Multi-component multiscatter capture of dark matter

In recent years, the usefulness of astrophysical objects as dark matter probes has become increasingly evident. The potentially observable signatures of DM gravitationally trapped inside a compact astrophysical object have been used to forecast stringent constraints on the nucleon-dark matter interaction cross-section. Currently, the probes of interest are: at high red-shifts, Population III stars that form in isolation, or in small numbers, in very dense DM minihalos at z=15-40, and, in our own Milky Way, neutron stars, white dwarfs, brown dwarfs, exoplanets, etc. None of those objects are truly single-component, and, as such, capture rates calculated with the common assumption made in the literature of single-component capture, i.e. capture of DM by multiple scatterings with one single type of nucleus inside the object, are not accurate. In this work, we present an extension of this formalism to multi-component objects and apply it to Pop III stars, investigating the role of He on the capture rate. As expected, we find that the inclusion of helium leads to an enhancement of the overall capture rate, improving the potential of Pop III stars as Dark Matter probes.