Physics of tidal disruption events around black holes

Abstract

A nearly self contained and detailed introduction to TDE physics with novel aspects and a summary of observations is provided.

We have constructed a dynamical model of tidal disruption events (TDEs) that includes physical parameters such as black hole (BH) mass M•, specific orbital energy E and angular momentum J, star mass M? and radius R?, and the pericenter of the star orbit rp(E, J, M•). We have calculated the capture rate of stars N ̇ t , in the galactic center

for a stellar density profile ρ ∝ r

−γ with an initial mass function given by Kroupa (2001), by solving the steady state Fokker-Planck equation and integrating over the {E, J} phase space. Following the steady accretion model of Strubbe and Quataert (2009), we calculate the rise time, the peak bolometric luminosity in terms of these physical parameters and a typical light curve of TDEs which is then compared with the detectors sensitivity to obtain the duration of flare detection. For the standard ΛCDM model, black hole mass function of quiescent galaxies, we calculated the detection rate

of TDEs by various surveys such as Large Synoptic Survey Telescope (LSST), Pan- STARRS 3π in optical bands and eROSITA in X-ray band and discuss the follow up of

TDEs through observations in various spectral bands from X-rays to radio wavelengths. The crucial point is that the J plays an important role in the stellar dynamical process through N ̇

t and the accretion process through pericenter rp(E, J) which impacts the detectable TDE rates; this has not been taken into account in previous calculations.

We have also constructed a self similar model of a time dependent accretion disk in both super and sub-Eddington phase with fallback from outer debris and a general viscosity prescription Πrφ ∝ Σ b d r d where Σd is surface density, r is the radius and b and d are constants that depends on the nature of pressure in the disk. The specific choice of radiative and alpha viscosities and its parameters is decided by the expected

disk luminosity and evolution time scale being in the observed range. The outflow wind structure in super-Eddington phase is modeled analytically using vertical momentum

equation. We have also constructed the transition dynamics of disk between the super- Eddington to sub-Eddington phases and modeled the evolutionary track of TDEs. We

have fit our time dependent accretion models to the observations in X-ray, UV and optical bands and found that the time dependent model shows a good fit to the observations compared to steady accretion models.

We study the distribution of black hole mass and star mass in redshift obtained from time-dependent models fit described above to the observations and found that the TDEs are dominated by the disruption of low mass star by low mass super-massive black holes with black hole mass M• ≤ 2.1 × 107 M

. We also use the steady accre- tion model with time varying accretion rate of Mageshwaran & Mangalam (2015) to

obtain the peak luminosity Lp with corresponding time tp in the given spectral bands and assuming luminosity L ∝ t −5/3 , obtained the flare’s detection duration which is then compared with the detectors sensitivity to obtain the redshift limit of detection. Using the stellar dynamical model of theoretical capture rate given in Mageshwaran & Mangalam (2015), the Schechter black hole mass function with a duty cycle δ(z), and the detector survey parameters such as sensitivity fl

, cadence tcad and integra- tion time tint, the expected detection rate was calculated which is then equated with

the observed detected rates of TDEs by the previous and ongoing surveys to derive

the Schechter parameters. We find that the discrepancy between theoretical and ob- servational capture rates can be explained by the fact that the theoretical TDE rate

statitistically galaxy averaged over the black hole mass function is close to the observed values of ∼ 2 × 10−5/yr.