Shape Shifting Light Dark Matter Solitons

Abstract

Dark matter consisting of a Bose--Einstein condensate (BEC) of ultra-light particles is predicted to have a soliton shape that shifts with the dark matter mass fraction in galaxies containing a centrally localized point mass (or black hole), consistent with previous numerical results and analytical approximations in both the cored self-gravitating and cusped hydrogenic limits. Solutions of the Schr\"{o}dinger-Poisson equation with baryonic coupling are here accurately represented as a sum of five Gaussians with numerically optimized amplitudes and widths, thereby facilitating galactic predictions and observational comparisons as a function of dark matter mass fraction. The results are used to derive mass, energy and velocity scaling relations as functions of soliton mass fraction, as well as to predict dark matter halo size, mass and core density in terms of observed half-light radii and velocity dispersions by invoking observationally validated approximations relating rotational velocity and velocity dispersion. Applications of the predictions, as well as challenges associated with critically testing dark matter models, are illustrated using comparisons with dwarf spheroidal (dSph) and ultra-faint dwarf (UFD) galaxy observations, which, under the present soliton-based modeling assumptions, are found to be compatible with soliton particle masses of the order of $10^{-22}$ (eV/c$^2$), with an upper bound of approximately $3\times 10^{-22}$ (eV/c$^2$). Implications of the results are discussed, including speculations regarding the role of dark matter evaporation in galactic evolution.