Limits on the dark matter particle mass from black hole growth in galaxies

I review the properties of degenerate fermion balls and investigate the dark matter distribution at galactic centers using NFW, Moore and isothermal density profiles. I show that dark matter becomes degenerate for particles masses of a few keV at distances less than a few parsec from the center of our galaxy. To explain the galactic center black hole of mass of $\sim 3.5 \times 10^{6}M_{\odot}$ and a supermassive black hole of $\sim 3 \times 10^{9}M_{\odot}$ at a redshift of 6.41 in SDSS quasars, the mass of the fermion ball is assumed to be between $3 \times 10^{3} M_{\odot}$ and $3.5 \times 10^{6}M_{\odot}$. This constrains the mass of the dark matter particle between $0.6 {\rm keV}$ and $82 {\rm keV}$. The lower limit on the dark matter mass is improved to about {\rm 6 keV} if exact solutions of Poisson's equation are used in the isothermal power law case. The constrained dark matter particle could be interpreted as a sterile neutrino.