Quasi-periodic oscillations and the global modes of relativistic, MHD accretion discs

Abstract

The high-frequency quasi-periodic oscillations (HFQPOs) that punctuate the light curves of X-ray binary systems present a window onto the intrinsic properties of stellar-mass black holes and hence a testbed for general relativity. One explanation for these features is that relativistic distortion of the accretion disc's differential rotation creates a trapping region in which inertial waves (r-modes) might grow to observable amplitudes. Local analyses, however, predict that large-scale magnetic fields push this trapping region to the inner disc edge, where conditions may be unfavorable for r-mode growth. We revisit this problem from a pseudo-Newtonian but fully global perspective, deriving linearized equations describing a relativistic, magnetized accretion flow, and calculating normal modes with and without vertical density stratification. In an unstratified model, the choice of vertical wavenumber determines the extent to which vertical magnetic fields drive the r-modes toward the inner edge. In a global model fully incorporating density stratification, we confirm that this susceptibility to magnetic fields depends on disc thickness. Our calculations suggest that in thin discs, r-modes may remain independent of the inner disc edge for vertical magnetic fields with plasma betas as low as β ≈ 100 − 300. We posit that the appearance of r-modes in observations may be more determined by a competition between excitation and damping mechanisms near the ISCO than the modification of the trapping region by magnetic fields.

HFQPOs and discoseismic mode excitation in eccentric, relativistic discs. I. Hydrodynamic simulations

“…Large-scale, smooth poloidal magnetic fields alter trapped axisymmetric inertial waves if they are sufficiently strong (Fu & Lai 2009). But large-scale poloidal fields modify r-mode trapping merely by applying an additional restoring force, and this need not 'destroy' the oscillation (Dewberry et al 2018). In fact, inhomogeneous radial distributions of vertical magnetic flux may actually strengthen r-mode confinement.…”

Focusing of non-linear eccentric waves in astrophysical discs

“…Eccentric waves in the inner region of XRBs are of interest as a driving mechanism for high frequency quasi-periodic oscillations (QPOs), a type of variability observed in the Xray spectra of some black hole systems, via the excitation of trapped inertial waves (Kato 2008;Ferreira & Ogilvie 2008, 2009Dewberry et al 2018Dewberry et al , 2019). It appears from our work that the short-wavelength limit of eccentric waves is important for the inner regions of XRBs, which is a nonlinear extension of those considered by Ferreira & Ogilvie (2008), Ferreira & Ogilvie (2009) in this context.…”

“…Of particular relevance to this paper, the theory of Ferreira & Ogilvie (2009) predicts its own breakdown -with eccentric waves in the inner regions of black holes attaining very strong eccentricity gradients highlighting the need for a nonlinear theory to describe this regime. Ferreira & Ogilvie (2008) showed that the eccentricity gradients are important in determining the growth rates of inertial waves via a para-metric type instability, which have been proposed as the origin of high frequency quasi-periodic oscillations (QPOs) (Kato 2008;Ferreira & Ogilvie 2008, 2009Dewberry et al 2018Dewberry et al , 2019.…”

Focusing of nonlinear eccentric waves in astrophysical discs. II. Excitation and damping of tightly-wound waves

“…Although we omit it here, a more careful treatment of the disc vertical structure in a self-gravitating disc shows that the disc self-gravity will excite inertial waves when the disc density varies with height in the disc. The inertial waves excited through self-gravity will combine with those expected to be present due to wave-coupling (Kato 2008;Ferreira & Ogilvie 2008;Dewberry et al 2018Dewberry et al , 2019, likely leading to turbulence in the disc. Substituting the virial relation (Equation A13) into Equation A10 and orbit averaging we obtain the secular Lagrangian for a tightly-wound wave in a fluid disc with self gravity,…”