  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 case of bosonic
dark matter the 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.
