Primordial black holes as dark matter: Constraints from compact ultra-faint dwarfs

The ground-breaking detections of gravitational waves from black hole mergers by LIGOhave rekindled interest in primordial black holes (PBHs) and the possibility of dark matterbeing composed of PBHs. It has been suggested that PBHs of tens of solar masses could serveas dark matter candidates. Recent analytical studies demonstrated that compact ultra-faintdwarf galaxies can serve as a sensitive test for the PBH dark matter hypothesis, since stars insuch a halo-dominated system would be heated by the more massive PBHs, their present-daydistribution can provide strong constraints on PBH mass. In this study, we further explore thisscenario with more detailed calculations, using a combination of dynamical simulations andBayesian inference methods. The joint evolution of stars and PBH dark matter is followedwith a Fokker-Planck code PHASEFLOW. We run a large suite of such simulations for differentdark matter parameters, then use a Markov chain Monte Carlo approach to constrain the PBHproperties with observations of ultra-faint galaxies. We find that two-body relaxation betweenthe stars and PBH drives up the stellar core size, and increases the central stellar velocitydispersion. Using the observed half-light radius and velocity dispersion of stars in the compactultra-faint dwarf galaxies as joint constraints, we infer that these dwarfs may have a cored darkmatter halo with the central density in the range of 1-2 M pc^-3, and that the PBHs may havea mass range of 2-14 M if they constitute all or a substantial fraction of the dark matter.