On velocity-dependent dark matter annihilations in dwarf satellites

Milky Way dwarf spheroidal satellites are a prime target for Dark Matter (DM) indirect searches. There have been recent reassessments of the expected DM gamma-ray signals in case of long-range interactions, commonly known as Sommerfeld enhancement. Since details of the underlying DM phase-space distribution function become critical, there are potentially large uncertainties in the final result. We provide here a first attempt towards a comprehensive investigation of these systematics, addressing the impact on the expected DM flux from Milky Way dwarfs via Bayesian inference on the available stellar kinematic datasets. After reconsidering the study case of ergodic systems, we investigate for the first time scenarios where DM particle orbits may have a radial or tangential bias. We consider both cuspy and cored parametric DM density profiles, together with the case of a non-parametric halo modelling directly connected to line-of-sight observable quantities. The main findings of our work highlight the relevance of the assumed phase-space distribution: Referring to a generalized J-factor, namely the line-of-sight convolution of the spatial part in case of velocity-dependent annihilation rate, an enhancement (suppression) with respect to the limit of isotropic phase-space distributions is obtained for the case of tangentially (radially) biased DM particle orbits. We provide new estimates for J-factors for the eight brightest Milky Way dwarfs also in the limit of velocity-independent DM annihilation, in good agreement with previous results in literature, and derive data-driven lower-bounds based on the non-parametric modelling of the halo density. The outcome of our broad study stands out as a representative of the state-of-the-art in the field, and falls within the interest of current and future experimental collaborations involved in DM indirect detection programs.