A universal minimal mass scale for present-day central black holes
  Intermediate-mass black holes (IMBHs) of mass $M_{\bullet} \approx 10^{2} -
10^{5}$ solar masses, $M_{\odot}$, are the long-sought missing link between
stellar black holes, born of supernovae, and massive black holes, tied to
galaxy evolution by the empirical $M_{\bullet}/\sigma_{\star}$ correlation. We
show that low-mass black hole seeds that accrete stars from locally dense
environments in galaxies following a universal $M_{\bullet}/\sigma_{\star}$
relation grow over the age of the Universe to be above
${\mathcal{M}}_{0}\approx3\times10^{5}M_{\odot}$ ($5\%$ lower limit),
independent of the unknown seed masses and formation processes. The mass
${\mathcal{M}}_{0}$ depends weakly on the uncertain formation redshift, and
sets a universal minimal mass scale for present-day black holes. This can
explain why no IMBHs have yet been found, and it implies that present-day
galaxies with
${\sigma_{\star}<{\mathcal{S}}_{0}\approx40\,\mathrm{km\,s}^{-1}}$ lack a
central black hole, or formed it only recently. A dearth of IMBHs at low
redshifts has observable implications for tidal disruptions and gravitational
wave mergers.
