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The ground-breaking detections of gravitational waves from black hole mergersby LIGO have rekindled interest in primordial black holes (PBHs) and thepossibility of dark matter being composed of PBHs. It has been suggested thatPBHs of tens of solar masses could serve as dark matter candidates. Recentanalytical studies demonstrated that compact ultra-faint dwarf galaxies canserve 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, theirpresent-day distribution can provide strong constraints on PBH mass. In thisstudy, we further explore this scenario with more detailed calculations, usinga combination of dynamical simulations and Bayesian inference methods. Thejoint evolution of stars and PBH dark matter is followed with a Fokker-Planckcode PhaseFlow. We run a large suite of such simulations for different darkmatter parameters, then use a Markov Chain Monte Carlo approach to constrainthe PBH properties with observations of ultra-faint galaxies. We find thattwo-body relaxation between the stars and PBH drives up the stellar core size,and increases the central stellar velocity dispersion. Using the observedhalf-light radius and velocity dispersion of stars in the compact ultra-faintdwarf galaxies as joint constraints, we infer that these dwarfs may have acored dark matter halo with the central density in the range of 1-2$\rm{M_{\odot}/pc^3}$, and that the PBHs may have a mass range of 2-14$\rm{M_{\odot}}$ if they constitute all or a substantial fraction of the darkmatter.

Primordial Black Holes as Dark Matter: Constraints From Compact Ultra-Faint Dwarfs