arXiv subjects

Gordon I. Ogilvie

Publications and source records attributed to Gordon I. Ogilvie.

At least 73 records · Page 4Linked to original sources

arXiv2012

Transport of magnetic flux and the vertical structure of accretion discs: I. Uniform diffusion coefficients

The evolution of a large-scale poloidal magnetic field in accretion discs is an important problem because of its role in the launching of jets and winds and in determining the intensity of turbulence. In this paper, we develop a formalism to calculate the transport magnetic flux in a thin accretion disc, thus determining its evolution on a viscous/resistive timescale. The governing equations are derived by performing an asymptotic expansion in the limit of a thin disc, in the regime where the magnetic field is dominated by its vertical component. Turbulent viscosity and resistivity are included, with an arbitrary vertical profile that can be adjusted to mimic the vertical structure of the turbulence. At a given radius and time, the rates of transport of mass and magnetic flux are determined by a one-dimensional problem in the vertical direction, in which the radial gradients of various quantities appear as source terms. We solve this problem to obtain the transport rates and the vertical structure of the disc. The present paper is then restricted to the idealised case of uniform diffusion coefficients, while a companion paper will study more realistic vertical profiles of these coefficients. We show the advection of weak magnetic fields to be significantly faster than the advection of mass, contrary to what a crude vertical averaging might suggest. This results from the larger radial velocities away from the mid-plane, which barely affect the mass accretion owing to the low density in these regions but do affect the advection of magnetic flux. Possible consequences of this larger accretion velocity include a potentially interesting time-dependence with the magnetic flux distribution evolving faster than the mass distribution. If the disc is not too thin, this fast advection may also partially solve the long-standing problem of too efficient diffusion of an inclined magnetic field.

astro-ph.HE↗

arXiv2012

The gravitational instability of a stream of co-orbital particles

We describe the dynamics of a stream of equally spaced macroscopic particles in orbit around a central body (e.g. a planet or star). A co-orbital configuration of small bodies may be subject to gravitational instability, which takes the system to a spreading, disordered and collisional state. We detail the linear instability's mathematical and physical features using the shearing sheet model and subsequently track its nonlinear evolution with local N-body simulations. This model provides a convenient tool with which to understand the gravitational and collisional dynamics of narrow belts, such as Saturn's F-ring and the streams of material wrenched from tidally disrupted bodies. In particular, we study the tendency of these systems to form long-lived particle aggregates. Finally, we uncover an unexpected connection between the linear dynamics of the gravitational instability and the magnetorotational instability.

astro-ph.EP↗

arXiv2012

Jet launching from accretion discs in the local approximation

The acceleration of an outflow along inclined magnetic field lines emanating from an accretion disc can be studied in the local approximation, as employed in the computational model known as the shearing box. By including the slow magnetosonic point within the computational domain, the rate of mass loss in the outflow can be calculated. The accretion rates of mass and magnetic flux can also be determined, although some effects of cylindrical geometry are omitted. We formulate a simple model for the study of this problem and present the results of one-dimensional numerical simulations and supporting calculations. Quasi-steady solutions are obtained for relatively strong poloidal magnetic fields for which the magnetorotational instability is suppressed. In this regime the rate of mass loss decreases extremely rapidly with increasing field strength, or with decreasing surface density or temperature. If the poloidal magnetic field in an accretion disc can locally achieve an appropriate strength and inclination then a rapid burst of ejection may occur. For weaker fields it may be possible to study the launching process in parallel with the magnetorotational instability, but this will require three-dimensional simulations.

astro-ph.SR↗

arXiv2012

On the interaction between tides and convection

We study the interaction between tides and convection in astrophysical bodies by analysing the effect of a homogeneous oscillatory shear on a fluid flow. This model can be taken to represent the interaction between a large-scale periodic tidal deformation and a smaller-scale convective motion. We first consider analytically the limit in which the shear is of low amplitude and the oscillation period is short compared to the timescales of the unperturbed flow. In this limit there is a viscoelastic response and we obtain expressions for the effective elastic modulus and viscosity coefficient. The effective viscosity is inversely proportional to the square of the oscillation frequency, with a coefficient that can be positive, negative or zero depending on the properties of the unperturbed flow. We also carry out direct numerical simulations of Boussinesq convection in an oscillatory shearing box and measure the time-dependent Reynolds stress. The results indicate that the effective viscosity of turbulent convection falls rapidly as the oscillation frequency is increased, attaining small negative values in the cases we have examined, although significant uncertainties remain because of the turbulent noise. We discuss the implications of this analysis for astrophysical tides.

astro-ph.SR↗

arXiv2010

Hydrodynamical simulations of viscous overstability in Saturn's rings

We perform axisymmetric hydrodynamical simulations that describe the nonlinear outcome of the viscous overstability in dense planetary rings. These simulations are particularly relevant for Cassini observations of fine-scale structure in Saturn's A and B-ring, which take the form of periodic microstructure on the 0.1 km scale, and irregular larger-scale structure on 1-10 km. Nonlinear wavetrains dominate all the simulations, and we associate them with the observed periodic microstructure. The waves can undergo small chaotic fluctuations in their phase and amplitude, and may be punctuated by more formidable `wave defects' distributed on longer scales. It is unclear, however, whether the defects are connected to the irregular larger-scale variations observed by Cassini. The long-term behaviour of the simulations is dominated by the imposed boundary conditions, and more generally by the limitations of the local model we use: the shearing box. When periodic boundary conditions are imposed, the system eventually settles on a uniform travelling wave of a predictable wavelength, while reflecting boundaries, and boundaries with buffer zones, maintain a disordered state. The simulations omit self-gravity, though we examine its influence in future work.

astro-ph.EP↗

arXiv2010

A model of the entropy flux and Reynolds stress in turbulent convection

We propose a closure model for the transport of entropy and momentum in astrophysical turbulence, intended for application to rotating stellar convective regions. Our closure model is first presented in the Boussinesq formalism, and compared with laboratory and numerical experimental results on Rayleigh-Benard convection and Homogeneous Rayleigh-Benard convection. The predicted angular momentum transport properties of the turbulence in the slowly rotating case recover the well-known Lambda-effect, with an amplitude uniquely related to the convective heat flux. The model is then extended to the anelastic case as well as the fully compressible case. In the special case of spherical symmetry, the predicted radial heat flux is equivalent to that of mixing-length theory. For rotating stars, our model describes the coupled transport of heat and angular momentum, and provides a unified formalism in which to study both differential rotation and thermal inhomogeneities in stellar convection zones.

astro-ph.SR↗

arXiv2009

The viscous overstability, nonlinear wavetrains, and finescale structure in dense planetary rings

This paper addresses the fine-scale axisymmetric structure exhibited in Saturn's A and B-rings. We aim to explain both the periodic microstructure on 150-220m, revealed by the Cassini UVIS and RSS instruments, and the irregular variations in brightness on 1-10km, reported by the Cassini ISS. We propose that the former structures correspond to the peaks and troughs of the nonlinear wavetrains that form naturally in a viscously overstable disk. The latter variations on longer scales may correspond to modulations and defects in the wavetrains' amplitudes and wavelength. We explore these ideas using a simple hydrodynamical model which captures the correct qualitative behaviour of a disk of inelastically colliding particles, while also permitting us to make progress with analytic and semi-analytic techniques. Specifically, we calculate a family of travelling nonlinear density waves and determine their stability properties. Detailed numerical simulations that confirm our basic results will appear in a following paper.

astro-ph.EP↗

arXiv2009

Tidal dissipation in rotating fluid bodies: a simplified model

We study the tidal forcing, propagation and dissipation of linear inertial waves in a rotating fluid body. The intentionally simplified model involves a perfectly rigid core surrounded by a deep ocean consisting of a homogeneous incompressible fluid. Centrifugal effects are neglected, but the Coriolis force is considered in full, and dissipation occurs through viscous or frictional forces. The dissipation rate exhibits a complicated dependence on the tidal frequency and generally increases with the size of the core. In certain intervals of frequency, efficient dissipation is found to occur even for very small values of the coefficient of viscosity or friction. We discuss the results with reference to wave attractors, critical latitudes and other features of the propagation of inertial waves within the fluid, and comment on their relevance for tidal dissipation in planets and stars.

astro-ph.EP↗

arXiv2009

Diurnal Thermal Tides in a Non-synchronized Hot Jupiter

We perform a linear analysis to investigate the dynamical response of a non-synchronized hot Jupiter to stellar irradiation. In this work, we consider the diurnal Fourier harmonic of the stellar irradiation acting at the top of a radiative layer of a hot Jupiter with no clouds and winds. In the absence of the Coriolis force, the diurnal thermal forcing can excite internal waves propagating into the planet's interior when the thermal forcing period is longer than the sound crossing time of the planet's surface. When the Coriolis effect is taken into consideration, the latitude-dependent stellar heating can excite weak internal waves (g modes) and/or strong baroclinic Rossby waves (buoyant r modes) depending on the asynchrony of the planet. When the planet spins faster than its orbital motion (i.e. retrograde thermal forcing), these waves carry negative angular momentum and are damped by radiative loss as they propagate downwards from the upper layer of the radiative zone. As a result, angular momentum is transferred from the lower layer of the radiative zone to the upper layer and generates a vertical shear. We estimate the resulting internal torques for different rotation periods based on the parameters of HD 209458b.

astro-ph.EP↗

arXiv2008

Warp and eccentricity propagation in discs around black holes

We consider the inward propagation of warping and eccentric disturbances in discs around black holes under a wide variety of conditions. In our calculations we use secular theories of warped and eccentric discs and assume the deformations to be stationary and propagating in a disc model similar to regions (a) and (b) of Shakura and Sunyaev discs. We find that the propagation of deformations to the innermost regions of the disc is facilitated for low viscous damping and high accretion rate. We relate our results to the possible excitation of trapped inertial modes, and to the observations of high-frequency quasi-periodic oscillations (QPOs) in black hole systems in the very high spectral state.

astro-ph↗

arXiv2008

Excitation of trapped oscillations in discs around black holes

High-frequency quasi-periodic oscillations detected in the light curves of black hole candidates can, according to one model, be identified with hydrodynamic oscillations of the accretion disc. We describe a non-linear coupling mechanism, suggested by Kato, through which inertial waves trapped in the inner regions of accretion discs around black holes are excited. Global warping and/or eccentricity of the disc have a fundamental role in this coupling: they combine with trapped modes, generating negative energy waves, that are damped as they approach the inner edge of the disc or their corotation resonance. As a result of this damping, inertial oscillations are amplified. We calculate the resulting eigenfunctions and their growth rates.

astro-ph↗

arXiv2008

Warped and eccentric discs around black holes

Accretion discs around black holes in X-ray binary stars are warped if the spin axis of the black hole is not perpendicular to the binary orbital plane. They can also become eccentric through an instability involving a resonance with the binary orbit. Depending on the thickness of the disc and the efficiency of dissipative processes, these global deformations may be able to propagate into the innermost part of the disc in the form of stationary bending or density waves. We describe the solutions in the linear regime and discuss the conditions under which a warp or eccentricity is likely to produce significant activity in the inner region, which may include the excitation of quasi-periodic oscillations.

astro-ph↗

arXiv2008

Three-dimensional eccentric discs around Be stars

One-armed oscillation modes in the circumstellar discs of Be stars may explain the cyclical variations in their emission lines. We show that a three-dimensional effect, involving vertical motion and neglected in previous treatments, profoundly influences the dynamics. Using a secular theory of eccentric discs that reduces the problem to a second-order differential equation, we show that confined prograde modes are obtained for all reasonable disc temperatures and stellar rotation rates. We confirm these results using a numerical analysis of the full set of linearized equations for three-dimensional isothermal discs including viscous terms that couple the horizontal motions at different altitudes. In order to make these modes grow, viscous damping must be overcome by an excitation mechanism such as viscous overstability.

astro-ph↗

arXiv2008

Dense planetary rings and the viscous overstability

This paper examines the onset of the viscous overstability in dense particulate rings. First, we formulate a dense gas kinetic theory that is applicable to the Saturnian system. Our model is essentially that of Araki and Tremaine (1986), which we show can be both simplified and generalised. Second, we put this model to work computing the equilibrium properties of dense planetary rings, which we subsequently compare with the results of N-body simulations, namely those of Salo (1991). Finally, we present the linear stability analyses of these equilibrium states, and derive criteria for the onset of viscous overstability in the self-gravitating and non-self-gravitating cases. These are framed in terms of particle size, orbital frequency, optical depth, and the parameters of the collision law. Our results compare favourably with the simulations of Salo et al. (2001). The accuracy and practicality of the continuum model we develop encourages its general use in future investigations of nonlinear phenomena.

astro-ph↗

arXiv2008

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

According to one model, high-frequency quasi-periodic oscillations (QPOs) can be identified with inertial waves, trapped in the inner regions of accretion discs around black holes due to relativistic effects. In order to be detected, their amplitudes need to reach large enough values via some excitation mechanism. We work out in detail a non-linear coupling mechanism suggested by Kato, in which a global warping or eccentricity of the disc has a fundamental role. These large-scale deformations combine with trapped modes to generate `intermediate' waves of negative energy that are damped as they approach either their corotation resonance or the inner edge of the disc, resulting in amplification of the trapped waves. We determine the growth rates of the inertial modes, as well as their dependence on the spin of the black hole and the properties of the disc. Our results indicate that this coupling mechanism can provide an efficient excitation of trapped inertial waves, provided the global deformations reach the inner part of the disc with non-negligible amplitude.

astro-ph↗

arXiv2008

James Clerk Maxwell and the dynamics of astrophysical discs

Maxwell's investigations into the stability of Saturn's rings provide one of the earliest analyses of the dynamics of astrophysical discs. Current research in planetary rings extends Maxwell's kinetic theory to treat dense granular gases of particles undergoing moderately frequent inelastic collisions. Rather than disrupting the rings, local instabilities may be responsible for generating their irregular radial structure. Accretion discs around black holes or compact stars consist of a plasma permeated by a tangled magnetic field and may be compared with laboratory fluids through an analogy that connects Maxwell's researches in electromagnetism and viscoelasticity. A common theme in this work is the appearance of a complex fluid with a dynamical constitutive equation relating the stress in the medium to the history of its deformation.

astro-ph↗

arXiv2008

Magnetorotational-type instability in Couette-Taylor flow of a viscoelastic polymer liquid

We describe an instability of viscoelastic Couette-Taylor flow that is directly analogous to the magnetorotational instability (MRI) in astrophysical magnetohydrodynamics, with polymer molecules playing the role of magnetic field lines. By determining the conditions required for the onset of instability and the properties of the preferred modes, we distinguish it from the centrifugal and elastic instabilities studied previously. Experimental demonstration and investigation should be much easier for the viscoelastic instability than for the MRI in a liquid metal. The analogy holds with the case of a predominantly toroidal magnetic field such as is expected in an accretion disk and it may be possible to access a turbulent regime in which many modes are unstable.

astro-ph↗

arXiv2006

Mean-motion resonances in satellite-disc interactions

Mean-motion resonances between a Keplerian disc and an orbiting companion are analysed within a Hamiltonian formulation using complex canonical Poincare variables, which are ideally suited to the description of eccentricity and inclination dynamics. Irreversibility is introduced by allowing for dissipation within the disc. A method is given for determining the rates of change of eccentricity and inclination variables of the disc and companion associated with resonances of various orders, including both reversible and irreversible effects, which extend and generalize previous results. Preliminary applications to protoplanetary systems and close binary stars are discussed.

astro-ph↗