Corotation resonance and overstable oscillations in black-hole accretion discs: general-relativistic calculations

Abstract

We study the dynamics of spiral waves and oscillation modes in relativistic rotating discs around black holes. Generalizing the Newtonian theory, we show that wave absorption can take place at the corotation resonance, where the pattern frequency of the wave matches the background disc rotation rate. We derive the general relativistic expression for the disc vortensity (vorticity divided by surface density), which governs the behaviour of density perturbation near corotation. Depending on the gradient of the generalized disc vortensity, corotational wave absorption can lead to the amplification or damping of the spiral wave. We apply our general theory of relativistic wave dynamics to calculate the non-axisymmetric inertial-acoustic modes (also called p-modes) trapped in the inner-most region of a black hole accretion disc. Because general relativity changes the profiles of the radial epicyclic frequency and disc vortensity near the inner disc edge close to the black hole, these p-modes can become overstable under appropriate conditions. We present the numerical results of the frequencies and growth rates of p-modes for various black hole spin and model disc parameters (the surface density profile and sound speed), and discuss their implications for understanding the enigmatic high-frequency quasi-periodic oscillations observed in black hole X-ray binaries.

12 pages, 11 figures; accepted for the publication in MNRAS

References in corpus (19)

• X-ray Properties of Black-Hole Binaries
• Modelling the behaviour of accretion flows in X-ray binaries
• High-Frequency Quasi-Periodic Oscillations in black-hole binaries
• Advection of Magnetic Fields in Accretion Disks: Not So Difficult After All
• Accretion-Ejection Instability, MHD Rossby Wave Instability, diskoseismology, and the high-frequency QPO of microquasars
• Rossby Wave Instability in three dimensional discs
• Corotational Instability of Inertial-Acoustic Modes in Black Hole Accretion Discs and Quasi-Periodic Oscillations
• On an excitation mechanism for trapped inertial waves in discs around black holes
• Diskoseismology and QPOs Confront Black Hole Spin
• Super-Reflection in Fluid Discs: Corotation Amplifier, Corotation Resonance, Rossby Waves, and Overstable Modes
• Quasi-Periodic Oscillations from Magnetorotational Turbulence
• Weak nonlinear coupling between epicyclic modes in slender tori
• Corotational Instability, Magnetic Resonances and Global Inertial-Acoustic Oscillations in Magnetized Black-Hole Accretion Discs
• Normal Modes of Black Hole Accretion Disks
• Rossby Wave Instability in Accretion Discs with Large-Scale Poloidal Magnetic Fields
• A Resonantly-Excited Disk-Oscillation Model of High-Frequency QPOs of Microquasars
• Corotation Resonance and Diskoseismology Modes of Black Hole Accretion Disks
• Simulations of Overstable Inertial-acoustic Modes in Black-Hole Accretion Discs
• Papaloizou-Pringle Instability of Magnetized Accretion Tori

Cited by in corpus (5)

• Possible ~ 1 hour quasi-periodic oscillation in narrow-line Seyfert 1 galaxy MCG--06--30--15
• Viscous Driving of Global Oscillations in Accretion Discs Around Black Holes
• Super-spinning compact objects and models of high-frequency quasi-periodic oscillations observed in Galactic microquasars. II. Forced resonances
• Inertial-Acoustic Oscillations of Black-Hole Accretion Discs with Large-Scale Poloidal Magnetic Fields
• Orbital Motion in Spacetimes Influenced by the Presence of Scalar and Electromagnetic Fields