Tidal Disruption Event Demographics with the Zwicky Transient Facility: Volumetric Rates, Luminosity Function, and Implications for the Local Black Hole Mass Function

We conduct a systematic tidal disruption event (TDE) demographics analysis using the largest sample of optically selected TDEs. A flux-limited, spectroscopically complete sample of 33 TDEs is constructed using the Zwicky Transient Facility over three years (from October 2018 to September 2021). We infer the black hole (BH) mass ($M_{\mathrm{B}\mathrm{H}}$) with host galaxy scaling relations, showing that the sample $M_{\mathrm{B}\mathrm{H}}$ ranges from ${10}^{5.1}{M}_{\odot }$ to ${10}^{8.2}{M}_{\odot }$. We developed a survey efficiency corrected maximum volume method to infer the rates. The rest-frame $g$-band luminosity function (LF) can be well described by a broken power-law of $\phi (L_g)\propto [(L_g\mathrm{/}{L}_{\mathrm{b}\mathrm{k}}{)}^{0.3}+(L_g\mathrm{/}{L}_{\mathrm{b}\mathrm{k}}{)}^{2.6}{]}^{-1}$, with $L_{\mathrm{b}\mathrm{k}}={10}^{43.1}\mathrm{e}\mathrm{r}\mathrm{g}{\mathrm{s}}^{-1}$. In the BH mass regime of ${10}^{5.3}\lesssim (M_{\mathrm{B}\mathrm{H}}\mathrm{/}{M}_{\odot })\lesssim {10}^{7.3}$, the TDE mass function follows $\phi (M_{\mathrm{B}\mathrm{H}})\propto M_{\mathrm{B}\mathrm{H}}^{-0.25}$, which favors a flat local BH mass function ($d{n}_{\mathrm{B}\mathrm{H}}\mathrm{/}d\mathrm{l}\mathrm{o}\mathrm{g}{M}_{\mathrm{B}\mathrm{H}}\approx \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}$). We confirm the significant rate suppression at the high-mass end ($M_{\mathrm{B}\mathrm{H}}\gtrsim {10}^{7.5}{M}_{\odot }$), which is consistent with theoretical predictions considering direct capture of hydrogen-burning stars by the event horizon. At a host galaxy mass of $M_{\mathrm{g}\mathrm{a}\mathrm{l}}\sim {10}^{10}{M}_{\odot }$, the average optical TDE rate is $\approx 3.2\times {10}^{-5}\mathrm{g}\mathrm{a}\mathrm{l}\mathrm{a}\mathrm{x}{\mathrm{y}}^{-1}\mathrm{y}{\mathrm{r}}^{-1}$. We constrain the optical TDE rate to be [3.7, 7.4, and 1.6$]\times {10}^{-5}\mathrm{g}\mathrm{a}\mathrm{l}\mathrm{a}\mathrm{x}{\mathrm{y}}^{-1}\mathrm{y}{\mathrm{r}}^{-1}$ in galaxies with red, green, and blue colors.