Singularities in the Gravitational Capture of Dark Matter through Long-Range Interactions

TL;DR

This paper revisits dark matter gravitational capture via long-range interactions, highlighting the importance of thermal motion and showing that it significantly enhances capture rates, especially for light mediators, with implications for astrophysical bodies.

Contribution

It introduces a corrected calculation for long-range dark matter capture that accounts for thermal motion, revealing a quadratic sensitivity to mediator mass and providing the first self-evaporation rate estimate.

Findings

Thermal motion significantly increases capture rates for light mediators.

Capture can reach a geometric limit in certain parameter regimes.

Thermal corrections are relevant for massive bodies like Population III stars.

Abstract

We re-examine the gravitational capture of dark matter (DM) through long-range interactions. We demonstrate that neglecting the thermal motion of target particles, which is often a good approximation for short-range capture, results in parametrically inaccurate results for long-range capture. When the particle mediating the scattering process has a mass that is small in comparison to the momentum transfer in scattering events, correctly incorporating the thermal motion of target particles results in a quadratic, rather than logarithmic, sensitivity to the mediator mass, which substantially enhances the capture rate. We quantitatively assess the impact of this finite temperature effect on the captured DM population in the Sun as a function of mediator mass. We find that capture of DM through light dark photons, as in e.g. mirror DM, can be powerfully enhanced, with self-capture attaining a geometric limit over much of parameter space. For visibly-decaying dark photons, thermal corrections are not large in the Sun, but may be important in understanding long-range DM capture in more massive bodies such as Population III stars. We additionally provide the first calculation of the long-range DM self-evaporation rate.