The Local Stability of Accretion Disks with Advection

Abstract

The local stability of accretion disks with advection is studied together with the considerations of radial viscous force and thermal diffusion. For a geometrically thin, radiative cooling dominated disk, the thermal diffusion has nearly no effects on the thermal and viscous modes. The including of thermal diffusion, however, tends to stabilize the acoustic modes which, if without advection, are unstable if the disk is optically thick, radiation pressure dominated or optically thin, and are stable if the disk is optically thick, gas pressure dominated. The including of very little advection has significant effects on two acoustic modes. Independent on the optical depth, the instability of the outward propagating mode (O-mode) is enhanced and that of the inward propagating mode (I-mode) is damped if the disk is gas pressure dominated, while the instability of O-mode is damped and that of I-mode is enhanced if the disk is radiation pressure dominated. For a geometrically slim, advection-dominated disk, both the thermal and viscous modes, as well as I-mode, are always stable if the disk is optically thin. The including of thermal diffusion tends to make these modes more stable. However, the O-mode can become unstable when $q/m$ is very large ($q$ is the ratio of advective to viscous dissipated energy and $m$ the Mach number), even if the thermal diffusion is considered. On the other hand, if the advection-dominated disk is optically thick, we found there is no self-consistent acoustic modes in our local analyses. The thermal diffusion has no effect on the stable viscous mode but has a significant contribution to enhance the thermal instability.