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-center dot. 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, tpeak, on both stellar mass and age, with 15 days less than or similar to t(peak) less than or similar to 10 yr for main sequence stars with masses 0.2 <= M star/M-circle dot <= 5 and M-center dot = 10(6)M(circle dot). The second estimate, which postulates that the star is completely destroyed when tides dominate the maximum stellar self-gravity, predicts that tpeak is very weakly dependent on stellar type, with t(peak) = (23.2 +/- 4.0days) (M center dot/10(6)M(circle dot))(1/2) for 0.2 <= M-star/M-circle dot <= 5, while t(peak)=29.8 +/- 3.6days (M-center dot/106M(circle dot))(1/2) for a Kroupa initial mass function truncated at 1.5M(circle dot). 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.