Motivated by Genzel et al.s observations of high-redshift star-forming galaxies, containing clumpy and turbulent rings or disks, we build a set of equations describing the dynamical evolution of gaseous disks with inclusion of star formation and its
feedback. Transport of angular momentum is due to turbulent viscosity induced by supernova explosions in the star formation region. Analytical solutions of the equations are found for the initial cases of a gaseous ring and the integrated form for a gaseous disk, respectively. For a ring with enough low viscosity, it evolves in a slow processes of gaseous diffusion and star formation near the initial radius. For a high viscosity, the ring rapidly diffuses in the early phase. The diffusion drives the ring into a region with a low viscosity and start the second phase undergoing pile-up of gas at a radius following the decreased viscosity torque. The third is a sharply deceasing phase because of star formation consumption of gas and efficient transportation of gas inward forming a stellar disk. We apply the model to two $zsim 2$ galaxies BX 482 and BzK 6004, and find that they are undergoing a decline in their star formation activity.
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.
The rapid TeV $gamma-$ray variability detected in the well-known nearby radio galaxy M87 implies an extremely compact emission region (5-10 Schwarzschild radii) near the horizon of the supermassive black hole in the galactic center. TeV photons are a
ffected by dilution due to interaction with the radiation field of the advection-dominated accretion flow (ADAF) around the black hole, and can thus be used to probe the innermost regions around the black hole. We calculate the optical depth of the ADAF radiation field to the TeV photons and find it strongly depends on the spin of the black hole. We find that transparent radii of 10 TeV photons are of $5R_{rm S}$ and $13R_{rm S}$ for the maximally rotating and non-rotating black holes, respectively. With the observations, the calculated transparent radii strongly suggest the black hole is spinning fast in the galaxy. TeV photons could be used as a powerful diagnostic for estimating black hole spins in galaxies in the future.
