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 ($M_{\rm BH}$) with host galaxy scaling relations, showing that the sample $M_{\rm BH}$ 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 $\phi (L_g)\propto [(L_g / L_{\rm bk})^{0.3} + (L_g / L_{\rm bk})^{2.6}]^{-1}$, with $L_{\rm bk}=10^{43.1}\,{\rm erg\,s^{-1}}$. In the BH mass regime of $10^{5.3}\lesssim (M_{\rm BH}/M_\odot) \lesssim 10^{7.3}$, the TDE mass function follows $\phi(M_{\rm BH})\propto M_{\rm BH}^{-0.25}$, which favors a flat local BH mass function ($dn_{\rm BH}/d{\rm log}M_{\rm BH}\approx{\rm constant}$). We confirm the significant rate suppression at the high-mass end ($M_{\rm BH}\gtrsim 10^{7.5}\,M_\odot$), which is consistent with theoretical predictions considering direct capture of hydrogen-burning stars by the event horizon. At a host galaxy mass of $M_{\rm gal}\sim 10^{10}\,M_\odot$, the average optical TDE rate is $\approx 3.2\times 10^{-5}\,{\rm galaxy^{-1}\,yr^{-1}}$. We constrain the optical TDE rate to be [3.7, 7.4, and 1.6$]\times 10^{-5}\,{\rm galaxy^{-1}\,yr^{-1}}$ in galaxies with red, green, and blue colors.