Simulations of Overstable Inertial-acoustic Modes in Black-Hole Accretion Discs

Abstract

We present two-dimensional inviscid hydrodynamic simulations of overstable inertial-acoustic oscillation modes (p-modes) in black-hole accretion discs. These global spiral waves are trapped in the inner-most region of the disc, and are driven overstable by wave absorption at the corotation resonance ($r_c$) when the gradient of the background disc vortensity (vorticity divided by surface density) at $r_c$ is positive and the disc inner boundary is sufficiently reflective. Previous linear calculations have shown that the growth rates of these modes can be as high as 10% of the rotation frequency at the disc inner edge. We confirm these linear growth rates and the primary disc oscillation frequencies in our simulations when the mode amplitude undergoes exponential growth. We show that the mode growth saturates when the radial velocity perturbation becomes comparable to the disc sound speed. During the saturation stage, the primary disc oscillation frequency differs only slightly (by less than a few percent) from the linear mode frequency. Sharp features in the fluid velocity profiles at this stage suggest that the saturation results from nonlinear wave steepening and mode-mode interactions.

8 pages, 5 figures; submitted to MNRAS

References in corpus (13)

• X-ray Properties of Black-Hole Binaries
• PLUTO: a Numerical Code for Computational Astrophysics
• A comparative study of disc-planet interaction
• Global General Relativistic MHD Simulation of a Tilted Black-Hole Accretion Disk
• MHD simulations of the magnetorotational instability in a shearing box with zero net flux. II. The effect of transport coefficients
• High-Frequency Quasi-Periodic Oscillations in black-hole binaries
• Accretion-Ejection Instability, MHD Rossby Wave Instability, diskoseismology, and the high-frequency QPO of microquasars
• Where is the Radiation Edge in Magnetized Black Hole Accretion discs?
• Corotational Instability of Inertial-Acoustic Modes in Black Hole Accretion Discs and Quasi-Periodic Oscillations
• Super-Reflection in Fluid Discs: Corotation Amplifier, Corotation Resonance, Rossby Waves, and Overstable Modes
• Quasi-Periodic Oscillations from Magnetorotational Turbulence
• Corotational Instability, Magnetic Resonances and Global Inertial-Acoustic Oscillations in Magnetized Black-Hole Accretion Discs
• Rossby Wave Instability in Accretion Discs with Large-Scale Poloidal Magnetic Fields

Cited by in corpus (6)

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• Viscous Driving of Global Oscillations in Accretion Discs Around Black Holes
• Corotation resonance and overstable oscillations in black-hole accretion discs: general-relativistic calculations
• Fermionic greybody factors in Schwarzschild acoustic black holes
• Inertial-Acoustic Oscillations of Black-Hole Accretion Discs with Large-Scale Poloidal Magnetic Fields