the DM halo is not generically aligned with the baryonic one. Theoretical
errors are similar to those of the Eddington inversion though, at the 10-20%
level for velocity-dependent predictions related to particle DM searches in
spiral galaxies. We extensively describe the approach and comment on the
results.
