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 3 yr (from 2018 October to 2021 September). We infer the black hole (BH) mass (M BH) with host galaxy scaling relations, showing that the sample M BH ranges from 105.1 M & ODOT; to 108.2 M & ODOT;. We developed a survey efficiency corrected maximum volume method to infer the rates. The rest-frame g-band luminosity function can be well described by a broken power law of & phi;(Lg)& PROP;Lg/Lbk0.3+Lg/Lbk2.6-1 , with L bk = 1043.1 erg s-1. In the BH mass regime of 105.3 & LSIM; (M BH/M & ODOT;) & LSIM; 107.3, the TDE mass function follows & phi;(MBH)& PROP;MBH-0.25 , which favors a flat local BH mass function ( dnBH/dlogMBH & AP;constant ). We confirm the significant rate suppression at the high-mass end (M BH & GSIM; 107.5 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 gal & SIM; 1010 M & ODOT;, the average optical TDE rate is & AP;3.2 x 10-5 galaxy-1 yr-1. We constrain the optical TDE rate to be [3.7, 7.4, and 1.6] x 10-5 galaxy-1 yr-1 in galaxies with red, green, and blue colors.