arXiv subjects

G. I. Ogilvie

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

At least 37 records · Page 2Linked to original sources

arXiv2006

The effect of planetary migration on the corotation resonance

The migration of a planet through a gaseous disc causes the locations of their resonant interactions to drift and can alter the torques exerted between the planet and the disc. We analyse the time-dependent dynamics of a non-coorbital corotation resonance under these circumstances. The ratio of the resonant torque in a steady state to the value given by Goldreich & Tremaine (1979) depends essentially on two dimensionless quantities: a dimensionless turbulent diffusion time-scale and a dimensionless radial drift speed. When the drift speed is comparable to the libration speed and the viscosity is small, the torque can become much larger than the unsaturated value in the absence of migration, but is still proportional to the large-scale vortensity gradient in the disc. Fluid that is trapped in the resonance and drifts with it acquires a vortensity anomaly relative to its surroundings. If the anomaly is limited by viscous diffusion in a steady state, the resulting torque is inversely proportional to the viscosity, although a long time may be required to achieve this state. A further, viscosity-independent, contribution to the torque comes from fluid that streams through the resonant region. In other cases, torque oscillations occur before the steady value is achieved. We discuss the significance of these results for the evolution of eccentricity in protoplanetary systems. We also describe the possible application of these findings to the coorbital region and the concept of runaway (or type III) migration. [Abridged]

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arXiv2005

Nonlinear bending waves in Keplerian accretion discs

The nonlinear dynamics of a warped accretion disc is investigated in the important case of a thin Keplerian disc with negligible viscosity and self-gravity. A one-dimensional evolutionary equation is formally derived that describes the primary nonlinear and dispersive effects on propagating bending waves other than parametric instabilities. It has the form of a derivative nonlinear Schroedinger equation with coefficients that are obtained explicitly for a particular model of a disc. The properties of this equation are analysed in some detail and illustrative numerical solutions are presented. The nonlinear and dispersive effects both depend on the compressibility of the gas through its adiabatic index Gamma. In the physically realistic case Gamma<3, nonlinearity does not lead to the steepening of bending waves but instead enhances their linear dispersion. In the opposite case Gamma>3, nonlinearity leads to wave steepening and solitary waves are supported. The effects of a small effective viscosity, which may suppress parametric instabilities, are also considered. This analysis may provide a useful point of comparison between theory and numerical simulations of warped accretion discs.

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arXiv2005

Aligning spinning black holes and accretion discs

We consider the alignment torque between a spinning black hole and an accretion disc whose angular momenta are misaligned. This situation must hold initially in almost all gas accretion events on to supermassive black holes, and may occur in binaries where the black hole receives a natal supernova kick. We show that the torque always acts to align the hole's spin with the total angular momentum without changing its magnitude. The torque acts dissipatively on the disc, reducing its angular momentum, and aligning it with the hole if and only if the angle theta between the angular momenta J_d of the disc and J_h of the hole satisfies the inequality cos theta > -J_d / 2 J_h. If this condition fails, which requires both theta > pi/2 and J_d < 2 J_h, the disc counteraligns.

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arXiv2003

Tidal dissipation in rotating giant planets

[Abridged] Tides may play an important role in determining the observed distributions of mass, orbital period, and eccentricity of the extrasolar planets. In addition, tidal interactions between giant planets in the solar system and their moons are thought to be responsible for the orbital migration of the satellites, leading to their capture into resonant configurations. We treat the underlying fluid dynamical problem with the aim of determining the efficiency of tidal dissipation in gaseous giant planets. In cases of interest, the tidal forcing frequencies are comparable to the spin frequency of the planet but small compared to its dynamical frequency. We therefore study the linearized response of a slowly and possibly differentially rotating planet to low-frequency tidal forcing. Convective regions of the planet support inertial waves, while any radiative regions support generalized Hough waves. We present illustrative numerical calculations of the tidal dissipation rate and argue that inertial waves provide a natural avenue for efficient tidal dissipation in most cases of interest. The resulting value of Q depends in a highly erratic way on the forcing frequency, but we provide evidence that the relevant frequency-averaged dissipation rate may be asymptotically independent of the viscosity in the limit of small Ekman number. In short-period extrasolar planets, if the stellar irradiation of the planet leads to the formation of a radiative outer layer that supports generalized Hough modes, the tidal dissipation rate can be enhanced through the excitation and damping of these waves. These dissipative mechanisms offer a promising explanation of the historical evolution and current state of the Galilean satellites as well as the observed circularization of the orbits of short-period extrasolar planets.

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arXiv2003

Three-dimensional Calculations of High and Low-mass Planets Embedded in Protoplanetary Discs

We analyse the non-linear, three-dimensional response of a gaseous, viscous protoplanetary disc to the presence of a planet of mass ranging from one Earth mass (1 M$_e$) to one Jupiter mass (1 M$_J$) by using the ZEUS hydrodynamics code. We determine the gas flow pattern, and the accretion and migration rates of the planet. The planet is assumed to be in a fixed circular orbit about the central star. It is also assumed to be able to accrete gas without expansion on the scale of its Roche radius. Only planets with masses $M \gsim 0.1$ M$_J$ produce significant perturbations in the disc's surface density. The flow within the Roche lobe of the planet is fully three-dimensional. Gas streams generally enter the Roche lobe close to the disc midplane, but produce much weaker shocks than the streams in two-dimensional models. The streams supply material to a circumplanetary disc that rotates in the same sense as the planet's orbit. Much of the mass supply to the circumplanetary disc comes from non-coplanar flow. The accretion rate peaks with a planet mass of approximately 0.1 M$_J$ and is highly efficient, occurring at the local viscous rate. The migration timescales for planets of mass less than 0.1 M$_J$, based on torques from disc material outside the planets' Roche lobes, are in excellent agreement with the linear theory of Type I (non-gap) migration for three-dimensional discs. The transition from Type I to Type II (gap) migration is smooth, with changes in migration times of about a factor of 2. Starting with a core which can undergo runaway growth, a planet can gain up to a few M$_J$ with little migration. Planets with final masses of order 10 M$_J$ would undergo large migration, which makes formation and survival difficult.

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arXiv2003

Saturation of the corotation resonance in a gaseous disk

We determine the torque exerted in a steady state by an external potential on a three-dimensional gaseous disk at a non-coorbital corotation resonance. Our model accounts for the feedback of the torque on the surface density and vorticity in the corotation region, and assumes that the disk has a barotropic equation of state and a nonzero effective viscosity. The ratio of the torque to the value given by the formula of Goldreich & Tremaine depends essentially on a single dimensionless parameter, which quantifies the extent to which the resonance is saturated. We discuss the implications for the eccentricity evolution of young planets.

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arXiv2002

On the dynamics of magnetorotational turbulent stresses

[Abridged] The turbulent stresses that lead to angular momentum transport in accretion discs have often been treated as resulting from an isotropic effective viscosity, related to the pressure through the alpha parametrization of Shakura & Sunyaev. This simple approach may be adequate for the simplest aspects of accretion disc theory, and was necessitated historically by an incomplete understanding of the origin of the turbulence. More recently, Balbus & Hawley have shown that the magnetorotational instability provides a robust mechanism of generating turbulent Reynolds and Maxwell stresses in sufficiently ionized discs. The alpha viscosity model fails to describe numerous aspects of this process. This paper introduces a new analytical model that aims to represent more faithfully the dynamics of magnetorotational turbulent stresses and bridge the gap between analytical studies and numerical simulations. Covariant evolutionary equations for the mean Reynolds and Maxwell tensors are presented, which correctly include the linear interaction with the mean flow. Non-linear and dissipative effects, in the absence of an imposed magnetic flux and in the limit of large Reynolds number and magnetic Reynolds number, are modelled through five non-linear terms that represent known physical processes and are strongly constrained by symmetry properties and dimensional considerations. The resulting model should be particularly useful in understanding the dynamics of warped, eccentric and tidally distorted discs, non-Keplerian accretion flows close to black holes, and a variety of time-dependent accretion phenomena.

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arXiv2002

Viscous Effects on the Interaction between the Coplanar Decretion Disc and the Neutron Star in Be/X-Ray Binaries

We study the viscous effects on the interaction between the coplanar Be-star disc and the neutron star in Be/X-ray binaries, using a three-dimensional, smoothed particle hydrodynamics code. For simplicity, we assume the Be disc to be isothermal at the temperature of half the stellar effective temperature. In order to mimic the gas ejection process from the Be star, we inject particles with the Keplerian rotation velocity at a radius just outside the star. Both Be star and neutron star are treated as point masses. We find that the Be-star disc is effectively truncated if the Shakura-Sunyaev viscosity parameter alpha_SS >> 1, which confirms the previous semi-analytical result. In the truncated disc, the material decreted from the Be star accumulates, so that the disc becomes denser more rapidly than if around an isolated Be star. The resonant truncation of the Be disc results in a significant reduction of the amount of gas captured by the neutron star and a strong dependence of the mass capture rate on the orbital phase. We also find that an eccentric mode is excited in the Be disc through direct driving due to a one-armed bar potential of the binary. The strength of the mode becomes greater in the case of a smaller viscosity. In a high-resolution simulation with alpha_SS=0.1, the eccentric mode is found to precess in a prograde sense. The mass capture rate by the neutron star modulates as the mode precesses.

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arXiv2002

The evolution of a warped disc around a Kerr black hole

We consider the evolution of a warped disc around a Kerr black hole, under conditions such that the warp propagates in a wavelike manner. This occurs when the dimensionless effective viscosity, alpha, that damps the warp is less than the characteristic angular semi-thickness, H/R, of the disc. We adopt linearized equations that are valid for warps of sufficiently small amplitude in a Newtonian disc, but also account for the apsidal and nodal precession that occur in the Kerr metric. Through analytical and time-dependent studies, we confirm the results of Demianski & Ivanov, and of Ivanov & Illarionov, that such a disc takes on a characteristic warped shape. The inner part of the disc is not necessarily aligned with the equator of the hole, even in the presence of dissipation. We draw attention to the fact that this might have important implications for the directionality of jets emanating from discs around rotating black holes.

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arXiv2002

The Excitation, Propagation and Dissipation of Waves in Accretion Discs: The Non-linear Axisymmetric Case

We analyse the non-linear propagation and dissipation of axisymmetric waves in accretion discs using the ZEUS-2D hydrodynamics code. The waves are numerically resolved in the vertical and radial directions. Both vertically isothermal and thermally stratified accretion discs are considered. The waves are generated by means of resonant forcing and several forms of forcing are considered. Compressional motions are taken to be locally adiabatic ($γ= 5/3$). Prior to non-linear dissipation, the numerical results are in excellent agreement with the linear theory of wave channelling in predicting the types of modes that are excited, the energy flux by carried by each mode, and the vertical wave energy distribution as a function of radius. In all cases, waves are excited that propagate on both sides of the resonance (inwards and outwards). For vertically isothermal discs, non-linear dissipation occurs primarily through shocks that result from the classical steepening of acoustic waves. For discs that are substantially thermally stratified, wave channelling is the primary mechanism for shock generation. Wave channelling boosts the Mach number of the wave by vertically confining the wave to a small cool region at the base of the disc atmosphere. In general, outwardly propagating waves with Mach numbers near resonance ${\cal M}_{\rm r} \ga 0.01$ undergo shocks within a distance of order the resonance radius.

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arXiv2001

A non-linear theory of vertical resonances in accretion discs

An important and widely neglected aspect of the interaction between an accretion disc and a massive companion with a coplanar orbit is the vertical component of the tidal force. As shown by Lubow, the response of the disc to vertical forcing is resonant at certain radii, at which a localized torque is exerted, and from which a compressive wave (p mode) may be emitted. Although these vertical resonances are weaker than the corresponding Lindblad resonances, the m=2 inner vertical resonance in a binary star is typically located within the tidal truncation radius of a circumstellar disc. In this paper I develop a general theory of vertical resonances, allowing for non-linearity of the response, and dissipation by radiative damping and turbulent viscosity. The problem is reduced to a universal, non-linear ordinary differential equation with two real parameters. Solutions of the complex non-linear Airy equation are presented to illustrate the non-linear saturation of the resonance and the effects of dissipation. It is argued that the m=2 inner vertical resonance is unlikely to truncate the disc in cataclysmic variable stars, but contributes to angular momentum transport and produces a potentially observable non-axisymmetric structure.

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arXiv2001

Tidally distorted accretion discs in binary stars

The non-axisymmetric features observed in the discs of dwarf novae in outburst are usually considered to be spiral shocks, which are the non-linear relatives of tidally excited waves. This interpretation suffers from a number of problems. For example, the natural site of wave excitation lies outside the Roche lobe, the disc must be especially hot, and most treatments of wave propagation do not take into account the vertical structure of the disc. In this paper I construct a detailed semi-analytical model of the non-linear tidal distortion of a thin, three-dimensional accretion disc by a binary companion on a circular orbit. The analysis presented here allows for vertical motion and radiative energy transport, and introduces a simple model for the turbulent magnetic stress. The m=2 inner vertical resonance has an important influence on the amplitude and phase of the tidal distortion. I show that the observed patterns find a natural explanation if the emission is associated with the tidally thickened sectors of the outer disc, which may be irradiated from the centre. According to this hypothesis, it may be possible to constrain the physical parameters of the disc through future observations.

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arXiv2001

On the wake generated by a planet in a disc

A planet of low mass orbiting in a two-dimensional gaseous disc generates a one-armed spiral wake. We explain this phenomenon as the result of constructive interference between wave modes in the disc, somewhat similar to the Kelvin wedge produced in the wake of a ship. The same feature is not expected in a three-dimensional disc with thermal stratification.

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arXiv2001

Secular interactions between inclined planets and a gaseous disk

In a planetary system, a secular particle resonance occurs at a location where the precession rate of a test particle (e.g. an asteroid) matches the frequency of one of the precessional modes of the planetary system. We investigate the secular interactions of a system of mutually inclined planets with a gaseous protostellar disk that may contain a secular nodal particle resonance. We determine the normal modes of some mutually inclined planet-disk systems. The planets and disk interact gravitationally, and the disk is internally subject to the effects of gas pressure, self-gravity, and turbulent viscosity. The behavior of the disk at a secular resonance is radically different from that of a particle, owing mainly to the effects of gas pressure. The resonance is typically broadened by gas pressure to the extent that global effects, including large-scale warps, dominate. The standard resonant torque formula is invalid in this regime. Secular interactions cause a decay of the inclination at a rate that depends on the disk properties, including its mass, turbulent viscosity, and sound speed. For a Jupiter-mass planet embedded within a minimum-mass solar nebula having typical parameters, dissipation within the disk is sufficient to stabilize the system against tilt growth caused by mean-motion resonances.

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arXiv2001

Magnetohydrodynamic turbulence in warped accretion discs

Warped, precessing accretion discs appear in a range of astrophysical systems, for instance the X-ray binary Her X-1 and in the active nucleus of NGC4258. In a warped accretion disc there are horizontal pressure gradients that drive an epicyclic motion. We have studied the interaction of this epicyclic motion with the magnetohydrodynamic turbulence in numerical simulations. We find that the turbulent stress acting on the epicyclic motion is comparable in size to the stress that drives the accretion, however an important ingredient in the damping of the epicyclic motion is its parametric decay into inertial waves.

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arXiv2001

Non-linear fluid dynamics of eccentric discs

A new theory of eccentric accretion discs is presented. Starting from the basic fluid-dynamical equations in three dimensions, I derive the fundamental set of one-dimensional equations that describe how the mass, angular momentum and eccentricity vector of a thin disc evolve as a result of internal stresses and external forcing. The analysis is asymptotically exact in the limit of a thin disc, and allows for slowly varying eccentricities of arbitrary magnitude. The theory is worked out in detail for a Maxwellian viscoelastic model of the turbulent stress in an accretion disc. This generalizes the conventional alpha viscosity model to account for the non-zero relaxation time of the turbulence, and is physically motivated by a consideration of the nature of magnetohydrodynamic turbulence. It is confirmed that circular discs are typically viscously unstable to eccentric perturbations, as found by Lyubarskij, Postnov & Prokhorov, if the conventional alpha viscosity model is adopted. However, the instability can usually be suppressed by introducing a sufficient relaxation time and/or bulk viscosity. It is then shown that an initially uniformly eccentric disc does not retain its eccentricity as had been suggested by previous analyses. The evolutionary equations should be useful in many applications, including understanding the origin of planetary eccentricities and testing theories of quasi-periodic oscillations in X-ray binaries.

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arXiv2000

Precessing warped accretion discs in X-ray binaries

We study the radiation-driven warping of accretion discs in the context of X-ray binaries. The latest evolutionary equations are adopted, which extend the classical alpha theory to time-dependent thin discs with non-linear warps. We also develop accurate, analytical expressions for the tidal torque and the radiation torque, including self-shadowing. We investigate the possible non-linear dynamics of the system within the framework of bifurcation theory. First, we re-examine the stability of an initially flat disc to the Pringle instability. Then we compute directly the branches of non-linear solutions representing steadily precessing discs. Finally, we determine the stability of the non-linear solutions. Each problem involves only ordinary differential equations, allowing a rapid, accurate and well resolved solution. We find that radiation-driven warping is probably not a common occurrence in low-mass X-ray binaries. We also find that stable, steadily precessing discs exist for a narrow range of parameters close to the stability limit. This could explain why so few systems show clear, repeatable `super-orbital' variations. The best examples of such systems, Her X-1, SS 433 and LMC X-4, all lie close to the stability limit for a reasonable choice of parameters. Systems far from the stability limit, including Cyg X-2, Cen X-3 and SMC X-1, probably experience quasi-periodic or chaotic variability as first noticed by Wijers & Pringle. We show that radiation-driven warping provides a coherent and persuasive framework but that it does not provide a generic explanation for the long-term variabilities in all X-ray binaries.

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arXiv2000

Observational Implications of Precessing Protostellar Discs and Jets

We consider the dynamics of a protostellar disc in a binary system where the disc is misaligned with the orbital plane of the binary, with the aim of determining the observational consequences for such systems. The disc wobbles with a period approximately equal to half the binary's orbital period and precesses on a longer timescale. We determine the characteristic timescale for realignment of the disc with the orbital plane due to dissipation. If the dissipation is determined by a simple isotropic viscosity then we find, in line with previous studies, that the alignment timescale is of order the viscous evolution timescale. However, for typical protostellar disc parameters, if the disc tilt exceeds the opening angle of the disc, then tidally induced shearing within the disc is transonic. In general, hydrodynamic instabilities associated with the internally driven shear result in extra dissipation which is expected to drastically reduce the alignment timescale. For large disc tilts the alignment timescale is then comparable to the precession timescale, while for smaller tilt angles $δ$, the alignment timescale varies as $(\sin δ)^{-1}$. We discuss the consequences of the wobbling, precession and rapid realignment for observations of protostellar jets and the implications for binary star formation mechanisms.

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