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.

Possible ~1 hour quasi-periodic oscillation in narrow-line Seyfert 1 galaxy MCG–06–30–15

“…The wavelet approach to the current observation of MCG-06-30-15 does not provide additional evidence for such a trend, as the QPO frequency around 3670 s appears to be very stable. According to Pan et al (2016), only models invoking pmodes trapped in the innermost part of an accretion disk (e.g., Li et al 2003, Horák &Lai 2013, andreferences therein) or those involving magnetized disks subject to accretion-ejection instabilities (Tagger & Pellat 1999) naturally tie HFQPOs to high accretion rate situations.…”

Super-spinning compact objects and models of high-frequency quasi-periodic oscillations observed in Galactic microquasars

“…Through this approach, using miscellaneous QPO models, a number of authors have attempted to estimate the spin of the central Kerr BH in three Galactic microquasars -GRS 1915+105, XTE J1550−564, and GRO J1655−40 -that display the 3:2 twin peak QPOs and have known masses (e.g. Wagoner et al 2001;Kato 2004;Török 2005b;Wagoner 2012;Horák & Lai 2013;Ortega-Rodríguez et al 2014;Motta et al 2014;Stuchlík & Kološ 2016a,b).…”