Towards a more rigorous treatment of uncertainties on the velocity distribution of dark matter particles for capture in stars

Abstract: Dark matter (DM) capture in stars offers a rich phenomenology that makes it possible to probe a wide variety of particle DM scenarios in diverse astrophysical environments. In spite of decades of improvements to refine predictions of capture-related observables and better quantify astrophysical and particle-physics uncertainties, the actual impact of the Galactic phase-space distribution function of DM has been overlooked. In this work, we tackle this problem by making use of self-consistent equilibrium phase-space models based on the Eddington inversion formalism and an extension of this method to a DM halo with some degree of anisotropy in velocity space. We demonstrate that incorrectly accounting for the variation of the DM velocity distribution with position in the Galaxy leads to a systematic error between a factor two and two orders of magnitude, depending in particular on the target star, the DM candidate mass and the type of interaction involved. Moreover, we show that underlying phase-space properties, such as the anisotropy of the velocity tensor, actually play an important part -- previously disregarded -- and can have a sizable impact on predictions of capture rates and subsequent observables. We argue that Eddington-like methods, which self-consistently account for kinematic constraints on the components of the Galaxy, actually provide a reliable next-to-minimal approach to narrow down uncertainties from phase-space modeling on predictions of observables related to DM capture in stars.