Constraints on sterile neutrino models from strong gravitational lensing, Milky Way satellites, and Lyman-$\alpha$ forest

The nature of dark matter is one of the most important unsolved questions in science. Some dark matter candidates do not have sufficient nongravitational interactions to be probed in laboratory or accelerator experiments. It is thus important to develop astrophysical probes which can constrain or lead to a discovery of such candidates. We illustrate this using state-of-the-art measurements of strong gravitationally-lensed quasars to constrain four of the most popular sterile neutrino models, and also report the constraints for other independent methods that are comparable in procedure. First, we derive effective relations to describe the correspondence between the mass of a thermal relic warm dark matter particle and the mass of sterile neutrinos produced via Higgs decay and GUT-scale scenarios, in terms of large-scale structure and galaxy formation astrophysical effects. Second, we show that sterile neutrinos produced through the Higgs decay mechanism are allowed only for mass $>26$ keV, and GUT-scale scenario $>5.3$ keV. Third, we show that the single sterile neutrino model produced through active neutrino oscillations is allowed for mass $>92$ keV, and the 3 sterile neutrino minimal standard model ($\nu$MSM) for mass $>16$ keV. These are the most stringent experimental limits on these models.