Gravitational Clustering of Relic Neutrinos in the Milky Way: Overdensity as a Function of Neutrino Mass

Gravity has been gathering relic neutrinos into the Milky Way halo for billions of years, but only modestly. In the calibrated approximation used here, a 0.05 eV neutrino is overdense locally by a factor of only 1.039, while a 0.15 eV neutrino reaches a factor of 1.350, corresponding to a local density of 75.6 per cubic centimetre for that eigenstate. The mean speed of a 0.05 eV relic neutrino today is still 3177 kilometres per second, well above the Galactic escape speed, which is why the enhancement stays small. This paper derives the velocity comparison, states the clustering approximation and its limits honestly, and converts overdensity into the density a terrestrial detector actually samples. Computed from stated assumptions, not measured.