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

Abstract

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, $t_{\mathrm{peak}}$, on both stellar mass and age, with $15\text{ days}\lesssim t_{\mathrm{peak}}\lesssim 10$ yr for main sequence stars with masses $0.2\le M_{\star }/M_{\odot }\le 5$ and $M_{\bullet }=10^6{M}_{\odot }$. The second estimate, which postulates that the star is completely destroyed when tides dominate the maximum stellar self-gravity, predicts that $t_{\mathrm{peak}}$ is very weakly dependent on stellar type, with $t_{\mathrm{peak}}=\left(23.2\pm 4.0\text{ days}\right){\left(M_{\bullet }/10^6{M}_{\odot }\right)}^{1/2}$ for $0.2\le M_{\star }/M_{\odot }\le 5$, while $t_{\mathrm{peak}}=\left(29.8\pm 3.6\text{ days}\right){\left(M_{\bullet }/10^6{M}_{\odot }\right)}^{1/2}$ for a Kroupa initial mass function truncated at $1.5M_{\odot }$. 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.

10 pages, 4 figures, ApJL accepted