arXiv subjects

G. I. Ogilvie

Publications and source records attributed to G. I. Ogilvie.

45 records · Page 3Linked to original sources

arXiv2000

An alpha theory of time-dependent warped accretion discs

The non-linear fluid dynamics of a warped accretion disc was investigated in an earlier paper by developing a theory of fully non-linear bending waves in a thin, viscous disc. That analysis is here extended to take proper account of thermal and radiative effects by solving an energy equation that includes viscous dissipation and radiative transport. The problem is reduced to simple one-dimensional evolutionary equations for mass and angular momentum, expressed in physical units and suitable for direct application. This result constitutes a logical generalization of the alpha theory of Shakura & Sunyaev to the case of a time-dependent warped accretion disc. The local thermal-viscous stability of such a disc is also investigated.

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arXiv2000

On the tilting of protostellar disks by resonant tidal effects

We consider the dynamics of a protostellar disk surrounding a star in a circular-orbit binary system. Our aim is to determine whether, if the disk is initially tilted with respect to the plane of the binary orbit, the inclination of the system will increase or decrease with time. The problem is formulated in the binary frame in which the tidal potential of the companion star is static. We consider a steady, flat disk that is aligned with the binary plane and investigate its linear stability with respect to tilting or warping perturbations. The dynamics is controlled by the competing effects of the m=0 and m=2 azimuthal Fourier components of the tidal potential. In the presence of dissipation, the m=0 component causes alignment of the system, while the m=2 component has the opposite tendency. We find that disks that are sufficiently large, in particular those that extend to their tidal truncation radii, are generally stable and will therefore tend to alignment with the binary plane on a time-scale comparable to that found in previous studies. However, the effect of the m=2 component is enhanced in the vicinity of resonances where the outer radius of the disk is such that the natural frequency of a global bending mode of the disk is equal to twice the binary orbital frequency. Under such circumstances, the disk can be unstable to tilting and acquire a warped shape, even in the absence of dissipation. The outer radius corresponding to the primary resonance is always smaller than the tidal truncation radius. For disks smaller than the primary resonance, the m=2 component may be able to cause a very slow growth of inclination through the effect of a near resonance that occurs close to the disk center. We discuss these results in the light of recent observations of protostellar disks in binary systems.

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arXiv1999

Time-dependent quasi-spherical accretion

Differentially rotating, "advection-dominated" accretion flows are considered in which the heat generated by viscous dissipation is retained in the fluid. The equations of time-dependent quasi-spherical accretion are solved in a simplified one-dimensional model that neglects the latitudinal dependence of the flow. A self-similar solution is presented that has finite size, mass, angular momentum and energy. This may be expected to be an attractor for the initial-value problem in which a cool and narrow ring of fluid orbiting around a central mass heats up, spreads radially and is accreted. The solution provides some insight into the dynamics of quasi-spherical accretion and avoids many of the strictures of the steady self-similar solution of Narayan & Yi. Special attention is given to the astrophysically important case in which the adiabatic exponent gamma=5/3; even in this case, the flow is found to be differentially rotating and bound to the central object, and accretion can occur without the need for powerful outflows.

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arXiv1998

The non-linear fluid dynamics of a warped accretion disc

The dynamics of a viscous accretion disc subject to a slowly varying warp of large amplitude is considered. Attention is restricted to discs in which self-gravitation is negligible, and to the generic case in which the resonant wave propagation found in inviscid Keplerian discs does not occur. The equations of fluid dynamics are derived in a coordinate system that follows the principal warping motion of the disc. They are reduced using asymptotic methods for thin discs, and solved to extract the equation governing the warp. In general, this is a wave equation of parabolic type with non-linear dispersion and diffusion, which describes fully non-linear bending waves. This method generalizes the linear theory of Papaloizou & Pringle (1983) to allow for an arbitrary rotation law, and extends it into the non-linear domain, where it connects with a generalized version of the theory of Pringle (1992). The astrophysical implications of this analysis are discussed briefly.

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arXiv1998

Nonlinear fluid dynamics of warped discs

A new description of the dynamics of warped accretion discs is presented. A theory of fully nonlinear, slowly varying bending waves is developed, involving a proper treatment of viscous fluid dynamics but neglecting self-gravitation. The special case of resonant wave propagation found in inviscid Keplerian discs is not considered. The resulting description goes beyond existing linear and nonlinear theories, and is suitable for numerical implementation.

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arXiv1998

Extracting energy from black holes: the relative importance of the Blandford-Znajek mechanism

We critically assess the role of the Blandford-Znajek mechanism in the powering of outflows from accretion disk-fed black holes. We argue that there is no reason to suppose that the magnetic field threading the central spinning black hole differs significantly in strength from that threading the central regions of the disk. In this case, we show that the electromagnetic output from the inner disk regions is expected in general to dominate over that from the hole. Thus the spin (or not) of the hole is probably irrelevant to the expected electromagnetic power output from the system. We also point out that the strength of the poloidal field in the center of a standard accretion disk has been generally overestimated, and discuss scenarios which might give rise to more significant central poloidal fields.

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arXiv1998

The effect of an isothermal atmosphere on the propagation of three-dimensional waves in a thermally stratified accretion disk

We extend our analysis of the three-dimensional response of a vertically polytropic disk to tidal forcing at Lindblad resonances by including the effects of a disk atmosphere. The atmosphere is modeled as an isothermal layer that joins smoothly on to an underlying polytropic layer. The launched wave progressively enters the atmosphere as it propagates away from the resonance. The wave never propagates vertically, however, and the wave energy rises to a (finite) characteristic height in the atmosphere. The increase of wave amplitude associated with this process of wave channeling is reduced by the effect of the atmosphere. For waves of large azimuthal mode number m generated by giant planets embedded in a disk, the increase in wave amplitude is still substantial enough to be likely to dissipate the wave energy by shocks for even modest optical depths (tau greater than about 10) over a radial distance of a few times the disk thickness. For low-m waves generated in circumstellar disks in binary stars, the effects of wave channeling are less important and the level of wave nonlinearity increases by less than a factor of 10 in going from the disk edge to the disk center. For circumbinary disks, the effects of wave channeling remain important, even for modest values of optical depth.

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arXiv1998

Three-dimensional waves generated at Lindblad resonances in thermally stratified disks

We analyze the linear, 3D response to tidal forcing of a disk that is thin and thermally stratified in the direction normal to the disk plane. We model the vertical disk structure locally as a polytrope which represents a disk of high optical depth. We solve the 3D gas-dynamic equations semi-analytically in the neighborhood of a Lindblad resonance. These solutions match asymptotically on to those valid away from resonances and provide solutions valid at all radii. We obtain the following results. 1) A variety of waves are launched at resonance. However, the f mode carries more than 95% of the torque exerted at the resonance. 2) These 3D waves collectively transport exactly the amount of angular momentum predicted by the 2D torque formula. 3) Near resonance, the f mode occupies the full vertical extent of the disk. Away from resonance, the f mode becomes confined near the surface of the disk, and, in the absence of other dissipation mechanisms, damps via shocks. The radial length scale for this process is roughly r_L/m (for resonant radius r_L and azimuthal wavenumber m), independent of the disk thickness H. This wave channeling process is due to the variations of physical quantities in r and is not due to wave refraction. 4) However, the inwardly propagating f mode launched from an m=2 inner Lindblad resonance experiences relatively minor channeling. We conclude that for binary stars, tidally generated waves in highly optically thick circumbinary disks are subject to strong nonlinear damping by the channeling mechanism, while those in circumstellar accretion disks are subject to weaker nonlinear effects. We also apply our results to waves excited by young planets for which m is approximately r/H and conclude that the waves are damped on the scale of a few H.

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arXiv1998

Waves and instabilities in a differentially rotating disc containing a poloidal magnetic field

The theory of waves and instabilities in a differentially rotating disc containing a poloidal magnetic field is developed within the framework of ideal magnetohydrodynamics. A continuous spectrum, for which the eigenfunctions are localized on individual magnetic surfaces, is identified but is found not to contain any instabilities associated with differential rotation. The normal modes of a weakly magnetized thin disc are studied by extending the asymptotic methods used previously to describe the equilibria. Waves propagate radially in the disc according to a dispersion relation which is determined by solving an eigenvalue problem at each radius. The dispersion relation for a hydrodynamic disc is re-examined and the modes are classified according to their behaviour in the limit of large wavenumber. The addition of a magnetic field introduces new, potentially unstable, modes and also breaks up the dispersion diagram by causing avoided crossings. The stability boundary to the magnetorotational instability in the parameter space of polytropic equilibria is located by solving directly for marginally stable equilibria. For a given vertical magnetic field in the disc, bending of the field lines has a stabilizing effect and it is shown that stable equilibria exist which are capable of launching a predominantly centrifugally driven wind.

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