Stellar and gas dynamical model for tidal disruption events in a quiescent galaxy

TL;DR

This paper develops a comprehensive dynamical model for tidal disruption events in quiescent galaxies, predicting star feeding rates, disk formation conditions, and observable signatures across different surveys.

Contribution

It introduces a detailed stellar and gas dynamical framework for TDEs, including star feeding rates, disk formation criteria, and light curve predictions, advancing understanding of TDE mechanisms.

Findings

Feeding rate scales as M_bh^-0.3 for M_bh > 10^7 M_sun

Disk formation is almost always achieved under typical parameters

Predicted TDE detection rates vary with galaxy density profile slope γ

Abstract

A detailed model of the tidal disruption events (TDEs) has been constructed using stellar dynamical and gas dynamical inputs that include black hole (BH) mass $M_{\bullet}$, specific orbital energy $E$ and angular momentum $J$, star mass $M_{\star}$ and radius $R_{\star}$, and the pericenter of the star orbit $r_{p}(E,\hspace{1mm}J,\hspace{1mm}M_{\bullet})$. We solved the steady state Fokker--Planck equation using the standard loss cone theory for the galactic density profile $\rho (r) \propto r^{-\gamma}$ and stellar mass function $\xi(m) $ where $m=M_{\star}/M_{\odot}$ and obtained the feeding rate of stars to the BH integrated over the phase space as $\dot{N}_{t} \propto M_{\bullet}^\beta$, where $\beta= -0.3\pm 0.01$ for $M_{\bullet}>10^7 M_{\odot}$ and $\sim 6.8 \hspace{1mm} \times 10^{-5}$ Yr$^{-1}$ for $\gamma=0.7$. We use this to model the in-fall rate of the disrupted debris, $\dot{M}(E,\hspace{1mm}J,\hspace{1mm}m,\hspace{1mm}t)$, and discuss the conditions for the disk formation, finding that the accretion disk is almost always formed for the fiduciary range of the physical parameters. We also find the conditions under which the disk formed from the tidal debris of a given star with a super Eddington accretion phase. We have simulated the light curve profiles in the relevant optical g band and soft X-rays for both super and sub-Eddington accretion disks as a function of $\dot{M}(E,\hspace{1mm}J,\hspace{1mm}t)$. Using this, standard cosmological parameters, and mission instrument details, we predict the detectable TDE rates for various forthcoming surveys finally as a function of $\gamma$.