Hollow Galactic Halos of Fermionic Dark Matter

Abstract

Fermi statistics and velocity anisotropy give a surprisingly rich structure to massive neutrino dark matter halos. If a spherically symmetric halo has an anisotropic phase space, then hollow halos with a minimum of the mass density at the center are possible. Hollowness of a halo is controlled by a dimensionless constant K_0 _= (g_v_/4π)(m^2^/M^2^_p_)(L^2^_0_/h^2^)(c/[μ]^1/12^) involving the fermion mass, m, the Planck mass M_p_, and parameters L_0_ and μ^1/2^ fixing the halo anisotropy. All dependence of a halo on fermion mass and the maximum phase-space density is contained in K_0_. For K_0 _ << 1, i.e., for small enough fermion mass and effective core size, most halos must be hollow to satisfy Fermi statistics. Thus, existing neutrino lower mass bounds not only are overly restrictive but become inapplicable. It follows that neutrinos or other fermions in the mass range m <~ 100 eV are viable candidates for galactic dark matter. A flat rotation curve is also shown to be a generic result of anisotropy in the same limit of interest. We discuss observable consequences of the possibility that isolated dwarf galaxies are associated with hollow dark matter halos.