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 \(M_{\bullet}\). 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, \(t_{\rm peak}\), on both stellar mass and age, with \(15\textrm{ days} \lesssim t_{\rm peak} \lesssim 10\) yr for main sequence stars with masses \(0.2\le M_{\star}/M_{\odot} \le 5\) and \(M_{\bullet} = 10^6M_{\odot}\). The second estimate, which postulates that the star is completely destroyed when tides dominate the maximum stellar self-gravity, predicts that \(t_{\rm peak}\) is very weakly dependent on stellar type, with \(t_{\rm peak} = \left(23.2\pm4.0\textrm{ days}\right)\left(M_{\bullet}/10^6M_{\odot}\right)^{1/2}\) for \(0.2\le M_{\star}/M_{\odot} \le 5\), while \(t_{\rm peak} = \left(29.8\pm3.6\textrm{ days}\right)\left(M_{\bullet}/10^6M_{\odot}\right)^{1/2}\) for a Kroupa initial mass function truncated at \(1.5 M_{\odot}\). 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.