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, ${\mathrm{\Sigma }}_{M_{\star }}$, 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 $35_{-17}^{+21}$ or $18_{-7}^{+8}$, depending on the strength of the H$\delta$ absorption line. For a subsample of hosts with homogeneous measurements, ${\mathrm{\Sigma }}_{M_{\star }}={10}^9$-${10}^{10}{\mathrm{M}}_{\odot }\mathrm{/}\mathrm{k}\mathrm{p}{\mathrm{c}}^2$, 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 ${\mathrm{\Sigma }}_{M_{\star }}$ than the star-forming galaxies that dominate the control, and (2) the star-forming hosts have higher average ${\mathrm{\Sigma }}_{M_{\star }}$ 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$\hat{\beta}=-1.0 \pm 0.6$\mathrm{.}Thisisbroadlyconsistentwith$R_$\text{TDE}$$ being tied to the dynamical relaxation of stars surrounding the SMBH.