On an excitation mechanism for trapped inertial waves in discs around black holes

Ferreira, Barbara T.; Ogilvie, Gordon I.

doi:10.1111/j.1365-2966.2008.13207.x

Cited by 44 publications

(86 citation statements)

References 42 publications

(65 reference statements)

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“…We have also tested how sensitive the results are to the magnitude of the artificial viscosity. The potential for unphysical numerical dissipation requires particularly careful consideration for the case of perpendicular kicks, since in this case the initial perturbation is an m = 0 warp that gives rise to a wave (Lubow & Pringle 1993; Ferreira & Ogilvie 2008). How such a wave physically dissipates is not obvious.…”

Section: Numerical Resultsmentioning

confidence: 99%

Black hole mergers: the first light

Rossi¹,

Lodato²,

Armitage³

et al. 2010

Monthly Notices of the Royal Astronomical Society

109

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The coalescence of supermassive black hole binaries occurs via the emission of gravitational waves, that can impart a substantial recoil to the merged black hole. We consider the energy dissipation, that results if the recoiling black hole is surrounded by a thin circumbinary disc. Our results differ significantly from those of previous investigations. We show analytically that the dominant source of energy is often potential energy, released as gas in the outer disc attempts to circularize at smaller radii. Thus, dimensional estimates, that include only the kinetic energy gained by the disc gas, underestimate the real energy loss. This underestimate can exceed an order of magnitude, if the recoil is directed close to the disc plane. We use three dimensional Smooth Particle Hydrodynamics (SPH) simulations and two dimensional finite difference simulations to verify our analytic estimates. We also compute the bolometric light curve, which is found to vary strongly depending upon the kick angle. A prompt emission signature due to this mechanism may be observable for low mass (10^6 Solar mass) black holes whose recoil velocities exceed about 1000 km/s. Emission at earlier times can mainly result from the response of the disc to the loss of mass, as the black holes merge. We derive analytically the condition for this to happen.Comment: 16 pages, accepted by MNRAS. Animations of the simulations are available at http://jilawww.colorado.edu/~pja/recoil.htm

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Section: Numerical Resultsmentioning

confidence: 99%

Black hole mergers: the first light

Rossi¹,

Lodato²,

Armitage³

et al. 2010

Monthly Notices of the Royal Astronomical Society

109

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“…Bachev 1999; Cadez et al 2003; Wu, Chen & Yuan 2010), etc. Ferreira & Ogilvie (2008, 2009) proposed that shear velocities induced by the disc twist (see below) provide a mechanism of excitation of high‐frequency quasi‐periodic oscillations observed in many astronomical objects. Light curves, forms of emission lines of precessing twisted tori around a Kerr black hole as well as their shapes as seen from large distances have recently been investigated numerically by Dexter & Fragile (2011).…”

Section: Introductionmentioning

confidence: 99%

A fully relativistic twisted disc around a slowly rotating Kerr black hole: derivation of dynamical equations and the shape of stationary configurations

Zhuravlev

Ivanov

2011

Monthly Notices of the Royal Astronomical Society

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In this paper we derive equations describing the dynamics and stationary configurations of a twisted fully relativistic thin accretion disc around a slowly rotating black hole. We assume that the inclination angle of the disc is small and that the standard relativistic generalization of the α model of accretion discs is valid when the disc is flat. We find that similar to the case of non‐relativistic twisted discs the disc dynamics and stationary shapes can be determined by a pair of equations formulated for two complex variables describing the orientation of the disc rings and velocity perturbations induced by the twist. We analyse analytically and numerically the shapes of stationary twisted configurations of accretion discs having non‐zero inclinations with respect to the black hole equatorial plane at large distances r from the black hole. It is shown that the stationary configurations depend on two parameters – the viscosity parameter α and the parameter , where δ* is the opening angle (δ*∼h/r, where h is the disc half‐thickness and r is large) of a flat disc and a is the black hole rotational parameter. When a > 0 and the shapes depend drastically on the value of α. When α is small the disc inclination angle oscillates with radius with amplitude and radial frequency of the oscillations dramatically increasing towards the last stable orbit, Rms. When α has a moderately small value the oscillations do not take place but the disc does not align with the equatorial plane at small radii. The disc inclination angle either is increasing towards Rms or exhibits a non‐monotonic dependence on the radial coordinate. Finally, when α is sufficiently large the disc aligns with the equatorial plane at small radii. When a < 0 the disc aligns with the equatorial plane for all values of α. The results reported here may have implications for determining the structure and variability of accretion discs close to Rms as well as for modelling of emission spectra coming from different sources, which are supposed to contain black holes.

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“…1 of Fu & Lai 2009): The so‐called p‐modes (also called inertial‐acoustic modes) have zero node in their wavefunctions along the vertical direction, while the g‐modes (also known as inertial modes or inertial‐gravity modes) 1 have at least one vertical nodes 2 . Discoseismic g‐modes have received wide theoretical attentions because they can be trapped by the GR effect without relying on special inner disc boundary conditions (Okazaki et al 1987), and they may be resonantly excited by global disc deformations (warp and eccentricity) through non‐linear effects (Kato 2003b, 2008; Ferreira & Ogilvie 2008). Kato (2003a) and Li, Goodman & Narayan (2003) (see also Zhang & Lai 2006; Latter & Balbus 2009) showed that the non‐axisymmetric g‐mode that contains a corotation resonance (CR; where the wave pattern frequency ω/ m equals the background rotation rate Ω; here ω is the mode frequency and m is the azimuthal mode number) in the wave zone is heavily damped (see Tsang & Lai 2009a for a similar study for the c‐modes).…”

Section: Introductionmentioning

confidence: 99%

Corotational instability, magnetic resonances and global inertial-acoustic oscillations in magnetized black hole accretion discs

Fu¹,

Lai²

2010

Monthly Notices of the Royal Astronomical Society

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Low‐order, non‐axisymmetric p‐modes (also referred as inertial‐acoustic modes) in hydrodynamic accretion discs around black holes are plausible candidates for high‐frequency quasi‐periodic oscillations (QPOs) observed in a number of accreting black hole systems. These modes are trapped in the innermost region of the accretion disc, and are subject to global instabilities due to wave absorption at the corotation resonance (where the wave pattern frequency ω/m equals the disc rotation rate Ω), when the fluid vortensity, ζ=κ2/(2ΩΣ) (where κ and Σ are the radial epicyclic frequency and disc surface density, respectively), has a positive gradient. We investigate the effects of disc magnetic fields on the wave absorption at corotation and the related wave super‐reflection of the corotation barrier, and on the overstability of disc p‐modes. In general, in the presence of magnetic fields, the p‐modes have the character of inertial‐fast magnetosonic waves in their propagation zone. For discs with a pure toroidal field, the corotation resonance is split into two magnetic resonances, where the wave frequency in the corotating frame of the fluid, , matches the slow magnetosonic wave frequency. Significant wave energy/angular momentum absorption occurs at both magnetic resonances, but with opposite signs, such that one of them enhances the super‐reflection while the other diminishes it. The combined effect of the two magnetic resonances is to reduce the super‐reflection and the growth rate of the overstable p‐modes. Our calculations show that even a subthermal toroidal field (with the magnetic pressure less than the gas pressure) may suppress the overstability of hydrodynamic (B= 0) p‐modes. For accretion discs with mixed (toroidal and vertical) magnetic fields, two additional Alfvén resonances appear, where matches the local Alfvén wave frequency. The effect of these additional resonances is to further reduce or diminish the growth rate of p‐modes. Our results suggest that in order for the non‐axisymmetric p‐modes to be a viable candidate for the observed high‐frequency QPOs, the disc magnetic field must be appreciably subthermal, or other mode excitation mechanisms are at work.

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On an excitation mechanism for trapped inertial waves in discs around black holes

Cited by 44 publications

References 42 publications

Black hole mergers: the first light

Black hole mergers: the first light

A fully relativistic twisted disc around a slowly rotating Kerr black hole: derivation of dynamical equations and the shape of stationary configurations

Corotational instability, magnetic resonances and global inertial-acoustic oscillations in magnetized black hole accretion discs

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