Predicting the Properties of the Fallback Rate from Tidal Disruption Events: Investigating the Maximum Gravity Model

Abstract A star destroyed by the tidal field of a supermassive black hole (SMBH) in a tidal disruption event (TDE) gives rise to a luminous flare. TDEs are being detected at an ever-increasing rate, motivating the need for accurate models of their lightcurves. The “maximum gravity” (MG) model posits that a star is completely destroyed when the tidal field of the SMBH exceeds the maximum self-gravitational field within the star, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">max</mml:mi> </mml:mrow> </mml:msub> </mml:math> , and predicts 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> and the time to peak t peak . Here we perform hydrodynamical simulations of the complete disruption of 24 stars with masses ranging from 0.2 to 5.0 M ⊙ , at different stages of their main sequence evolution, to test the predictions of this model. We find excellent agreement between the MG model predictions and our simulations for stars near the zero-age main sequence, while the predictions are less accurate (but still within ∼35%–50% of the simulation results) for highly evolved stars. We also generalize the MG model to incorporate the Paczyński–Wiita potential to assess the impact of strong-gravity effects, which are especially important for deep encounters that are required to completely destroy evolved and centrally concentrated stars, and find good agreement with recent works that include relativistic gravity. Our results demonstrate that this model provides accurate constraints on the peak timescale of TDE lightcurves and their correlation with black hole mass.