The Velocity-Dependent $J$-factor of the Milky Way Halo: Does What Happens in the Galactic Bulge Stay in the Galactic Bulge?

TL;DR

This paper investigates how velocity-dependent dark matter annihilation affects the angular distribution of gamma-ray signals from the Galactic bulge, highlighting differences between Sommerfeld-enhanced and p-/d-wave scenarios and implications for the Galactic Center excess.

Contribution

It provides an analytic relationship between dark matter profiles and annihilation signals in the bulge, emphasizing the importance of particle velocities and external profiles for different annihilation modes.

Findings

Sommerfeld-enhanced annihilation is dominated by slow particles confined in the bulge.

High-speed particles significantly influence p- and d-wave annihilation signals.

Explaining the Galactic Center excess via p-wave annihilation requires a steeper dark matter profile.

Abstract

We consider the angular distribution of the photon signal which could arise from velocity-dependent dark matter annihilation within the Galactic bulge. We find that, for the case of Sommerfeld-enhanced annihilation, dark matter annihilation within the bulge is dominated by slow speed particles which never leave the bulge, allowing one to find a simple analytic relationship between the dark matter profile within the Galactic bulge and the angular distribution. On the other hand, for the case $p$- or $d$-wave annihilation, we find that the small fraction of high-speed particles which can leave the bulge provide a significant, often dominant, contribution to dark matter annihilation within the bulge. For these scenarios, fully understanding dark matter annihilation deep within the Galactic bulge, and the angular distribution of the resulting photon signal, requires an understanding of the dark matter profile well outside the bulge. We consider the Galactic Center excess in light of these results, and find that an explanation of this excess in terms of $p$-wave annihilation would require the dark matter profile within the bulge to have a much steeper profile than usually considered, but with uncertainties related to the behavior of the profile outside the bulge.