Analytical insight into dark matter subhalo boost factors for Sommerfeld-enhanced $s$- and $p$-wave $γ$-ray signals

Abstract

As searches for thermal and self-annihilating dark matter (DM) intensify, it becomes crucial to include as many relevant physical processes and ingredients as possible to refine signal predictions, in particular those which directly relate to the intimate properties of DM. We investigate the combined impact of DM subhalos and the (velocity-dependent) Sommerfeld enhancement of the annihilation cross section, in both the s-and p-wave cases. Both features are expected to play an important role in searches for thermal DM particle candidates with masses around or beyond TeV, or in scenarios with a light dark sector. We provide a detailed analytical description of the phenomena at play, and show how they scale with the subhalo masses and the main Sommerfeld parameters. We derive approximate analytical expressions for the overall boost factors resulting from these combined effects, from which the intricate phenomenology can be better understood, and which strongly increase gamma-ray signal predictions for typical targets of different masses (from dwarf galaxies to galaxy clusters). DM subhalos lead to an increase of the Sommerfeld effect by several orders of magnitude (for both the s-and p-wave cases), especially on resonances, which makes them critical to get sensible predictions.

Classification of gamma-ray targets for velocity-dependent and subhalo-boosted dark-matter annihilation

“…We emphasise that all our results, based on full numerical calculations, have been crossvalidated (for all regimes) thanks to the analytical calculations presented in the companion paper [60]. This gives us a strong confidence in these results and the conclusions we draw.…”

“…We find that the s-wave signal is dominated by subhalos near the free-streaming cutoff, while the p-wave signal is dominated by subhalos near the mass scale which sets the transition between the Coulomb and saturation/resonant regime, which depends on φ . Details and scaling relations are provided in the companion paper [60]. We stress that the resonances do not appear at arbitrarily low φ , because subhalos cannot form below the free-streaming scale.…”

“…We study in particular the complex interplay between velocity dependence and substructure boost, and the implications in terms of ranking of the various targets. A more in-depth and analytical study of the boost factor is presented in a companion paper [60].…”

“…The approximation on the right-handside is valid only when the host is distant enough so that most of the annihilation rate is contained within the angular resolution of the telescope; in that case, J S,sm J S,host . Note that a detailed analytical study of the subhalo boost factor in the context of the Sommerfeld enhancement has been carried out in a companion paper [60].…”

“…The results derived in this section rely on the general formalism and methodology presented in section 2.3, and our calculations are based on up-to-date models for both the properties of the subhalo population and the velocity distribution in each subhalo (determined by a phase space); the numerical calculations in this section (for subhalos) have also been cross-checked and validated with analytical approximations (see the companion paper, [60]). First, we discuss the boost factors obtained for our representative targets and highlight the differences observed between the s-and p-wave cases (section 5.1).…”