The Maximum Gravity Model for Partial Tidal Disruption Events: Mass Loss, Peak Fallback Rate, and Dependence on Stellar Properties

Abstract 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, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">peak</mml:mi> </mml:mrow> </mml:msub> </mml:math> , the time at which the peak occurs, t peak , and the amount of mass removed from the star, Δ M , 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 10 6 M ⊙ 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">peak</mml:mi> </mml:mrow> </mml:msub> </mml:math> is weaker due to the influence of self-gravity on the debris stream dynamics, which remains dynamically important for partial TDEs; the agreement for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̇</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">peak</mml:mi> </mml:mrow> </mml:msub> </mml:math> is, however, to within a factor of ∼2–3 in the majority of cases considered, with larger differences for low-mass stars ( M ⋆ ≲ 0.5 M ⊙ ) on grazing orbits with small mass loss. We show that partial TDE light curves for disruptions caused by ∼10 6 M ⊙ 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.