  We generalize the formalism for DM capture in celestial bodies to account for
arbitrary mediator mass, and update the existing and projected astrophysical
constraints on DM-nucleon scattering cross section from observations of neutron
stars. We show that the astrophysical constraints on the DM-nucleon interaction
strength, that were thought to be the most stringent, drastically weaken for
light mediators and can be completely voided. For asymmetric DM, existing
astrophysical constraints are completely washed out for mediators lighter than
5 MeV, and for annihilating DM the projected constraints are washed out for
mediators lighter than 0.25 MeV. Related terrestrial direct detection bounds
also weaken, but in a complementary fashion; they supersede the astrophysical
capture bounds for small or large DM mass, respectively for asymmetric or
annihilating DM. Repulsive self-interactions of DM have an insignificant impact
on the total capture rate, but a significant impact on the black hole formation
criterion. This further weakens the constraints on DM-nucleon interaction
strength for asymmetric self-repelling DM, whereas constraints remain unaltered
for annihilating self-repelling DM. We use the correct Hawking evaporation rate
of the newly formed black hole, that was approximated as a blackbody in
previous studies, and show that, despite a more extensive alleviation of
collapse as a result, the observation of a neutron star collapse can probe a
wide range of DM self-interaction strengths.
