If dark matter annihilates with a velocity-dependent cross section within a subhalo, then the magnitude and angular distribution of the resulting photon signal will change. These effects are encoded in the J-factor. In this work we compute the J-factor for a variety of choices for the cross section velocity-dependence, and for a variety of choices for the dark matter profile, including generalized Navarro-Frenk-White (NFW), Einasto, Burkert and Moore. We include the results of these computations as data products alongside the article. We find that the angular distribution of a future signal would depend on the velocity-dependence of the annihilation cross section more strongly for cuspy profiles than for cored profiles. Interestingly, we find that for a density profile with an inner slope power law steeper than 4/3, Sommerfeld-enhanced annihilation in the Coulomb limit leads to a divergence at the center, requiring a more detailed treatment of departure from the Coulomb limit.
Cite
@article{arxiv.2110.09653,
title = {$J$-factors for Velocity-dependent Dark Matter},
author = {Bradly Boucher and Jason Kumar and Van B. Le and Jack Runburg},
journal= {arXiv preprint arXiv:2110.09653},
year = {2022}
}