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

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•, specific orbital energy E and angular momentum J, star mass Msstarf and radius Rsstarf, and the pericenter of the star orbit rp(E, J, M•). We solved the steady state Fokker–Planck equation using the standard loss cone theory for the galactic density profile ρ (r) ∝ r−γ and stellar mass function ξ(m) where m = Msstarf/M⊙ and obtained the feeding rate of stars to the BH integrated over the phase space as Nt∝m•β, where β=- 0.3± 0.01 for M• > 107M⊙ and ~6.8 × 10−5 Yr−1 for γ = 0.7. We use this to model the in-fall rate of the disrupted debris, M (E,J, m, 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 M (E,J,t) Using this, standard cosmological parameters, and mission instrument details, we predict the detectable TDE rates for various forthcoming surveys as a function of γ.