Degenerate sterile neutrino dark matter in the cores of galaxies

Aims. We study the distribution of fermionic dark matter at the center of galaxies using NFW, Moore and isothermal density profiles and show that dark matter becomes degenerate for particle masses of a few keV and for distances less than a few parsec from the center of our galaxy. Methods. A compact degenerate core forms after galaxy merging and boosts the growth of supermassive black holes at the center of galaxies. Results. To explain the galactic center black hole of mass of similar to 3.5 x 10(6) M-circle dot and a supermassive black hole of similar to 3 x 10(9) M-circle dot at a redshift of 6.41 in SDSS quasars, we require a degenerate core of mass between 3 x 10(3) M-circle dot and 3.5 x 10(6) M-circle dot. This constrains the mass of the dark matter particle between 0.6 keV and 82 keV. The lower limit on the dark matter mass is improved to 7 keV if exact solutions of Poisson's equation are used in the isothermal power law case. We argue that the constrained particle could be the long sought dark matter of the Universe that is interpreted here as a sterile neutrino.