ABSTRACT
The interaction between equilibrium tides and convection in stellar envelopes is often considered important for tidal evolution in close binary and extrasolar planetary systems. Its ...efficiency for fast tides has however long been controversial, when the tidal frequency exceeds the turnover frequency of convective eddies. Recent numerical simulations indicate that convection can act like an effective viscosity which decays quadratically with tidal frequency for fast tides, resulting in inefficient dissipation in many applications involving pre- and main-sequence stars and giant planets. A new idea was however recently proposed by Terquem (2021), who suggested Reynolds stresses involving correlations between tidal flow components dominate the interaction instead of correlations between convective flow components as usually assumed. They further showed that this can potentially significantly enhance tidal dissipation for fast tides in many applications. Motivated by the importance of this problem for tidal dissipation in stars and planets, we directly compute this new term using analytical arguments and global spherical simulations using Boussinesq and anelastic hydrodynamic models. We demonstrate that the new term proposed by Terquem vanishes identically for equilibrium tides interacting with convection in both Boussinesq and anelastic models; it is therefore unlikely to contribute to tidal dissipation in stars and planets.
We study the fate of internal gravity waves approaching the centre of an initially non-rotating solar-type star, by performing three-dimensional 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 two dimensions by Barker & Ogilvie. We first derive a linear wave solution, which is not exact in three dimensions; 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 linearized adiabatic tidal response throughout the star, in a wide range of solar-type stellar models with masses in the range 0.5 ≤m
★/M⊙≤ 1.1, throughout their main-sequence lifetimes. The aim is to study the influence of 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, which was derived under the assumption that all ingoing wave angular momentum is absorbed in a critical layer.
The main conclusion of this work is that this non-linear 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.
Abstract
We study how stably stratified or semiconvective layers alter tidal dissipation rates associated with the generation of inertial, gravito-inertial, interfacial, and surface gravity waves in ...rotating giant planets. We explore scenarios in which stable (nonconvective) layers contribute to the high rates of tidal dissipation observed for Jupiter and Saturn in our solar system. Our model is an idealized spherical Boussinesq system incorporating Coriolis forces to study effects of stable stratification and semiconvective layers on tidal dissipation. Our detailed numerical calculations consider realistic tidal forcing and compute the resulting viscous and thermal dissipation rates. The presence of an extended stably stratified fluid core significantly enhances tidal wave excitation of both inertial waves (due to rotation) in the convective envelope and gravito-inertial waves in the dilute core. We show that a sufficiently strongly stratified fluid core enhances inertial wave dissipation in a convective envelope much like a solid core does. We demonstrate that efficient tidal dissipation rates (and associated tidal quality factors
Q
′
)—sufficient to explain the observed migration rates of Saturn's moons—are predicted at the frequencies of the orbiting moons due to the excitation of inertial or gravito-inertial waves in our models with stable layers (without requiring resonance locking). Stable layers could also be important for tidal evolution of hot and warm Jupiters and hot Neptunes, providing efficient tidal circularization rates. Future work should study more sophisticated planetary models that also account for magnetism and differential rotation, as well as the interaction of inertial waves with turbulent convection.
ABSTRACT
We simulate the propagation and dissipation of tidally induced non-linear gravity waves in the cores of solar-type stars. We perform hydrodynamical simulations of a previously developed ...Boussinesq model using a spectral-element code to study the stellar core as a wave cavity that is periodically forced at the outer boundary with a given azimuthal wavenumber and an adjustable frequency. For low-amplitude forcing, the system exhibits resonances with standing g modes at particular frequencies, corresponding to a situation in which the tidal torque is highly frequency-dependent. For high-amplitude forcing, the excited waves break promptly near the centre and spin up the core so that subsequent waves are absorbed in an expanding critical layer (CL), as found in previous work, leading to a tidal torque with a smooth frequency-dependence. For intermediate-amplitude forcing, we find that linear damping of the waves gradually spins up the core such that the resonance condition can be altered drastically. The system can evolve towards or away from g-mode resonances, depending on the difference between the forcing frequency and the closest eigenfrequency. Eventually, a CL forms and absorbs the incoming waves, leading to a situation similar to the high-amplitude case in which the waves break promptly. We study the dependence of this process on the forcing amplitude and frequency, as well as on the diffusion coefficients. We emphasize that the small Prandtl number in the centre of solar-like stars facilitates the development of a differentially rotating core owing to the non-linear feedback of waves. Our simulations and analysis reveal that this important mechanism may drastically change the phase of gravity waves and thus the classical picture of resonance locking in solar-type stars needs to be revised.
Tidally distorted rotating stars and gaseous planets are subject to a well-known linear fluid instability - the elliptical instability. It has been proposed that this instability might drive enough ...energy dissipation to solve the long-standing problem of the origin of tidal dissipation in stars and planets. But the non-linear outcome of the elliptical instability has yet to be investigated in the parameter regime of interest, and the resulting turbulent energy dissipation has not yet been quantified. We do so by performing three-dimensional hydrodynamical simulations of a small patch of a tidally deformed fluid planet or star subject to the elliptical instability. We show that when the tidal deformation is weak, the non-linear outcome of the instability leads to the formation of long-lived columnar vortices aligned with the axis of rotation. These vortices shut off the elliptical instability, and the net result is insufficient energy dissipation to account for tidal dissipation. However, further work is required to account for effects neglected here, including magnetic fields, turbulent convection and realistic boundary conditions.
ABSTRACT
We present numerical simulations, using two complementary set-ups, of rotating Boussinesq thermal convection in a three-dimensional Cartesian geometry with misaligned gravity and rotation ...vectors. This model represents a small region at a non-polar latitude in the convection zone of a star or planet. We investigate the effects of rotation on the bulk properties of convection at different latitudes, focusing on determining the relation between the heat flux and temperature gradient. We show that our results may be interpreted using rotating mixing length theory (RMLT). The simplest version of RMLT (due to Stevenson) considers the single mode that transports the most heat. This works reasonably well in explaining our results, but there is a systematic departure from these predictions (up to approximately $30{{\ \rm per\ cent}}$ in the temperature gradient) at mid-latitudes. We develop a more detailed treatment of RMLT that includes the transport afforded by multiple modes, and we show that this accounts for most of the systematic differences. We also show that convectively generated zonal flows and meridional circulations are produced in our simulations, and that their properties depend strongly on the dimensions of the box. These flows also affect the heat transport, contributing to departures from RMLT at some latitudes. However, we find the theoretical predictions of the multi-mode theory for the mid-layer temperature gradient, the root-mean-square (rms) vertical velocity, the rms temperature fluctuation, and the spatial spectrum of the heat transport at different latitudes are all in reasonably good agreement with our numerical results when zonal flows are small.
Searching for Rapid Orbital Decay of WASP-18b Wilkins, Ashlee N.; Delrez, Laetitia; Barker, Adrian J. ...
Astrophysical journal. Letters,
02/2017, Letnik:
836, Številka:
2
Journal Article, Web Resource
Recenzirano
Odprti dostop
The WASP-18 system, with its massive and extremely close-in planet, WASP-18b (Mp = 10.3MJ, a = 0.02 au, P = 22.6 hr), is one of the best-known exoplanet laboratories to directly measure Q′, the ...modified tidal quality factor and proxy for efficiency of tidal dissipation, of the host star. Previous analysis predicted a rapid orbital decay of the planet toward its host star that should be measurable on the timescale of a few years, if the star is as dissipative as is inferred from the circularization of close-in solar-type binary stars. We have compiled published transit and secondary eclipse timing (as observed by WASP, TRAPPIST, and Spitzer) with more recent unpublished light curves (as observed by TRAPPIST and Hubble Space Telescope) with coverage spanning nine years. We find no signature of a rapid decay. We conclude that the absence of rapid orbital decay most likely derives from Q′ being larger than was inferred from solar-type stars and find that Q′ ≥ 1 × 106, at 95% confidence; this supports previous work suggesting that F stars, with their convective cores and thin convective envelopes, are significantly less tidally dissipative than solar-type stars, with radiative cores and large convective envelopes.
ABSTRACT
Tidal dissipation in star–planet systems can occur through various mechanisms, among which is the elliptical instability. This acts on elliptically deformed equilibrium tidal flows in ...rotating fluid planets and stars, and excites inertial waves in convective regions if the dimensionless tidal amplitude (ϵ) is sufficiently large. We study its interaction with turbulent convection, and attempt to constrain the contributions of both elliptical instability and convection to tidal dissipation. For this, we perform an extensive suite of Cartesian hydrodynamical simulations of rotating Rayleigh–Bénard convection in a small patch of a planet. We find that tidal dissipation resulting from the elliptical instability, when it operates, is consistent with ϵ3, as in prior simulations without convection. Convective motions also act as an effective viscosity on large-scale tidal flows, resulting in continuous tidal dissipation (scaling as ϵ2). We derive scaling laws for the effective viscosity using (rotating) mixing-length theory, and find that they predict the turbulent quantities found in our simulations very well. In addition, we examine the reduction of the effective viscosity for fast tides, which we observe to scale with tidal frequency (ω) as ω−2. We evaluate our scaling laws using interior models of Hot Jupiters computed with mesa. We conclude that rotation reduces convective length-scales, velocities, and effective viscosities (though not in the fast tides regime). We estimate that elliptical instability is efficient for the shortest period Hot Jupiters, and that effective viscosity of turbulent convection is negligible in giant planets compared with inertial waves.
We study the fate of internal gravity waves approaching the centre of an initially non-rotating solar-type star, primarily using two-dimensional numerical simulations based on a cylindrical model. A ...train of internal gravity waves is excited by tidal forcing at the interface between the convection and radiation zones of such a star. We derive a Boussinesq-type model of the central region of a star and find a non-linear wave solution that is steady in the frame rotating with the angular pattern speed of the tidal forcing. We then use spectral methods to integrate the equations numerically, with the aim of studying at what amplitude the wave is subject to instabilities. These instabilities are found to lead to wave breaking whenever the amplitude exceeds a critical value. Below this critical value, the wave reflects perfectly from the centre of the star. Wave breaking leads to mean flow acceleration, which corresponds to a spin-up of the central region of the star, and the formation of a critical layer, which acts as an absorbing barrier for subsequent ingoing waves. As these waves continue to be absorbed near the critical layer, the star is spun up from the inside out. Our results point to an important amplitude dependence of the (modified) tidal quality factor Q′, since non-linear effects are responsible for dissipation at the centre of the star. If the amplitude of the tidal forcing exceeds the critical amplitude for wave breaking to occur, then this mechanism produces efficient dissipation over a continuous range of tidal frequencies. This requires , for a planet of mass mp in an orbit of period P around the current Sun, neglecting stellar rotation. However, this criterion depends strongly on the strength of the stable stratification at the centre of the star, and so it depends on stellar mass and main-sequence age. If breaking occurs, we find , for the current Sun. This varies by no more than a factor of 5 throughout the range of solar-type stars with masses between 0.5 and 1.1 M⊙, for fixed orbital parameters. This estimate of Q′ is therefore quite robust and can be reasonably considered to apply to all solar-type main-sequence stars, if this mechanism operates. The strong frequency dependence of the resulting dissipation means that this effect could be very important in determining the fate of close-in giant planets around G and K stars. We predict fewer giant planets with orbital periods of less than about 2 d around such stars if they cause breaking at the centre, due to the efficiency of this process. Even if the waves are of too low amplitude to initiate breaking, radiative damping could, in principle, lead to a gradual spin-up of the stellar centre and to the formation of a critical layer. This process could provide efficient tidal dissipation in solar-type stars perturbed by less massive companions, but it may be prevented by effects that resist the development of differential rotation. These mechanisms 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.
On the orbital decay of the gas giant Kepler-1658b Barker, Adrian J; Efroimsky, Michael; Makarov, Valeri V ...
Monthly notices of the Royal Astronomical Society,
01/2024, Letnik:
527, Številka:
3
Journal Article
Recenzirano
Odprti dostop
ABSTRACT
The gas giant Kepler-1658b has been inferred to be spiralling into its sub-giant F-type host star Kepler-1658a (KOI-4). The measured rate of change of its orbital period is $\stackrel{\bf ...\centerdot }{\textstyle {P}}_{\rm orb}\, =\, -\, 131^{+20}_{-22}\,\rm {ms\,yr^{ -1}}$, which can be explained by tidal dissipation in the star if its modified tidal quality factor is as low as $Q^{\, \prime }\approx 2.50\times {10}^{4}$. We explore whether this could plausibly be consistent with theoretical predictions based on applying up-to-date tidal theory in stellar models (varying stellar mass, age, and metallicity) consistent with our newly derived observational constraints. In most of our models matching the combined constraints on the stellar effective temperature and radius, the dissipation in the star is far too weak, capable of providing $Q^{\, \prime }\gtrsim 10^9$, hence contributing negligibly to orbital evolution. Using only constraints on the stellar radius, efficient tidal dissipation sufficient to explain observations is possible due to inertial waves in the convective envelope during the sub-giant phase, providing $Q^{\, \prime }\sim 10^4$, but this period in the evolution is very short-lived (shorter than 102 yr in our models). We show that dissipation in the planet is capable of explaining the observed $\dot{P}_\mathrm{orb}$ only if the planet rotates non-synchronously. Tidally induced pericentre precession is a viable explanation if the periastron argument is near 3π/2 and the planet's quadrupolar Love number is above 0.26. Further observations constraining the stellar and planetary properties in this system have the exciting potential to test tidal theories in stars and planets.
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