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Dark matter (DM) capture in stars offers a rich phenomenology that makes itpossible to probe a wide variety of particle DM scenarios in diverseastrophysical environments. In spite of decades of improvements to refinepredictions of capture-related observables and better quantify astrophysicaland particle-physics uncertainties, the actual impact of the Galacticphase-space distribution function of DM has been overlooked. In this work, wetackle this problem by making use of self-consistent equilibrium phase-spacemodels based on the Eddington inversion formalism and an extension of thismethod to a DM halo with some degree of anisotropy in velocity space. Wedemonstrate that incorrectly accounting for the variation of the DM velocitydistribution with position in the Galaxy leads to a systematic error between afactor two and two orders of magnitude, depending in particular on the targetstar, the DM candidate mass and the type of interaction involved. Moreover, weshow that underlying phase-space properties, such as the anisotropy of thevelocity tensor, actually play an important part -- previously disregarded --and can have a sizable impact on predictions of capture rates and subsequentobservables. We argue that Eddington-like methods, which self-consistentlyaccount for kinematic constraints on the components of the Galaxy, actuallyprovide a reliable next-to-minimal approach to narrow down uncertainties fromphase-space modeling on predictions of observables related to DM capture instars.

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