QUASI-PERIODIC INWARD SHOCK FORMATIONS IN THE SYSTEM OF A BLACK HOLE AND AN ACCRETION DISK AND APPLICATION TO QUASI-PERIODIC OSCILLATIONS IN GALACTIC BLACK HOLE CANDIDATES

摘要

We performed 1.5-dimensional general relativistic hydrodynamic simulations with a Kerr metric to construct a model for high-frequency quasi-periodic oscillations (QPOs) in microquasars. The simulations were performed assuming an initial accretion disk without viscosity rotating around a Kerr black hole at sub-Keplerian velocity (sub-Keplerian case), which induces various wave modes everywhere in the disk. We found that quasi-periodic inward shock waves propagate from the accretion disk toward the black hole. The frequency of the shock formation is about the maximum epicyclic frequency in the disk (κ_(max)), which depends on the rotation of the black hole. In order to understand the mechanism of the shock formation, we also performed a simulation assuming an initial linear perturbation injected at one point in the Keplerian disk (linear perturbation case) and found an oscillation with frequency ～κ at the point where the perturbation injection occurred. To explain the simulation result, we derived an analytic solution for the time evolution of the linear perturbation of physical variables near the point of the perturbation injection and found that the time evolution of the oscillation can be described well. From comparison of the result in the sub-Keplerian case with that of the linear perturbation case, we found that the periodicity of the quasi-periodic shock formation in the sub-Keplerian case is due to a filtering effect by the epicyclic frequency distribution in the disk, which acts on the wave propagation toward the black hole. The only necessary condition for quasi-periodic shock formation is having a nonsteady character for the disks, which can be a source of acoustic waves. The frequency of the shock formation (～κ_(max)) is on the order of the frequency of the high-frequency QPOs in microquasars and depends on the rotation of the black hole. Hence, we can estimate the spin parameter (a) of a black hole candidate (BHC) in a microquasar by comparing the frequency of the high-frequency QPO with κ_(max). The spin parameters of the BHCs in microquasars are roughly estimated to be a = 0.345 ± 0.345 for GRS 1915+105 and a = 0.895 ± 0.105 for GRO J1655-40.