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Neutrino clustering around spherical dark matter halos

Cold dark matter halos form within a smoothly distributed background of relic neutrinos -- at least some of which are massive and non-relativistic at late times. We calculate the accumulation of massive neutrinos around spherically collapsing cold dark matter halos in a cosmological background. We identify the physical extent of the "neutrino halo" in the spherical collapse model, which is large in comparison with the virial radius of the dark matter, and conditions under which neutrinos reaching the cold dark matter halo will remain bound to the halo at late times. We calculate the total neutrino mass and bound neutrino mass associated with isolated spherical halos for several neutrino mass hierarchies and provide fitting formulae for these quantities in terms of the cold dark matter halo mass and the masses of the individual neutrino species.