Constraining spins of supermassive black holes from TeV variability. II. fully general relativistic calculations

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 effects. 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 \tautev\propto \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 $a\sim0.8$. The present methodology is applicable to M87-like sources with future detection of TeV emissions to constrain the spins of SMBHs.Comment: 12 pages, 11 figures. Minor typos corrected. published version in Ap

Simulation of Free Surface Compressible Flows Via a Two Fluid Model

The purpose of this communication is to discuss the simulation of a free surface compressible flow between two fluids, typically air and water. We use a two fluid model with the same velocity, pressure and temperature for both phases. In such a numerical model, the free surface becomes a thin three dimensional zone. The present method has at least three advantages: (i) the free-surface treatment is completely implicit; (ii) it can naturally handle wave breaking and other topological changes in the flow; (iii) one can easily vary the Equation of States (EOS) of each fluid (in principle, one can even consider tabulated EOS). Moreover, our model is unconditionally hyperbolic for reasonable EOS.Comment: 8 pages, 10 figures; OMAE2008, 27th International Conference on Offshore Mechanics and Arctic Engineering. Other authors papers and animations related to this work can be downloaded from: http://www.cmla.ens-cachan.fr/fileadmin/Membres/dutykh/ The paper was slightly modified according to referees comment