Standing Shock Instability in Advection-Dominated Accretion Flows
  Depending on the values of the energy and angular momentum per unit mass in
the gas supplied at large radii, inviscid advection-dominated accretion flows
can display velocity profiles with either preshock deceleration or preshock
acceleration. Nakayama has shown that these two types of flow configurations
are expected to have different stability properties. By employing the Chevalier
\& Imamura linearization method and the Nakayama instability boundary
conditions, we discover that there are regions of parameter space where
disks/shocks with outflows can be stable or unstable. In regions of
instability, we find that preshock deceleration is always unstable to the
zeroth mode with zero frequency of oscillation, but is always stable to the
fundamental mode and overtones. Furthermore, we also find that preshock
acceleration is always unstable to the zeroth mode and that the fundamental
mode and overtones become increasingly less stable as the shock location moves
away from the horizon when the disk half-height expands above $\sim 12$
gravitational radii at the shock radius. In regions of stability, we
demonstrate the zeroth mode to be stable for the velocity profiles that exhibit
preshock acceleration and deceleration. Moreover, for models that are linearly
unstable, our model suggests the possible existence of quasi-periodic
oscillations (QPOs) with ratios 2:3 and 3:5. These ratios are believed to occur
in stellar and supermassive black hole candidates, for example, in GRS 1915+105
and Sgr A*, respectively. We expect that similar QPO ratios also exist in
regions of stable shocks.
