  The tidal disruption of a star by a massive black hole is expected to yield a
luminous flare of thermal emission. About two dozen of these stellar tidal
disruption flares (TDFs) may have been detected in optical transient surveys.
However, explaining the observed properties of these events within the tidal
disruption paradigm is not yet possible. This theoretical ambiguity has led
some authors to suggest that optical TDFs are due to a different process, such
as a nuclear supernova or accretion disk instabilities. Here we present a test
of a fundamental prediction of the tidal disruption event scenario: a
suppression of the flare rate due to the direct capture of stars by the black
hole. Using a recently compiled sample of candidate TDFs with black hole mass
measurements, plus a careful treatment of selection effects in this
flux-limited sample, we confirm that the dearth of observed TDFs from high-mass
black holes is statistically significant. All the TDF impostor models we
consider fail to explain the observed mass function; the only scenario that
fits the data is a suppression of the rate due to direct captures. We find that
this suppression can explain the low volumetric rate of the luminous TDF
candidate ASASSN-15lh, thus supporting the hypothesis that this flare belongs
to the TDF family. Our work is the first to present the optical TDF luminosity
function. A steep power law is required to explain the observed rest-frame
g-band luminosity, $dN/dL_{g} \propto L_{g}^{-2.5}$. The mean event rate of the
flares in our sample is about $1 \times10^{-4}$ per galaxy per year, consistent
with the theoretically expected tidal disruption rate.
