Velocity-dependent J-factors for Milky Way dwarf spheroidal analogues in cosmological simulations

TL;DR

This study uses cosmological simulations to analyze how dark matter velocity distributions affect annihilation signals in Milky Way dwarf spheroidal galaxies, providing a new method to estimate these signals accurately.

Contribution

It introduces a simple power-law relation to estimate dark matter velocity distributions from galaxy properties, improving predictions of annihilation signals without detailed velocity calculations.

Findings

Maxwell-Boltzmann models introduce errors in velocity-dependent annihilation predictions.

A power-law relation links maximum circular velocity to peak velocity, enabling accurate estimations.

Scatter in J-factors from analogues dominates observational uncertainties.

Abstract

We study the impact of the dark matter velocity distribution modelling on signals from velocity-dependent dark matter annihilation in Milky Way dwarf spheroidal galaxies. Using the high resolution APOSTLE simulations, we identify analogues corresponding to Milky Way dwarf spheroidal galaxies, and from these directly determine the dark matter pair-wise relative velocity distribution, and compare to best-fitting Maxwell-Boltzmann distribution models. For three velocity-dependent annihilation models, p-wave, d-wave, and the Sommerfeld model, we quantify the errors introduced when using the Maxwell-Boltzmann parameterization. We extract a simple power-law relation between the maximum circular velocity of the dwarf spheroidal analogue and the peak speed of the Maxwell-Boltzmann distribution. We show that this relation can be used to accurately calculate the dark matter relative velocity distribution, and find that it allows us to estimate the dark matter annihilation signal without the need to directly calculate the relative velocity distribution for each galaxy. The scatter in the J-factors calculated from the analogues dominates the uncertainty obtained when compared to the J-factor as determined from the observational data for each dwarf spheroidal, with the largest scatter from d-wave models and the smallest from Sommerfeld models.