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

TL;DR

This paper introduces an analytical model for partial tidal disruption events, predicting key properties like mass loss and fallback rates, and compares these predictions with extensive hydrodynamical simulations to improve understanding of TDE lightcurves.

Contribution

The paper develops a new analytical model for partial TDEs that accurately predicts peak fallback times and rates, validated against over a thousand simulations, advancing theoretical understanding of these events.

Findings

Model predictions for peak fallback time agree within tens of percent with simulations.

Peak fallback rate predictions are within a factor of 2-3, with larger deviations for low-mass stars.

Partial TDE lightcurves can have peak timescales from 20 to over 1000 days depending on star and SMBH 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, $\dot{M}_{\rm peak}$, the time at which the peak occurs, $t_{\rm peak}$, and the amount of mass removed from the star, $\Delta M$, 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 $10^6 M_\odot$ SMBH. The model yields $t_{\rm peak}$ 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 $\sim 2-3$ in the majority of cases considered, with larger differences for low-mass stars ($M_\star \lesssim 0.5 M_\odot$) on grazing orbits with small mass loss. We show that partial TDE lightcurves for disruptions caused by $\sim 10^6M_\odot$ SMBHs can span $\sim 20-100$ day peak timescales, whereas grazing encounters of high-mass stars with high-mass SMBHs can yield longer peak timescales ($t\gtrsim 1000$ days), associated with some observed transients. Our model provides a significant step toward an analytical prescription for TDE lightcurves and luminosity functions.