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

TL;DR

This paper introduces a simple, accurate method to estimate the tidal disruption radius and peak accretion rate in tidal disruption events, improving understanding of SMBH-star interactions and TDE characteristics.

Contribution

The authors propose a new definition for the tidal disruption radius based on the maximum gravitational field within the star, validated across various stellar types and ages.

Findings

Accurately reproduces critical disruption parameters across stellar models.

Provides a simple approximation for the partial disruption radius.

Aligns well with hydrodynamical simulation results.

Abstract

A star destroyed by a supermassive black hole (SMBH) in a tidal disruption event (TDE) enables the study of SMBHs. We propose that the distance within which a star is completely destroyed by a SMBH, defined $r_{\rm t, c}$, is accurately estimated by equating the SMBH tidal field (including numerical factors) to the maximum gravitational field in the star. We demonstrate that this definition accurately reproduces the critical $\beta_{\rm c} = r_{\rm t}/r_{\rm t, c}$, where $r_{\rm t} = R_{\star}\left(M_{\bullet}/M_{\star}\right)^{1/3}$ is the standard tidal radius with $R_{\star}$ and $M_{\star}$ the stellar radius and mass and $M_{\bullet}$ the SMBH mass, for multiple stellar progenitors at various ages, and can be reasonably approximated by $\beta_{\rm c} \simeq \left[\rho_{\rm c}/(4\rho_{\star})\right]^{1/3}$, where $\rho_{\rm c}$ ($\rho_{\star}$) is the central (average) stellar density. We also calculate the peak fallback rate and time at which the fallback rate peaks, finding excellent agreement with hydrodynamical 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 SMBH populations, this model yields, e.g., the fraction of partial TDEs, the peak luminosity distribution of TDEs, and the number of directly captured stars.