Stellar and gas dynamical model for tidal disruption events in a
  quiescent galaxy
  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 $\gamma$.
