arXiv subjects

A. J. Barker

Publications and source records attributed to A. J. Barker.

At least 19 recordsLinked to original sources

arXiv2026

Magnetic Dynamo Driven by Inertial Waves

We demonstrate, by studying precession-driven flows, that inertial wave hydrodynamic turbulence can drive a robust magnetic dynamo action. Motivated by the stronger damping of large-scale geostrophic vortices in rapidly rotating planetary and stellar interiors, we introduce a controlled damping of the vortices, which usually accompany inertial wave turbulence and feed on wave energy. It is shown that even a small vortex damping results in a significant increase of the growth rate of the dynamo due to inertial waves in the kinematic regime, allowing it to persist for magnetic Prandtl numbers as low as $Pm \sim 10^{-3}$ and Poincaré numbers $Po\sim 0.025$. These critical values of $Po$ and $Pm$ for the dynamo onset decrease with increasing Reynolds number. The onset and growth of the dynamo appear to correlate with the coherent fluctuations of kinetic helicity. Spectral analysis shows that magnetic energy growth is primarily due to inertial-wave-induced induction over a broad range of scales. These results establish inertial waves as an efficient mechanism for magnetic field amplification in rapidly rotating low-$Pm$ flows relevant to planetary and stellar interiors.

physics.flu-dyn↗

arXiv2025

A search for transit timing variations in the transiting hot Jupiter systems HIP 65, NGTS-6, NGTS-10 and WASP-173

Hot Jupiters are Jupiter-mass planets with orbital periods of less than ten days. Their short orbital separations make tidal dissipation within the stellar host especially efficient, potentially leading to a measurable evolution of the orbit. One possible manifestation of this is orbital decay, which presents itself observationally through variations in the orbital period and thus times of transit. Here we select four promising exoplanetary systems for detecting this effect: HIP 65, NGTS-6, NGTS-10 and WASP-173. We present 33 new transit light curves taken with the 1.54 m Danish Telescope, and analyse these alongside photometric data from the Transiting Exoplanet Survey Satellite and transit timing data from the literature. We construct two ephemeris models for each target: a linear ephemeris and a shrinking orbital period due to tidal decay. The linear ephemeris is preferred for three of the four models - the highest significance for the quadratic ephemeris is over 3-sigma for WASP-173. We compare these results to theoretical predictions for tidal dissipation of gravity waves in radiation zones, and find that wave breaking is predicted only in WASP-173, making rapid decay plausible in this system but unclear in the other three. The sensitivity of transit timings to orbital decay depends on the square of the time interval covered by available observations, so our results establish a useful baseline against which future measurements can be compared. NGTS-6 and NGTS-10 are important objects for future study as they are in the first field to be observed by the upcoming PLATO mission.

astro-ph.EP↗

arXiv2024

Dynamo action driven by precessional turbulence

We reveal and analyze an efficient magnetic dynamo action due to precession-driven hydrodynamic turbulence in the local model of a precessional flow, focusing on the kinematic stage of this dynamo. The growth rate of magnetic field monotonically increases with Poincaré number, $\rm Po$, characterizing precession strength, and magnetic Prandtl number, $\rm Pm$, equal to the ratio of viscosity to resistivity, for the considered ranges of these parameters. The critical ${\rm Po}_c$ for the dynamo onset decreases with increasing $\rm Pm$. To understand the scale-by-scale evolution (growth) of the precession dynamo and its driving processes, we perform spectral analysis by calculating the spectra of magnetic energy and of different terms in the induction equation in Fourier space. To this end, we decompose the velocity field of precession-driven turbulence into 2D vortical and 3D inertial wave modes. It is shown that the dynamo operates across a broad range of scales and exhibits a remarkable transition from a primarily vortex-driven regime at lower $\rm Po$ to a more complex regime at higher $\rm Po$ where it is driven jointly by vortices, inertial waves and the shear of the background precessional flow. The vortices and shear drive the dynamo mostly at large scales, comparable to the flow system size, and at intermediate scales, while at smaller scales it is mainly driven by inertial waves. This study can be important not only for understanding the magnetic dynamo action in precession-driven flows, but also in a general context of flows where vortices emerge and govern the flow dynamics and evolution.

physics.flu-dyn↗

arXiv2024

Predicting the Slowing of Stellar Differential Rotation by Instability-Driven Turbulence

Differentially rotating stars and planets transport angular momentum internally due to turbulence at rates that have long been a challenge to predict reliably. We develop a self-consistent saturation theory, using a statistical closure approximation, for hydrodynamic turbulence driven by the axisymmetric Goldreich--Schubert--Fricke (GSF) instability at the stellar equator with radial differential rotation. This instability arises when fast thermal diffusion eliminates the stabilizing effects of buoyancy forces in a system where a stabilizing entropy gradient dominates over the destabilizing angular momentum gradient. Our turbulence closure invokes a dominant three-wave coupling between pairs of linearly unstable eigenmodes and a near-zero frequency, viscously damped eigenmode that features latitudinal jets. We derive turbulent transport rates of momentum and heat, and provide them in analytic forms. Such formulae, free of tunable model parameters, are tested against direct numerical simulations; the comparison shows good agreement. They improve upon prior quasi-linear or ``parasitic saturation" models containing a free parameter. Given model correspondences, we also extend this theory to heat and compositional transport for axisymmetric thermohaline instability-driven turbulence in certain regimes.

astro-ph.SR↗

arXiv2023

The interactions of the elliptical instability and convection

The elliptical instability is an instability of elliptical streamlines, which can be excited by large-scale tidal flows in rotating fluid bodies, and excites inertial waves if the dimensionless tidal amplitude ($ε$) is sufficiently large. It operates in convection zones but its interactions with turbulent convection have not been studied in this context. We perform an extensive suite of Cartesian hydrodynamical simulations in wide boxes to explore the interactions of the elliptical instability and Rayleigh-Bénard convection. We find that geostrophic vortices generated by the elliptical instability dominate the flow, with energies far exceeding those of the inertial waves. Furthermore, we find that the elliptical instability can operate with convection, but it is suppressed for sufficiently strong convection, primarily by convectively-driven large-scale vortices. We examine the flow in Fourier space, allowing us to determine the energetically dominant frequencies and wavenumbers. We find that power primarily concentrates in geostrophic vortices, in wavenumbers that are convectively unstable, and along the inertial wave dispersion relation, even in non-elliptically deformed convective flows. Examining linear growth rates on a convective background, we find that convective large-scale vortices suppress the elliptical instability in the same way as the geostrophic vortices created by the elliptical instability itself. Finally, convective motions act as an effective viscosity on large-scale tidal flows, providing a sustained energy transfer (scaling as $ε^2$). Furthermore, we find that the energy transfer resulting from bursts of elliptical instability, when it operates, is consistent with the $ε^3$ scaling found in prior work.

physics.flu-dyn↗

arXiv2022

Interplay between geostrophic vortices and inertial waves in precession-driven turbulence

The properties of rotating turbulence driven by precession are studied using direct numerical simulations and analysis of the underlying dynamical processes in Fourier space. The study is carried out in the local rotating coordinate frame, where precession gives rise to a background shear flow, which becomes linearly unstable and breaks down into turbulence. We observe that this precession-driven turbulence is in general characterized by coexisting two dimensional (2D) columnar vortices and three dimensional (3D) inertial waves, whose relative energies depend on the precession parameter $Po$. The vortices resemble the typical condensates of geostrophic turbulence, are aligned along the rotation axis (with zero wavenumber in this direction, $k_z=0$) and are fed by the 3D waves through nonlinear transfer of energy, while the waves (with $k_z\neq0$) in turn are directly fed by the precessional instability of the background flow. The vortices themselves undergo inverse cascade of energy and exhibit anisotropy in Fourier space. For small $Po<0.1$ and sufficiently high Reynolds numbers, the typical regime for most geo- and astrophysical applications, the flow exhibits strongly oscillatory (bursty) evolution due to the alternation of vortices and small-scale waves. On the other hand, at larger $Po>0.1$ turbulence is quasi-steady with only mild fluctuations, the coexisting columnar vortices and waves in this state give rise to a split (simultaneous inverse and forward) cascade. Increasing the precession magnitude causes a reinforcement of waves relative to vortices with the energy spectrum approaching Kolmogorov scaling and, therefore, the precession mechanism counteracts the effects of the rotation.

physics.flu-dyn↗

arXiv2022

The effects of nonlinearities on tidal flows in the convective envelopes of rotating stars and planets in exoplanetary systems

In close exoplanetary systems, tidal interactions drive orbital and spin evolution of planets and stars over long timescales. Tidally-forced inertial waves (restored by the Coriolis acceleration) in the convective envelopes of low-mass stars and giant gaseous planets contribute greatly to the tidal dissipation when they are excited and subsequently damped (e.g. through viscous friction), especially early in the life of a system. These waves are known to be subject to nonlinear effects, including triggering differential rotation in the form of zonal flows. In this study, we use a realistic tidal body forcing to excite inertial waves through the residual action of the equilibrium tide in the momentum equation for the waves. By performing 3D nonlinear hydrodynamical simulations in adiabatic and incompressible convective shells, we investigate how the addition of nonlinear terms affects the tidal flow properties, and the energy and angular momentum redistribution. In particular, we identify and justify the removal of terms responsible for unphysical angular momentum evolution observed in a previous numerical study. Within our new set-up, we observe the establishment of strong cylindrically-sheared zonal flows, which modify the tidal dissipation rates from prior linear theoretical predictions. We demonstrate that the effects of this differential rotation on the waves neatly explains the discrepancies between linear and nonlinear dissipation rates in many of our simulations. We also highlight the major role of both corotation resonances and parametric instabilities of inertial waves, which are observed for sufficiently high tidal forcing amplitudes or low viscosities, in affecting the tidal flow response.

astro-ph.SR↗

arXiv2022

A search for transit timing variations in the HATS-18 planetary system

HATS-18b is a transiting planet with a large mass and a short orbital period, and is one of the best candidates for the detection of orbital decay induced by tidal effects. We present extensive photometry of HATS-18 from which we measure 27 times of mid-transit. Two further transit times were measured from data from the Transiting Exoplanet Survey Satellite (TESS) and three more taken from the literature. The transit timings were fitted with linear and quadratic ephemerides and an upper limit on orbital decay was determined. This corresponds to a lower limit on the modified stellar tidal quality factor of $Q_\star^{\,\prime} > 10^{5.11 \pm 0.04}$. This is at the cusp of constraining the presence of enhanced tidal dissipation due to internal gravity waves. We also refine the measured physical properties of the HATS-18 system, place upper limits on the masses of third bodies, and compare the relative performance of TESS and the 1.54-m Danish Telescope in measuring transit times for this system.

astro-ph.EP↗

arXiv2022

Nonlinear tidal excitation of super-harmonic gravity waves in main-sequence stars in binary and exoplanetary systems

We study the role of nonlinear effects on tidally-excited internal gravity waves in stellar radiation zones in exoplanetary or binary systems. We are partly motivated to study tides due to massive short-period hot Jupiters, which preferentially orbit stars with convective cores, for which wave breaking near the stellar centre cannot operate. We develop a theory (and test it with numerical calculations) for the nonlinear excitation of super-harmonic "secondary" waves (with frequencies $2ω_p$) by a "primary" tidal wave (with frequency $ω_p$) near the interface between the radiation zone and convective envelope. These waves have the same horizontal phase speeds to leading order, and this nonlinear effect could contribute importantly to tidal dissipation if the secondary waves can efficiently damp the primary. We derive criteria involving the orbital and stellar parameters required to excite these secondary waves to large amplitudes using a local model of the radiative/convective interface, which we convert to apply to tides in a spherical star. We numerically evaluate the critical amplitudes required for this new nonlinear effect to become important using stellar models, comparing them to the "conventional" criteria for wave breaking in radiative cores and the application of WKBJ theory near convective cores. The criteria for this new effect are easier to satisfy than the conventional measures of nonlinearity in $1.4$ and $2M_\odot$ stars on the main-sequence. We predict nonlinear effects to be important even for planetary-mass companions around the latter, but this effect is probably less important in stars with radiative cores.

astro-ph.SR↗

arXiv2021

Nonlinear simulations of tides in the convective envelopes of low-mass stars and giant gaseous planets

In close two-body astrophysical systems, such as binary stars or Hot Jupiter systems, tidal interactions often drive dynamical evolution on secular timescales. Many host stars and presumably giant gaseous planets feature a convective envelope. Tidal flows generated therein by the tidal potential of the companion can be dissipated through viscous friction, leading to the redistribution and exchange of angular momentum within the convective shell and with the companion, respectively. In the tightest systems, nonlinear effects are likely to have a significant impact on the tidal dissipation and trigger differential rotation in the form of zonal flows, as has been shown in previous studies. In this context, we investigate how the addition of nonlinearities affect the tidal flow properties, and energy and angular momentum balances, using 3D nonlinear simulations of an adiabatic and incompressible convective shell. In our study, we have chosen a body forcing where the equilibrium tide (the quasi-hydrostatic tidal flow component) acts via an effective forcing to excite tidal inertial waves in a spherical shell. Within this set-up, we show new results for the amplitude of the energy stored in zonal flows, angular momentum evolution, and its consequences on tidal dissipation in the envelopes of low-mass stars and giant gaseous planets.

astro-ph.SR↗

arXiv2020

Realising a species-selective double well with multiple-radiofrequency-dressed potentials

Techniques to manipulate the individual constituents of an ultracold mixture are key to investigating impurity physics. In this work, we confine a mixture of the hyperfine ground states of Rb-87 in a double-well potential. The potential is produced by dressing the atoms with multiple radiofrequencies. The amplitude and phase of each frequency component of the dressing field are individually controlled to independently manipulate each species. Furthermore, we verify that our mixture of hyperfine states is collisionally stable, with no observable inelastic loss.

cond-mat.quant-gas↗

arXiv2017

Layered semi-convection and tides in giant planet interiors

Layered semi-convection could operate in giant planets, potentially explaining the constraints on the heavy elements distribution in Jupiter deduced recently from Juno observations, and contributing to Saturn's luminosity excess or the abnormally large radius of some hot Jupiters. This is a state consisting of density staircases, in which convective layers are separated by thin stably stratified interfaces. The efficiency of tidal dissipation in a planet depends strongly on its internal structure. It is crucial to improve our understanding of the mechanisms driving this dissipation, since it has important consequences to predict the long-term evolution of any planetary system. In this work, our goal is to study the resulting tidal dissipation when internal waves are excited by other bodies (such as the moons of giant planets) in a region of layered semi-convection. We find that the rates of tidal dissipation can be significantly enhanced in a layered semi-convective medium compared to a uniformly convective medium, especially in the astrophysically relevant sub-inertial frequency range. Thus, layered semi-convection is a possible candidate to explain high tidal dissipation rates recently observed in Jupiter and Saturn.

astro-ph.EP↗

arXiv2014

Nonlinear evolution of tidally forced inertial waves in rotating fluid bodies

We perform one of the first studies into the nonlinear evolution of tidally excited inertial waves in a uniformly rotating fluid body, exploring a simplified model of the fluid envelope of a planet (or the convective envelope of a solar-type star) subject to the gravitational tidal perturbations of an orbiting companion. Our model contains a perfectly rigid spherical core, which is surrounded by an envelope of incompressible uniform density fluid. The corresponding linear problem was studied in previous papers which this work extends into the nonlinear regime, at moderate Ekman numbers (the ratio of viscous to Coriolis accelerations). By performing high-resolution numerical simulations, using a combination of pseudo-spectral and spectral element methods, we investigate the effects of nonlinearities, which lead to time-dependence of the flow and the corresponding dissipation rate. Angular momentum is deposited non-uniformly, leading to the generation of significant differential rotation in the initially uniformly rotating fluid, i.e. the body does not evolve towards synchronism as a simple solid body rotator. This differential rotation modifies the properties of tidally excited inertial waves, changes the dissipative properties of the flow, and eventually becomes unstable to a secondary shear instability provided that the Ekman number is sufficiently small. Our main result is that the inclusion of nonlinearities eventually modifies the flow and the resulting dissipation from what linear calculations would predict, which has important implications for tidal dissipation in fluid bodies. We finally discuss some limitations of our simplified model, and propose avenues for future research to better understand the tidal evolution of rotating planets and stars.

astro-ph.EP↗

arXiv2011

Internal wave breaking and the fate of planets around solar-type stars

Internal gravity waves are excited at the interface of convection and radiation zones of a solar-type star by the tidal forcing of a short-period planet. The fate of these waves as they approach the centre of the star depends on their amplitude. We discuss the results of numerical simulations of these waves approaching the centre of a star, and the resulting evolution of the spin of the central regions of the star, and the orbit of the planet. If the waves break, we find efficient tidal dissipation, which is not present if the waves perfectly reflect from the centre. This highlights an important amplitude dependence of the (stellar) tidal quality factor Q', which has implications for the survival of planets on short-period orbits around solar-type stars, with radiative cores.

astro-ph.EP↗

arXiv2011

Three-dimensional simulations of internal wave breaking and the fate of planets around solar-type stars

We study the fate of internal gravity waves approaching the centre of a non-rotating solar-type star, by performing 3D numerical simulations using a Boussinesq-type model. These waves are excited at the top of the radiation zone by the tidal forcing of a short-period planet on a circular, coplanar orbit. This extends previous work done in 2D by Barker & Ogilvie. We first derive a linear wave solution, which is not exact in 3D; however, the reflection of ingoing waves from the centre is close to perfect for moderate amplitude waves. Waves with sufficient amplitude to cause isentropic overturning break, and deposit their angular momentum near the centre. This forms a critical layer, at which the angular velocity of the flow matches the orbital angular frequency of the planet. This efficiently absorbs ingoing waves, and spins up the star from the inside out, while the planet spirals into the star. We also perform numerical integrations to determine the linearised adiabatic tidal response throughout the star, for solar-type stellar models with masses in the range 0.5 < m_star/M_sun < 1.1, throughout their main sequence lifetimes. The aim is to study the launching region for these waves at the top of the radiation zone in more detail, and to determine the accuracy of a semi-analytic approximation for the tidal torque on the star, that was derived under the assumption that all ingoing wave angular momentum is absorbed in a critical layer. The main conclusions are that this nonlinear mechanism of tidal dissipation could provide an explanation for the survival of all short-period extrasolar planets observed around FGK stars, while it predicts the destruction of more massive planets. This work provides further support for the model outlined in a previous paper by Barker & Ogilvie, and makes predictions that will be tested by ongoing observational studies, such as WASP and Kepler.

astro-ph.EP↗

arXiv2010

On internal wave breaking and tidal dissipation near the centre of a solar-type star

We study the fate of internal gravity waves, which are excited by tidal forcing by a short-period planet at the interface of convection and radiation zones, approaching the centre of a solar-type star. We study at what amplitude these wave are subject to instabilities. These instabilities lead to wave breaking whenever the amplitude exceeds a critical value. Below this value, the wave reflects perfectly from the centre of the star. Wave breaking results in spinning up the central regions of the star, and the formation of a critical layer, which acts as an absorbing barrier for ingoing waves. As these waves are absorbed, the star is spun up from the inside out. This results in an important amplitude dependence of the tidal quality factor Q'. If the tidal forcing amplitude exceeds the value required for wave breaking, efficient dissipation results over a continuous range of tidal frequencies, leading to Q' \approx 10^5 (P/1day)^(8/3), for the current Sun. This varies by less than a factor of 5 throughout the range of G and K type main sequence stars, for a given orbit. We predict fewer giant planets with orbital periods of less than about 2 days around such stars, if they cause breaking at the centre, due to the efficiency of this process. This mechanism would, however, be ineffective in stars with a convective core, such as WASP-18, WASP-12 and OGLE-TR-56, perhaps partly explaining the survival of their close planetary companions.

astro-ph.EP↗

arXiv2009

Effects of Magnetic Braking and Tidal Friction on Hot Jupiters

Tidal friction is thought to be important in determining the long-term spin-orbit evolution of short-period extrasolar planetary systems. Using a simple model of the orbit-averaged effects of tidal friction Eggleton, Kiseleva & Hut (1998), we analyse the effects of the inclusion of stellar magnetic braking on the evolution of such systems. A phase-plane analysis of a simplified system of equations, including only the stellar tide together with a model of the braking torque proposed by Verbunt & Zwaan (1981), is presented. The inclusion of stellar magnetic braking is found to be extremely important in determining the secular evolution of such systems, and its neglect results in a very different orbital history. We then show the results of numerical integrations of the full tidal evolution equations, using the misaligned spin and orbit of the XO-3 system as an example, to study the accuracy of simple timescale estimates of tidal evolution. We find that it is essential to consider coupled evolution of the orbit and the stellar spin in order to model the behaviour accurately. In addition, we find that for typical Hot Jupiters the stellar spin-orbit alignment timescale is of the same order as the inspiral time, which tells us that if a planet is observed to be aligned, then it probably formed coplanar. This reinforces the importance of Rossiter-McLaughlin effect observations in determining the degree of spin-orbit alignment in transiting systems.

astro-ph.EP↗

arXiv2009

On the tidal evolution of Hot Jupiters on inclined orbits

Tidal friction is thought to be important in determining the long-term spin-orbit evolution of short-period extrasolar planetary systems. Using a simple model of the orbit-averaged effects of tidal friction, we study the evolution of close-in planets on inclined orbits, due to tides. We analyse the effects of the inclusion of stellar magnetic braking by performing a phase-plane analysis of a simplified system of equations, including the braking torque. The inclusion of magnetic braking is found to be important, and its neglect can result in a very different system history. We then present the results of numerical integrations of the tidal evolution equations, where we find that it is essential to consider coupled evolution of the orbital and rotational elements, including dissipation in both the star and planet, to accurately model the evolution. The main result of our integrations is that for typical Hot Jupiters, tidal friction aligns the stellar spin with the orbit on a similar time as it causes the orbit to decay. This means that if a planet is observed to be aligned, then it probably formed coplanar. This reinforces the importance of Rossiter-McLaughlin effect observations in determining the degree of spin-orbit alignment in transiting systems. We apply these results to the XO-3 system, and constrain the tidal quality factors Q' in both the star and planet in this system. Using a model in which inertial waves are excited by tidal forcing in the outer convective envelope and dissipated by turbulent viscosity, we calculate Q' for a range of F-star models, and find it to vary considerably within this class of stars. This means that assuming a single Q' applies to all stars is probably incorrect. We propose an explanation for the survival of WASP-12 b & OGLE-TR-56 b, in terms of weak dissipation in the star.

astro-ph.EP↗