Stability of a slim accretion disk around a black hole

Stability is examined for an optically thick, slim accretion disk around a black hole. We derive the fourth-order dispersion relation in a framework of a linear stability analysis. Also we obtain the approximate second-order relation which is convenient to diagnose the stability. By solving these relations for slim disk models with a low viscous parameter α, we find that not only the viscous and thermal modes but the acoustic modes are stabilized at the inner region of the disk when the accretion rate Ṁ ≥ Ṁcr = 16LEdd/c. On the other hand, when Ṁ < Ṁcr, the outward (inward) going acoustic mode is unstable (stable) in the outer region of the disk, though it becomes stable (unstable) at the inner region. The stabilization and destabilization of the acoustic modes are ascribed to such dynamical processes on perturbations as the pressure gradient and advection. Therefore, even if the disk is geometricaly thin (Ṁ < Ṁcr), the radial derivatives of physical quantities do play a crucial role for stabilizing the acoustic modes, in contrast to the viscous and thermal modes. The stability of the acoustic modes is very sensitive to the value of α. For models with α ∼ 1, both the dynamical and thermal effects are important for the stability of the acoustic modes.