Corotational instability, magnetic resonances and global inertial-acoustic oscillations in magnetized black hole accretion discs

Low-order, non-axisymmetric p-modes (also referred as inertial-acoustic modes) in hydrodynamic accretion discs around black holes are plausible candidates for high-frequency quasi-periodic oscillations (QPOs) observed in a number of accreting black hole systems. These modes are trapped in the innermost region of the accretion disc, and are subject to global instabilities due to wave absorption at the corotation resonance (where the wave pattern frequency omega/m equals the disc rotation rate ), when the fluid vortensity, zeta = kappa 2/(2 Sigma) (where kappa and Sigma are the radial epicyclic frequency and disc surface density, respectively), has a positive gradient. We investigate the effects of disc magnetic fields on the wave absorption at corotation and the related wave super-reflection of the corotation barrier, and on the overstability of disc p-modes. In general, in the presence of magnetic fields, the p-modes have the character of inertial-fast magnetosonic waves in their propagation zone. For discs with a pure toroidal field, the corotation resonance is split into two magnetic resonances, where the wave frequency in the corotating frame of the fluid, , matches the slow magnetosonic wave frequency. Significant wave energy/angular momentum absorption occurs at both magnetic resonances, but with opposite signs, such that one of them enhances the super-reflection while the other diminishes it. The combined effect of the two magnetic resonances is to reduce the super-reflection and the growth rate of the overstable p-modes. Our calculations show that even a subthermal toroidal field (with the magnetic pressure less than the gas pressure) may suppress the overstability of hydrodynamic (B = 0) p-modes. For accretion discs with mixed (toroidal and vertical) magnetic fields, two additional Alfven resonances appear, where matches the local Alfven wave frequency. The effect of these additional resonances is to further reduce or diminish the growth rate of p-modes. Our results suggest that in order for the non-axisymmetric p-modes to be a viable candidate for the observed high-frequency QPOs, the disc magnetic field must be appreciably subthermal, or other mode excitation mechanisms are at work.