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

TL;DR

This paper improves the modeling of dark matter velocity distributions in the galaxy, revealing significant impacts on capture predictions in stars and emphasizing the importance of anisotropy and self-consistent phase-space models.

Contribution

It introduces a self-consistent equilibrium phase-space modeling approach for dark matter, extending Eddington inversion to include anisotropy, and quantifies its impact on stellar capture predictions.

Findings

Incorrect velocity distribution modeling causes errors up to two orders of magnitude.

Velocity anisotropy significantly affects dark matter capture rates.

Eddington-like methods provide reliable, minimal-uncertainty predictions for dark matter 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.