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

TL;DR

This paper investigates how relativistic, magnetized accretion discs around black holes can support inertial waves (r-modes) that may explain high-frequency QPOs, considering effects of magnetic fields and disc stratification.

Contribution

It provides a global, relativistic analysis of accretion disc modes, incorporating magnetic fields and density stratification, to better understand the conditions for r-mode growth.

Findings

In thin discs, magnetic fields with plasma beta around 100-300 do not prevent r-modes.

Vertical magnetic fields influence the trapping region depending on disc thickness.

R-mode observability depends more on excitation and damping than on magnetic modification of the trapping region.

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 $\beta\approx 100-300$. 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.