  What if the dark matter-nucleon scattering cross section is too small to be
detected by direct detection experiments? It is well known in the literature
that some interactions lead to dark matter-nucleon scattering cross sections
that can be velocity and momentum suppressed. We show that in the case of
bosonic dark matter, neutron star spectroscopy offers a possible detection.
Firstly, we discuss the case of scalar dark matter with scalar, pseudoscalar,
and vector mediators. Later, we do this exercise for vector dark matter. We
show that, depending on the nature of dark matter and the interaction involved,
neutron stars can improve the sensitivity on the dark matter-nucleon scattering
cross section by orders of magnitude, representing a major step forward in the
dark matter siege.
