The Existence of Sterile Neutrino Halos in Galactic Centers as an Explanation of the Black Hole mass - Velocity Dispersion Relation

If sterile neutrinos exist and form halos in galactic centers, they can give rise to observational consequences. In particular, the sterile neutrinos decay radiatively and heat up the gas in the protogalaxy to achieve hydrostatic equilibrium, and they provide the mass to form supermassive blackholes. A natural correlation between the blackhole mass and velocity dispersion thus arises $\log(M_{BH,f}/M_{\odot})=\alpha \log (\sigma /200 {\rm km s^{-1}})+ \beta$ with $\alpha \approx 4$ and $\beta \approx 8$.