Diskoseismology

Abstract

Abstract. The normal mode oscillations of (geometrically thin) accretion disks around black holes and other compact objects will be analyzed and contrasted with those in stars. For black holes, the most robust modes are gravitationally trapped near the radius at which the radial epicyclic frequency is maximum. Their eigenfrequencies depend mainly on the mass and angular momentum of the black hole. The fundamental g-mode has recently been seen in numerical simulations of black hole accretion disks. For stars such as white dwarfs, the modes are trapped near the inner boundary (magnetospheric or stellar) of the accretion disk. Their eigenfrequencies are approximately multiples of the (Keplerian) angular velocity of the inner edge of the disk. The relevance of these modes to the high frequency quasi-periodic oscillations observed in the power spectra of accreting binaries will be discussed. In contrast to most stellar oscillations, most of these modes are unstable in the presence of viscosity (if the turbulent viscosity induced by the magnetorotational instability acts hydrodynamically). Introduction; comparison with helio-and asteroseismologyWe shall briefly review the application of normal mode analysis, so successfully employed in stars (as this conference illustrates), to the ubiquitous accretion disks that surround a wide variety of objects (black holes, neutron stars, white dwarfs, and protostars). In the first three cases (except for the supermassive black holes observed at the center of galaxies), they are usually maintained by gas tidally drawn through the inner Lagrange point from their companion star in a binary. The relativistic formulation of diskoseismology was initiated by S. Kato and J. Fukue in 1980 [1], and reviews can be found in [2,3,4].Let us briefly compare the adiabatic hydrodynamic perturbations of stars and accretion disks in the Newtonian limit. We shall assume that the gravitational field of the disk (including that of the perturbations) is negligible, which is an excellent approximation for most accretion disks since their mass is much less than that of the central object. To facilitate the comparison, we shall also make the same (Cowling) approximation for the perturbations of the star. We shall consider the usual case of geometrically thin (and optically thick) accretion disks: thickness h(r) ∼ c s /Ω much less than the radial distance r, where c s (then much less than v φ = rΩ) is the sound speed and Ω(r) is the angular velocity of the disk. The pressure gradient is then much greater vertically than radially; and the motion of the unperturbed gas is close to that of free-particle orbits, with v z v r v φ . The unperturbed disk is axially symmetric, with z the distance from its midplane (about which it is reflection symmetric). Throughout, we also make a WKB approximation (usually valid) that the perturbation radial wavelength λ r r. The governing equations of motion of perturbations of a (slowly rotating) star (left) and an

Simulations of overstable inertial-acoustic modes in black hole accretion discs

“…In several recent papers (Lai & Tsang 2009;Tsang & Lai 2009c;Fu & Lai 2011;Horak & Lai 2013), we have presented detailed study of the linear instability of non-axisymmetric inertial-acoustic modes [also called p-modes; see Kato (2001) and Wagoner (2008) for review] trapped in the inner-most region of black-hole (BH) accretion discs. This global instability arises because of wave absorption at the corotation resonance (where the wave pattern rotation frequency matches the background disc rotation rate) and requires that the disc vortensity has a positive gradient at the corotation radius (see Narayan et al 1987, Tsang &Lai 2008 andreferences therein).…”

Inertial-acoustic oscillations of black hole accretion discs with large-scale poloidal magnetic fields

“…In this paper, we study the effect of large-scale magnetic fields on non-axisymmetric (m > 0) p-modes [also called inertial-acoustic modes; see Kato (2001) and Wagoner (2008) for reviews] trapped in the innermost region of the accretion disc around a BH. Lai & Tsang (2009) and Tsang & Lai (2009b) showed that these modes, which consist of nearly horizontal oscillations with no vertical structure, can grow in amplitude due to wave absorption at the corotation resonance (where the wave pattern speed ω/m matches the disc rotation rate Ω).…”

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

“…Another class of theoretical models is based on the relativistic diskoseismology (for reviews, see Kato 2001Kato , 2008Wagoner 2008). Okazaki et al (1987) first noticed that general-relativistic effects allow oscillation modes to be trapped in the inner region of a BH accretion disc.…”

“…But a quantitative description of the corotational instability and overstable pmodes of BH accretion discs requires full GR. Note that although oscillation modes of relativistic discs were studied in several previous works (see Ortega-Rodríguez et al 2008;Wagoner 2008, for reviews), the important role of CR was overlooked in these works.…”