Stability of the Transition Layer between Advection-Dominated and Cooling-Dominated Regions in Accretion Disks. I. Dynamical Instability of Thin Transition

Abstract

The time variations and Fe fluorescence lines observed in the hard state of stellar black-hole candidates and AGNs might be related to both the instability of and cool gas supply from the transition layer between advection-dominated and cooling-dominated regions. As a first step to examine this possibility, we consider the dynamical instability of the transition layer against non-axisymmetric perturbations under some idealizations. That is, the transition layer is assumed to have an infinitesimal thickness, and perturbations occur inviscidly and adiabatically. No magnetic field is assumed. The results show that the perturbations with m <mcrit (m being the wavenumber in the azimuthal direction) are pure oscillations due to the effects of disk rotation, but those with m > mcrit become overstable due to a density inversion (the Rayleigh-Taylor instability in a rotating system). Here, mcrit ∼ 0.085(r/H)2, r being the radius of the transition region and H the disk half-thickness outside the region. This means that perturbations grow if their size in the azimuthal direction is shorter than ∼ 74(H/r)H, which is ∼ 2H when H/r = 0.03. The limitations of applicability of our results and other possible mechanisms which make the transition layer unstable are discussed in the final section.