Testing the predictions of axisymmetric distribution functions of galactic dark matter with hydrodynamical simulations

TL;DR

This paper tests an axisymmetric extension of the Eddington inversion method to predict dark matter phase-space distribution functions in galaxies, comparing it with hydrodynamical simulations to assess its accuracy and limitations.

Contribution

It introduces and evaluates an axisymmetric method for predicting dark matter distributions, highlighting its limitations compared to spherical models.

Findings

Axisymmetric predictions do not significantly outperform spherical models.

Theoretical errors are around 10-20% for velocity-dependent dark matter signals.

Angular momentum misalignment affects the accuracy of axisymmetric models.

Abstract

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.