MG11 
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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 and for 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, we require a fermion ball mass between $3 \times 10^{3} M_{\odot}$ and $3.5 \times 10^{6}M_{\odot}$. This leads to strong limits on the mass of the dark matter particle between $0.64 \ {\rm keV}$ and $5.82 \ {\rm keV}$ for NFW profile, and between $0.97 \ {\rm keV}$ and $13.81 \ {\rm keV}$ for Moore profile and finally the dark matter mass is found to be constrained between $2.38 \ {\rm keV}$ and $ 81.65 \ {\rm keV}$ for the isothermal gas sphere case. I then argue that the constrained particle could be the long sought dark matter of the Universe that is interpreted as a sterile neutrino.