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 sub-parsec scales that are difficult to measure. Here 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, $\sigma_v$. We consider 34 TDE candidates, with and without known X-ray emission. The hosts range in type from star-forming to quiescent to quiescent with strong Balmer absorption lines. The last (often with post-starburst, aka "E+A," spectra) are overrepresented in our sample by a factor of $35^{+22}_{-17}$ or $17^{+8}_{-6}$, depending on the strength of the H$\delta$ absorption line. The $\Sigma_{M_\star}$ of TDE hosts is higher on average than for a volume-weighted control sample of SDSS galaxies with similar redshifts and stellar masses. This difference arises 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 sample, and (2) the star-forming TDE hosts have higher average $\Sigma_{M_\star}$ than the star-forming control galaxies. There is also evidence that the velocity dispersions of quiescent TDE hosts are lower than for the quiescent control galaxies. Assuming that $R_\text{TDE}$ depends on these global properties as $R_{\rm TDE}\propto \Sigma_{M_\star}^\alpha \times \sigma_v^\beta$, and applying a statistical model to the TDE hosts and control sample, we estimate $\hat{\alpha}=0.9\pm0.2$ and $\hat{\beta}=-1.1\pm0.7$. This significant, roughly linear dependence on $\Sigma_{M_\star}$ and inverse linear (though not significant) dependence on $\sigma_v$ is broadly consistent with the TDE rate being tied to the dynamical relaxation of stars surrounding the SMBH.