We report on the third phase of our study of the neutrino-cooled hyperaccreting torus around a black hole that powers the jet in Gamma Ray Bursts. We focus on the influence of the black hole spin on the properties of the torus. The structure of a sta
tionary torus around the Kerr black hole is solved numerically. We take into account the detailed treatment of the microphysics in the nuclear equation of state that includes the neutrino trapping effect. We find, that in the case of rapidly rotating black holes, the thermal instability discussed in our previous work is enhanced and develops for much lower accretion rates. We also find the important role of the energy transfer from the rotating black hole to the torus, via the magnetic coupling.
The fast variability of energetic TeV photons from the center of M87 has been detected, offering a new clue to estimate spins of supermassive black holes (SMBHs). We extend the study of Wang et al. (2008) by including all of general relativistic effe
cts. We numerically solve the full set of relativistic hydrodynamical equations of the radiatively inefficient accretion flows (RIAFs) and then obtain the radiation fields around the black hole. The optical depth of the radiation fields to TeV photons due to pair productions are calculated in the Kerr metric. We find that the optical depth strongly depends on: (1) accretion rates as $tautevpropto dot{M}^{2.5-5.0}$; (2) black hole spins; and (3) location of the TeV source. Jointly considering the optical depth and the spectral energy distribution radiated from the RIAFs, the strong degeneration of the spin with the other free parameters in the RIAF model can be largely relaxed. We apply the present model to M87, wherein the RIAFs are expected to be at work, and find that the minimum specific angular momentum of the hole is $asim0.8$. The present methodology is applicable to M87-like sources with future detection of TeV emissions to constrain the spins of SMBHs.
