  The ground-breaking detections of gravitational waves from black hole mergers
by LIGO have rekindled interest in primordial black holes (PBHs) and the
possibility of dark matter being composed of PBHs. It has been suggested that
PBHs of tens of solar masses could serve as dark matter candidates. Recent
analytical studies demonstrated that compact ultra-faint dwarf galaxies can
serve as a sensitive test for the PBH dark matter hypothesis, since stars in
such a halo-dominated system would be heated by the more massive PBHs, their
present-day distribution can provide strong constraints on PBH mass. In this
study, we further explore this scenario with more detailed calculations, using
a combination of dynamical simulations and Bayesian inference methods. The
joint evolution of stars and PBH dark matter is followed with a Fokker-Planck
code PhaseFlow. We run a large suite of such simulations for different dark
matter parameters, then use a Markov Chain Monte Carlo approach to constrain
the PBH properties with observations of ultra-faint galaxies. We find that
two-body relaxation between the stars and PBH drives up the stellar core size,
and increases the central stellar velocity dispersion. Using the observed
half-light radius and velocity dispersion of stars in the compact ultra-faint
dwarf galaxies as joint constraints, we infer that these dwarfs may have a
cored 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 dark
matter.
