Astrophysical constraints on a possible neutrino ball at the Galactic Center

The nature of the massive object at the Galactic Center (Sgr A$^{*}$) is still unclear even if various observational campaigns led many authors to believe that our Galaxy hosts a super-massive black hole with mass $M\simeq 2.6\times 10^6$ M$_{\odot}$. However, the black hole hypothesis, which theoretically implies a luminosity $\simeq 10^{41}$ erg s$^{-1}$, runs into problems if one takes into account that the observed luminosity, from radio to $\gamma$-ray wavelengths, is below $10^{37}$ erg s$^{-1}$. In order to solve this blackness problem, alternative models have been recently proposed. In particular, it has been suggested that the Galactic Center hosts a ball made up by non-baryonic matter (e.g. massive neutrinos and anti-neutrinos) in which the degeneracy pressure of fermions balances their self-gravity. Requiring to be consistent with all the available observations towards the Galactic Center allows us to put severe astrophysical constraints on the neutrino ball parameters. The presence of such an object in the Galactic Center may be excluded if the constituent neutrino mass $m_{\nu}$ is $\ut> 24$ keV, while if $m_{\nu}\ut< 24$ keV observations can not give a definite answer.