The Peak of the Fallback Rate from Tidal Disruption Events: Dependence on Stellar Type

A star completely destroyed in a tidal disruption event (TDE) ignites a luminous flare that is powered by the fallback of tidally stripped debris to a supermassive black hole (SMBH) of mass M _•. We analyze two estimates for the peak fallback rate in a TDE, one being the “frozen-in” model, which predicts a strong dependence of the time to peak fallback rate, t _peak, on both stellar mass and age, with 15 days ≲ t _peak ≲ 10 yr for main sequence stars with masses 0.2 ≤ M _⋆/M _⊙ ≤ 5 and M _• = 10⁶ M _⊙. The second estimate, which postulates that the star is completely destroyed when tides dominate the maximum stellar self-gravity, predicts that t _peak is very weakly dependent on stellar type, with t peak = 23.2 ± 4.0 days M • / 10 6 M ⊙ 1 / 2 for 0.2 ≤ M _⋆/M _⊙ ≤ 5, while t peak = 29.8 ± 3.6 days M • / 10 6 M ⊙ 1 / 2 for a Kroupa initial mass function truncated at 1.5M _⊙. This second estimate also agrees closely with hydrodynamical simulations, while the frozen-in model is discrepant by orders of magnitude. We conclude that (1) the time to peak luminosity in complete TDEs is almost exclusively determined by SMBH mass, and (2) massive-star TDEs power the largest accretion luminosities. Consequently, (a) decades-long extra-galactic outbursts cannot be powered by complete TDEs, including massive-star disruptions, and (b) the most highly super-Eddington TDEs are powered by the complete disruption of massive stars, which—if responsible for producing jetted TDEs—would explain the rarity of jetted TDEs and their preference for young and star-forming host galaxies.