Maximum likelihood fits to a cored halo enclosing finite mass

Abstract

The hybrid Ricci scalar $R_{\mu\nu}\eta^{\mu\nu}$ formed from a Robertson-Walker derived Ricci tensor and a distinct flat space metric becomes a dark, pseudo-isothermal density under asymptotic constraint. While extension of this constraint to more general scenarios is unclear, it is model independent and suggestive of a radical premise: all galactic dark matter halos are sourced by very many distinct Robertson-Walker spacetimes. We explore this premise and present a cored galactic halo, which encloses finite mass over all space. We compute fit parameters to published data on the Milky Way dwarf spheroidal galaxies, and find consistency with a predicted reciprocal square scaling relation. Spherical symmetry permits treatment of each individual halo as a point particle interacting under a modified gravitational force. This force is Newtonian at large separation with a leading dipole correction, and naturally softens to zero at small separation. Taken as cold dark matter, ensembles of such halos present a possible resolution to tension between large-scale $N$-body simulations and small-scale astrophysical data.