2026ApJ...998...81B

A star entering the tidal sphere of a supermassive black hole (SMBH) can be partially stripped of mass, resulting in a partial tidal disruption event (TDE). Here, we develop an analytical model for properties of these events, including the peak fallback rate, ${\dot{M}}_{{\rm{peak}}}$, the time at which the peak occurs, t_peak, and the amount of mass removed from the star, ΔM, for any star and any pericenter distance associated with the stellar orbit about the black hole. We compare the model predictions to 1276 hydrodynamical simulations of partial TDEs of main-sequence stars by a 10⁶M_⊙ SMBH. The model yields t_peak predictions that are in good agreement (to within tens of percent) with the numerical simulations for any stellar mass and age. The agreement for ${\dot{M}}_{{\rm{peak}}}$ is weaker due to the influence of self-gravity on the debris stream dynamics, which remains dynamically important for partial TDEs; the agreement for ${\dot{M}}_{{\rm{peak}}}$ is, however, to within a factor of ∼2-3 in the majority of cases considered, with larger differences for low-mass stars (M_⋆ ≲ 0.5M_⊙) on grazing orbits with small mass loss. We show that partial TDE light curves for disruptions caused by ∼10⁶M_⊙ SMBHs can span ∼20-100 days peak timescales, whereas grazing encounters of high-mass stars with high-mass SMBHs can yield longer peak timescales (t ≳ 1000 days), associated with some observed transients. Our model provides a significant step toward an analytical prescription for TDE light curves and luminosity functions.