Variability of accretion disks surrounding black holes: The role of inertial-acoustic mode instabilities

The global nonlinear time-dependent evolution of the inertial-acoustic mode instability in accretion disks surrounding black holes has been investigated. The viscous stress is assumed to be proportional to the gas pressure only, i.e., τ = -αp_g. It is found that an oscillatory nonsteady behavior exists in the inner regions of disks (r < 10r_g, where r_g is the Schwarzschild radius) for sufficiently large α (≳0.2) and for mass accretion rates less than about 0.3 times the Eddington value. The variations of the integrated bolometric luminosity from the disk, ΔL/L, are less than 3%. A power spectrum analysis of these variations reveals a power spectrum which can be fitted to a power-law function of the frequency P ∝ f^-γ, with index γ = 1.4-2.3 and a low-frequency feature at about 4 Hz in one case. In addition, a narrow peak centered at a frequency correuting to the power at high frequencies in the inner region of the accretion disk may make the detection of the high-frequency component difficult.