viscous pulsational instability of the transonic region of isothermal geometrically thin accretion discs – I. Analytical results

Viscous instability of the transonic region of the conventional geometrically thin α-type accretion discs is examined analytically. For simplicity, isothermal discs and isothermal perturbations are assumed. It is found that when the value of α is larger than a critical value (i.e. $$\alpha\gt v^{\prime}_c/\Omega_c$$ where Ω_c and $$v^{\prime}_c$$ are the angular velocity of rotation and the radial gradient of radial flow, respectively, at the sonic point), the disc is unstable against two types of perturbations. One is local propagating perturbations of inertial acoustic waves. Results suggest the possibility that unstable perturbations develop to overstable global oscillations which are restricted only in the innermost region of the disc. The other is standing growing perturbations localized just at the transonic point. The cause of these instabilities is that the azimuthal component of the Lagrangian velocity variation associated with the perturbations becomes in phase with the variation of the viscous stress force. Because of this phase matching work is done on perturbations, and they are amplified.