  Bramante, Delgado, and Martin [Phys. Rev. D96, 063002(2017)., hereafter
BDM17] extended the analytical formalism of dark matter (DM) capture in a very
important way, which allows, in principle, the use of compact astrophysical
objects, such as neutron stars (NS), as dark matter detectors. In this comment,
we point out the existence of a region in the dark matter neutron scattering
cross section $(\sigma_{nX})$ vs. dark matter mass $(m_{X})$ where the
constraining power of this method is lost. This corresponds to a maximal
temperature ($T_{crit}$) the NS has to have, in order to serve as a dark matter
detector. In addition, we point out several typos and errors in BDM17 that do
not affect drastically their conclusions. Moreover, we provide semi-analytical
approximations for the total capture rates of dark matter particle of arbitrary
mass for various limiting regimes. Those analytical approximations are used to
validate our numerical results.
