arXiv subjects

Gordon Ogilvie

Publications and source records attributed to Gordon Ogilvie.

15 recordsLinked to original sources

arXiv2022

Planet-Disk Interactions

Planet-disk interactions, where an embedded massive body interacts gravitationally with the protoplanetary disk it was formed in, can play an important role in reshaping both the disk and the orbit of the planet. Spiral density waves are launched into the disk by the planet, which, if they are strong enough, can lead to the formation of a gap. Both effects are observable with current instruments. The back-reaction of perturbations induced in the disk, both wave-like and non-wavelike, is a change in orbital elements of the planet. The efficiency of orbital migration is a long-standing problem in planet formation theory. We discuss recent progress in planet-disk interactions for different planet masses and disk parameters, in particular the level of turbulence, and progress in modeling observational signatures of embedded planets.

astro-ph.EP↗

arXiv2022

Nonlinear behaviour of warped discs around a central object with a quadrupole moment

The nonlinear behaviour of low-viscosity warped discs is poorly understood. We verified a nonlinear bending-wave theory, in which fluid columns undergo affine transformations, with direct 3D hydrodynamical simulations. We employed a second-order Godunov-type scheme, Meshless Finite Mass (MFM), and also the Smoothed Particle Hydrodynamics (SPH) method, with up to 128M particles. For moderate nonlinearity, MFM maintains well the steady nonlinear warp predicted by the affine model for a tilted inviscid disc around a central object with a quadrupole moment. However, numerical dissipation in SPH is so severe that even a low-amplitude nonlinear warp degrades at a resolution where MFM performs well. A low-amplitude arbitrary warp tends to evolve towards a nonlinear steady state. However, no such state exists in our thin disc with an angular semi-thickness H/R = 0.02 when the outer tilt angle is beyond about 14 degrees. The warp breaks tenuously and reconnects in adiabatic simulations, or breaks into distinct annuli in isothermal simulations. The breaking radius lies close to the location with the most extreme nonlinear deformation. Parametric instability is captured only in our highest-resolution simulation, leading to ring structures that may serve as incubators for planets around binaries.

astro-ph.EP↗

arXiv2021

Nonlinear resonant torus oscillations as a model of Keplerian disc warp dynamics

Observations of distorted discs have highlighted the ubiquity of warps in a variety of astrophysical contexts. This has been complemented by theoretical efforts to understand the dynamics of warp evolution. Despite significant efforts to understand the dynamics of warped discs, previous work fails to address arguably the most prevalent regime -- nonlinear warps in Keplerian discs for which there is a resonance between the orbital, epicyclic and vertical oscillation frequencies. In this work, we implement a novel nonlinear ring model, developed recently by Fairbairn and Ogilvie, as a framework for understanding such resonant warp dynamics. Here we uncover two distinct nonlinear regimes as the warp amplitude is increased. Initially we find a smooth modulation theory which describes warp evolution in terms of the averaged Lagrangian of the oscillatory vertical motions of the disc. This hints towards the possibility of connecting previous warp theory under a generalised secular framework. Upon the warp amplitude exceeding a critical value, which scales as the square root of the aspect-ratio of our ring, the disc enters into a bouncing regime with extreme vertical compressions twice per orbit. We develop an impulsive theory which predicts special retrograde and prograde precessing warped solutions, which are identified numerically using our full equation set. Such solutions emphasise the essential activation of nonlinear vertical oscillations within the disc and may have important implications for energy and warp dissipation. Future work should search for this behaviour in detailed numerical studies of the internal flow structure of warped discs.

astro-ph.SR↗

arXiv2019

Ohmic dissipation in the Earth's outer core resulting from the free inner core nutation

The diurnal tidal forces can excite a normal mode of the Earth's core, the free inner core nutation (FICN), which is characterized by a tilt of the rotation axis of the inner core with respect to the rotation axis of the outer core. The differential rotation between the inner core and the outer core induces fluid motions in the outer core and gives rise to Ohmic dissipation in the presence of the Earth's internal magnetic field. Nutation measurements can reflect such dissipation if it is sufficiently strong and thus can provide insights into the properties and dynamics of the Earth's core. In this study we perform a set of numerical calculations of the linear perturbations in the outer core induced by the FICN at very low Ekman numbers (as small as $10^{-11}$). Our numerical results show that the back-reaction of the magnetic field notably alters the structure and length scale of the perturbations induced by the FICN, and thus influences the Ohmic dissipation resulting from the perturbations. When the Ekman number is sufficiently small, Ohmic dissipation tends to be insensitive to the fluid viscosity and to the magnetic diffusivity, which allows us to estimate the Ohmic dissipation associated with the FICN without relying on an extrapolation. In contrast to the results of Buffett (2010b), the estimated Ohmic dissipation based on our numerical calculations is too weak to account for the observed damping of the FICN mode. This also implies that nutation measurements cannot provide effective constraints on the strength of the magnetic field inside the Earth's outer core.

physics.geo-ph↗

arXiv2018

Local numerical simulations of warped discs

We study the hydrodynamical stability of the laminar flows associated with warped astrophysical discs using numerical simulations of warped shearing boxes. We recover linear growth rates reported previously due to a parametric resonance of inertial waves, and show that the nonlinear saturated state can significantly reduce the laminar flows, meaning that the warp would evolve on much longer time scales than would be concluded from the internal torques due to these laminar flows. Towards larger warp amplitudes, we find first of all a reversal of angular momentum flux, indicating that the mass distribution would evolve in an anti-diffusive manner, and second that the linear growth rates disappear, possibly because of the very strong shear in the laminar flows in this regime. For discs with small enough viscosity, a nonlinear state can still be found when linear growth rates are absent by introducing a large enough perturbation, either by starting from a nonlinear state obtained at smaller warp amplitude, or by starting from a state with no laminar flows.

astro-ph.SR↗

arXiv2017

Tidal interactions in spin-orbit misaligned systems

Spin-orbit misalignments have been detected in exoplanetary systems and binary star systems. Tidal interactions may have played an important role in the evolution of the spin-orbit angle. In this study, we investigate the tidal interactions in spin-orbit misaligned systems. In particular, we focus on the tidal response of a rotating fluid body to the obliquity tide, which may be important for the evolution of the spin-orbit angle but hardly affects the orbital evolution. The obliquity tide also provides a torque for the mutual precession of the spin and orbital axes around the total angular momentum vector, which has not yet been considered in previous studies on the tidal interactions. In this paper, we first formulate a set of linearized equations describing the tidal response in spin-orbit misaligned systems, taking into account the precessional motion. Numerical solutions in a homogeneous fluid and in a polytrope of index 1 show that dissipative inertial waves can be excited on top of precession by the obliquity tide in the presence of a rigid core. The tidal quality factor associated with the obliquity tide $Q'_{210}$ can be several orders of magnitude smaller than those associated with other tidal components if their frequencies fall outside the frequency range of inertial waves. Therefore, it is possible that the spin-orbit misalignment undergoes much more rapid decay than the orbital decay in hot Jupiter systems owing to the enhanced dissipation of the obliquity tide.

astro-ph.EP↗

arXiv2016

Zonal flow evolution and overstability in accretion discs

This work presents a linear analytical calculation on the stability and evolution of a compressible, viscous self-gravitating (SG) Keplerian disc with both horizontal thermal diffusion and a constant cooling timescale when an axisymmetric structure is present and freely evolving. The calculation makes use of the shearing sheet model and is carried out for a range of cooling times. Although the solutions to the inviscid problem with no cooling or diffusion are well known, it is non-trivial to predict the effect caused by the introduction of cooling and of small diffusivities; this work focuses on perturbations of intermediate wavelengths, therefore representing an extension to the classical stability analysis on thermal and viscous instabilities. For density wave modes the analysis can be simplified by means of a regular perturbation analysis; considering both shear and thermal diffusivities, the system is found to be overstable for intermediate and long wavelengths for values of the Toomre parameter $Q \lesssim 2$; a non-SG instability is also detected for wavelengths $\gtrsim 18H$, where $H$ is the disc scale height, as long as $γ\lesssim 1.305$. The regular perturbation analysis does not however hold for the entropy and potential vorticity slow modes as their ideal growth rates are degenerate. To understand their evolution, equations for the axisymmetric structure's amplitudes in these two quantities are analytically derived and their instability regions obtained. The instability appears boosted by increasing the value of the adiabatic index and of the Prandtl number, while it is quenched by efficient cooling.

astro-ph.SR↗

arXiv2014

The ballistic transport instability in Saturn's rings III: numerical simulations

Saturn's inner B-ring and its C-ring support wavetrains of contrasting amplitudes but with similar length scales, 100-1000 km. In addition, the inner B-ring is punctuated by two intriguing `flat' regions between radii 93,000 km and 98,000 km in which the waves die out, whereas the C-ring waves coexist with a forest of plateaus, narrow ringlets, and gaps. In both regions the waves are probably generated by a large-scale linear instability whose origin lies in the meteoritic bombardment of the rings: the ballistic transport instability. In this paper, the third in a series, we numerically simulate the long-term nonlinear evolution of this instability in a convenient local model. Our C-ring simulations confirm that the unstable system forms low-amplitude wavetrains possessing a preferred band of wavelengths. B-ring simulations, on the other hand, exhibit localised nonlinear wave `packets' separated by linearly stable flat zones. Wave packets travel slowly while spreading in time, a result that suggests the observed flat regions in Saturn's B-ring are shrinking. Finally, we present exploratory runs of the inner B-ring edge which reproduce earlier numerical results: ballistic transport can maintain the sharpness of a spreading edge while building a `ramp' structure at its base. Moreover, the ballistic transport instability can afflict the ramp region, but only in low-viscosity runs.

astro-ph.EP↗

arXiv2014

The ballistic transport instability in Saturn's rings II: nonlinear wave dynamics

The ejecta discharged by impacting meteorites can redistribute a planetary ring's mass and angular momentum. This `ballistic transport' of ring properties instigates a linear instability that could generate the 100--1000-km undulations observed in Saturn's inner B-ring and in its C-ring. We present semi-analytic results demonstrating how the instability sustains steadily travelling nonlinear wavetrains. At low optical depths, the instability produces approximately sinusoidal waves of low amplitude, which we identify with those observed between radii 77,000 and 86,000 km in the C-ring. On the other hand, optical depths of 1 or more exhibit hysteresis, whereby the ring falls into multiple stable states: the homogeneous background equilibrium or large-amplitude wave states. Possibly the `flat zones' and `wave zones' between radii 93,000 and 98,000 km in the B-ring correspond to the stable homogeneous and wave states, respectively. In addition, we test the linear stability of the wavetrains and show that only a small subset are stable. In particular, stable solutions all possess wavelengths greater than the lengthscale of fastest linear growth. We supplement our calculations with a weakly nonlinear analysis that suggests the C-ring reproduces some of the dynamics of the complex Ginzburg--Landau equation. In the third paper in the series, these results will be tested and extended with numerical simulations.

astro-ph.EP↗

arXiv2014

Direct numerical simulations of an inertial wave attractor in linear and nonlinear regimes

In a uniformly rotating fluid, inertial waves propagate along rays that are inclined to the rotation axis by an angle that depends on the wave frequency. In closed domains, multiple reflections from the boundaries may cause inertial waves to focus on to particular structures known as wave attractors. Such structures have previously been studied from a theoretical point of view, in laboratory experiments, in linear numerical calculations and in some recent numerical simulations. In the present paper, two-dimensional direct numerical simulations of an inertial wave attractor are presented. In the linear regime, we first recover the results of the linear calculations and asymptotic theory of Ogilvie (2005) who considered a prototypical problem involving the focusing of linear internal waves into a narrow beam centred on a wave attractor in a steady state. The velocity profile of the beam and its scalings with the Ekman number, as well as the asymptotic value of the dissipation rate, are found to be in agreement with the linear theory. We also find that, as the beam builds up around the wave attractor, the power input by the applied force reaches its limiting value more rapidly than the dissipation rate, which saturates only when the beam has reached its final thickness. In the nonlinear regime, the beam is strongly affected and becomes unstable to a subharmonic instability. This instability transfers energy to secondary waves possessing shorter wavelengths and lower frequencies. The onset of the instability of a narrow inertial wave beam is investigated by means of a separate linear analysis and the results, such as the onset of the instability, are found to be consistent with the global simulations of the wave attractor. The excitation of such secondary waves described theoretically in this work has also been seen in recent laboratory experiments on internal gravity waves.

astro-ph.SR↗

arXiv2012

The magnetorotational instability as a jet launching mechanism

Magnetorotational turbulence and magnetically driven disc winds are often considered as separate processes. However, realistic astrophysical discs are expected to be subject to both effects, although possibly at different times and locations. We investigate here the potential link between these two phenomena using a mixed numerical and analytical approach. We show in particular that large-scale MRI modes which dominate strongly magnetised discs (plasma beta~10) naturally produce magnetically driven outflows in the nonlinear regime. We show that these outflows share many similarities with local and global disc wind solutions found in the literature. We also investigate the 3D stability of these outflows and show that they are unstable on dynamical timescales. The implications of these results for the transition between a jet-emitting disc and a standard "viscous" disc are discussed.

astro-ph.HE↗

arXiv2012

The ballistic transport instability in Saturn's rings I: formalism and linear theory

Planetary rings sustain a continual bombardment of hypervelocity meteoroids that erode the surfaces of ring particles on time scales of 10^5 - 10^7 years. The debris ejected from such impacts re-accretes on to the ring, though often at a slightly different orbital radius from the point of emission. This `ballistic transport' leads to a rearrangement of the disk's mass and angular momentum, and gives rise to a linear instability that generates structure on relatively large scales. It is likely that the 100-km undulations in Saturn's inner B-ring and the plateaus and 1000-km waves in Saturn's C-ring are connected to the nonlinear saturation of the instability. In this paper the physical problem is reformulated so as to apply to a local patch of disk (the shearing sheet). This new streamlined model helps facilitate our physical understanding of the instability, and also makes more tractable the analysis of its nonlinear dynamics. We concentrate on the linear theory in this paper, showing that the instability is restricted to a preferred range of intermediate wavenumbers and optical depths. We subsequently apply these general results to the inner B-ring and the C-ring and find that in both regions the ballistic transport instability should be near marginality, a fact that may have important consequences for its prevalence and nonlinear development. Owing to damping via self-gravity wakes, the instability should not be present in the A-ring. A following paper will explore the instability's nonlinear saturation and how it connects to the observed large-scale structure.

astro-ph.EP↗

arXiv2011

Stability analysis of a tidally excited internal gravity wave near the centre of a solar-type star

We perform a stability analysis of a tidally excited nonlinear internal gravity wave near the centre of a solar-type star in two-dimensions. The motivation is to understand the tidal interaction between short-period planets and their solar-type host stars, which involves the launching of gravity waves at the top of the radiation zone that propagate towards the stellar centre. Studying the instabilities of these waves near the centre, where nonlinearities are most important, is essential, since it may have implications for the survival of these planets. When the waves have sufficient amplitude to overturn the stratification, they break and form a critical layer, which efficiently absorbs subsequent ingoing wave angular momentum, and can result in the planet spiralling into the star. However, previous simulations do not find the waves to undergo instability for smaller amplitudes. This work has two aims: to determine any instabilities that set in for small-amplitude waves, and to further understand the breaking of large-amplitude waves. Our main result is that the waves undergo parametric instabilities for any amplitude. However, because the nonlinearity is spatially localised in the innermost wavelengths, their growth rates are sufficiently small that they do not result in astrophysically important tidal dissipation. The resulting modified tidal quality factors are estimated to be Q'_star>10^7, and possibly much greater, so the dissipation is much weaker than that which results from critical-layer absorption. These results support our explanation for the survival of all currently observed short-period planets around solar-type main-sequence stars: that planets unable to cause wave breaking at the centre of their host stars are likely to survive against tidal decay. This hypothesis will be tested by ongoing and future observations of transiting planets, such as WASP and Kepler.

astro-ph.EP↗

arXiv2008

Simulations of eccentric disks in close binary systems

We study the development of finite eccentricity in accretion disks in close binary systems using a two-dimensional grid-based numerical scheme. We perform detailed parameter studies to explore the dependence on viscosity, disk aspect ratio, the inclusion of a mass-transfer stream and the role of the boundary conditions. We consider mass ratios 0.05<q<0.3 appropriate to superoutbursting cataclysmic binary systems. Instability to the formation of a precessing eccentric disk that attains a quasi-steady state with mean eccentricity in the range 0.3-0.5 occurs readily. The shortest growth times are ~15 binary orbits for the largest viscosities and the instability mechanism is for the most part consistent with the mode-coupling mechanism associated with the 3:1 resonance proposed by Lubow. However, the results are sensitive to the treatment of the inner boundary and to the incorporation of the mass-transfer stream. In the presence of a stream we found a critical viscosity below which the disk remains circular. Incorporation of a mass-transfer stream tends to impart stability for small enough viscosity (or, equivalently, mass-transfer rate through the disk) and does assist in obtaining a prograde precession rate that is in agreement with observations. For the larger q the location of the 3:1 resonance is pushed outwards towards the Roche lobe where higher-order mode couplings and nonlinearity occur. It is likely that three-dimensional simulations that properly resolve the disk's vertical structure are required to make significant progress in this case.

astro-ph↗

arXiv2006

The dynamics of eccentric accretion discs in superhump systems

We have applied an eccentric accretion disc theory in simplified form to the case of an accretion disc in a binary system, where the disc contains the 3:1 Lindblad resonance. This is relevant to the case of superhumps in SU Ursae Majoris cataclysmic variables and other systems, where it is thought that this resonance leads to growth of eccentricity and a modulation in the light curve due to the interaction of a precessing eccentric disc with tidal stresses. A single differential equation is formulated which describes the propagation, resonant excitation and viscous damping of eccentricity. The theory is first worked out in the simple case of a narrow ring and leads to the conclusion that the eccentricity distribution is locally suppressed by the presence of the resonance, creating a dip in the eccentricity at the resonant radius. Application of this theory to the superhump case confirms this conclusion and produces a more accurate expression for the precession rate of the disc than has been previously accomplished with simple dynamical estimates.

astro-ph↗