A dependence of the tidal disruption event rate on global stellar
  surface mass density and stellar velocity dispersion
  The rate of tidal disruption events (TDEs), $R_\text{TDE}$, is predicted to
depend on stellar conditions near the super-massive black hole (SMBH), which
are on difficult-to-measure sub-parsec scales. We test whether $R_\text{TDE}$
depends on kpc-scale global galaxy properties, which are observable. We
concentrate on stellar surface mass density, $\Sigma_{M_\star}$, and velocity
dispersion, $\sigma_v$, which correlate with the stellar density and velocity
dispersion of the stars around the SMBH. We consider 35 TDE candidates, with
and without known X-ray emission. The hosts range from star-forming to
quiescent to quiescent with strong Balmer absorption lines. The last (often
with post-starburst spectra) are overrepresented in our sample by a factor of
$35^{+21}_{-17}$ or $18^{+8}_{-7}$, depending on the strength of the H$\delta$
absorption line. For a subsample of hosts with homogeneous measurements,
$\Sigma_{M_\star}=10^9$-$10^{10}~{\rm M_\odot / kpc^2}$, higher on average than
for a volume-weighted control sample of Sloan Digital Sky Survey galaxies with
similar redshifts and stellar masses. This is because: (1) most of the TDE
hosts here are quiescent galaxies, which tend to have higher $\Sigma_{M_\star}$
than the star-forming galaxies that dominate the control, and (2) the
star-forming hosts have higher average $\Sigma_{M_\star}$ than the star-forming
control. There is also a weak suggestion that TDE hosts have lower $\sigma_v$
than for the quiescent control. Assuming that $R_{\rm TDE}\propto
\Sigma_{M_\star}^\alpha \times \sigma_v^\beta$, and applying a statistical
model to the TDE hosts and control sample, we estimate $\hat{\alpha}=0.9 \pm
0.2$ and $\hat{\beta}=-1.0 \pm 0.6$. This is broadly consistent with
$R_\text{TDE}$ being tied to the dynamical relaxation of stars surrounding the
SMBH.
