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 10^5.1 M ⊙ to 10^8.2 M ⊙. 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 ϕ(L_g)∝L_g/L_bk^0.3+L_g/L_bk^2.6−1 , with L _bk = 10^43.1 erg s⁻¹. In the BH mass regime of 10^5.3 ≲ (M _BH/M ⊙) ≲ 10^7.3, the TDE mass function follows ϕ(M_BH)∝M_BH^−0.25, which favors a flat local BH mass function ( dn_BH/dlogM_BH≈constant ). We confirm the significant rate suppression at the high-mass end (M_BH ≳ 10^7.5 M ⊙), 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 ∼ 10¹⁰ M ⊙, the average optical TDE rate is ≈3.2 × 10⁻⁵ galaxy⁻¹ yr⁻¹. We constrain the optical TDE rate to be [3.7, 7.4, and 1.6] × 10⁻⁵ galaxy⁻¹ yr⁻¹ in galaxies with red, green, and blue colors.