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.