Dark Matter Velocity Distributions: Comparing Numerical Simulations to Analytic Results

TL;DR

This study compares dark matter velocity distributions from numerical simulations with analytic models, confirming their consistency under certain assumptions and discussing implications for dark matter detection.

Contribution

It demonstrates that simulation data align with analytic predictions based on energy distribution, validating key assumptions in dark matter modeling.

Findings

Simulation velocity distributions match analytic predictions inside the scale radius.

The assumptions of spherical symmetry, isotropy, and static potential are sufficiently accurate.

Implications for high-velocity tail behavior in dark matter annihilation are discussed.

Abstract

We test the consistency of dark matter velocity distributions obtained from dark matter-only numerical simulations with analytic predictions, using the publicly available Via Lactea 2 dataset as an example. We find that, well inside the scale radius, the velocity distribution obtained from numerical simulation is consistent with a function of a single integral of motion -- the energy -- and moreover is consistent with the result obtained from Eddington inversion. This indicates that the assumptions underlying the analytic result, namely, spherical symmetry, isotropy, and a static potential, are sufficiently accurate to govern the coarse properties of the velocity distribution in the inner regions of the halo. We discuss implications for the behavior of the high-velocity tail of the distribution, which can dominate dark matter annihilation from a $p$- or $d$-wave state.