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

Abstract

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 / d log M 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 ∼ 10 10 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.