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A star destroyed by a supermassive black hole (SMBH) in a tidal disruptionevent (TDE) enables the study of SMBHs. We propose that the distance withinwhich a star is completely destroyed by a SMBH, defined $r_{\rm t, c}$, isaccurately estimated by equating the SMBH tidal field (including numericalfactors) to the maximum gravitational field in the star. We demonstrate thatthis definition accurately reproduces the critical $\beta_{\rm c} = r_{\rmt}/r_{\rm t, c}$, where $r_{\rm t} =R_{\star}\left(M_{\bullet}/M_{\star}\right)^{1/3}$ is the standard tidal radiuswith $R_{\star}$ and $M_{\star}$ the stellar radius and mass and $M_{\bullet}$the SMBH mass, for multiple stellar progenitors at various ages, and can bereasonably approximated by $\beta_{\rm c} \simeq \left[\rho_{\rmc}/(4\rho_{\star})\right]^{1/3}$, where $\rho_{\rm c}$ ($\rho_{\star}$) is thecentral (average) stellar density. We also calculate the peak fallback rate andtime at which the fallback rate peaks, finding excellent agreement withhydrodynamical simulations, and also suggest that the partial disruption radius-- the distance at which any mass is successfully liberated from the star -- is$\beta_{\rm partial} \simeq 4^{-1/3} \simeq 0.6$. For given stellar and SMBHpopulations, this model yields, e.g., the fraction of partial TDEs, the peakluminosity distribution of TDEs, and the number of directly captured stars.

A simple and accurate prescription for the tidal disruption radius of a star and the peak accretion rate in tidal disruption events