Detecting bosonic dark matter with neutron stars

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.