Tidal dissipation due to the elliptical instability and turbulent viscosity in convection zones in rotating giant planets and stars

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 ($\epsilon$) 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 ${\epsilon }^3$, 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 ${\epsilon }^2$). 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 ($\omega$) as ${\omega }^{-2}$. 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.

arXiv comment23 pages, 15 figures, 2 tables; accepted for publication in MNRAS

References in corpus (68)

• Modules for Experiments in Stellar Astrophysics (MESA)
• Modules for Experiments in Stellar Astrophysics (MESA): Giant Planets, Oscillations, Rotation, and Massive Stars
• Modules for Experiments in Stellar Astrophysics (MESA): Binaries, Pulsations, and Explosions
• Modules for Experiments in Stellar Astrophysics (MESA): Convective Boundaries, Element Diffusion, and Massive Star Explosions
• Modules for Experiments in Stellar Astrophysics (MESA): Pulsating Variable Stars, Rotation, Convective Boundaries, and Energy Conservation
• Modules for Experiments in Stellar Astrophysics (MESA): Time-Dependent Convection, Energy Conservation, Automatic Differentiation, and Infrastructure
• Tidal dissipation in stars and giant planets
• Tidal dissipation in rotating giant planets
• Impact of dimensionless numbers on the efficiency of MRI-induced turbulent transport
• The Exoplanet Orbit Database II: Updates to exoplanets.org
• Strong tidal dissipation in Saturn and constraints on Enceladus' thermal state from astrometry
• Resonance locking as the source of rapid tidal migration in the Jupiter and Saturn moon systems
• WASP-19b: the shortest period transiting exoplanet yet discovered
• On the tidal interaction of a solar-type star with an orbiting companion: Excitation of g mode oscillation and orbital evolution
• Spin-Orbit Evolution Of Short-Period Planets
• New constraints on Saturn's interior from Cassini astrometric data
• Scaling regimes in spherical shell rotating convection
• Tides in rotating barotropic fluid bodies: the contribution of inertial waves and the role of internal structure
• Departure from the constant-period ephemeris for the transiting exoplanet WASP-12 b
• Magnetic field strengths of hot Jupiters from signals of star-planet interactions
• Inverse cascade and symmetry breaking in rapidly-rotating Boussinesq convection
• Tidal dissipation in evolving low-mass and solar-type stars with predictions for planetary orbital decay
• Large-scale vortices in rapidly rotating Rayleigh-Bénard convection
• Tidal Synchronization and Differential Rotation of Kepler Eclipsing Binaries
• Fast Tides in Slow Stars: the Efficiency of Eddy Viscosity
• Convective Lengthscale in Planetary Cores
• The continuing search for evidence of tidal orbital decay of hot Jupiters
• On the interaction between tides and convection
• Turbulent resistivity evaluation in MRI generated turbulence
• The Challenge of Forming a Fuzzy Core in Jupiter
• On Dissipation inside Turbulent Convection Zones from 3D Simulations of Solar Convection
• Revelations on Jupiter's Formation, Evolution and Interior: Challenges from Juno Results
• Decaying Orbit of the Hot Jupiter WASP-12b: Confirmation with TESS Observations
• Nonlinear evolution of the tidal elliptical instability in gaseous planets and stars
• Theory and simulations of rotating convection
• Intertial wave turbulence driven by elliptical instability
• Direct Calculation of the Turbulent Dissipation Efficiency in Anelastic Convection
• Convective turbulent viscosity acting on equilibrium tidal flows: new frequency scaling of the effective viscosity
• Elliptical instability in hot Jupiter systems
• Dissipation Efficiency in Turbulent Convective Zones in Low Mass Stars
• Stable stratification promotes multiple zonal jets in a turbulent Jovian dynamo model
• Detection of the tidal deformation of WASP-103b at $3\sigma$ with CHEOPS
• Nonlinear tides in a homogeneous rotating planet or star: global simulations of the elliptical instability
• Evolution of star-planet systems under magnetic braking and tidal interaction
• Tidal instability in a rotating and differentially heated ellipsoidal shell
• Nonlinear evolution of the elliptical instability in the presence of weak magnetic fields
• Turbulent viscosity acting on the equilibrium tidal flow in convective stars
• The impact of rotation on turbulent tidal friction in stellar and planetary convective regions
• Convection with Misaligned Gravity and Rotation: Simulations and Rotating Mixing Length Theory
• On a new formulation for energy transfer between convection and fast tides with application to giant planets and solar type stars
• Tidal flows with convection: frequency-dependence of the effective viscosity and evidence for anti-dissipation
• Libration driven elliptical instability
• Experimental observation of the geostrophic turbulence regime of rapidly rotating convection
• WIYN Open Cluster Study. LXXVII. Radial-Velocity Measurements and Spectroscopic Binary Orbits in the Open Cluster NGC 7789
• Efficiency of tidal dissipation in slowly rotating fully convective stars or planets
• On the interaction between fast tides and convection
• Dynamical tides in Jupiter and other rotationally flattened planets and stars with stable stratification
• Towards a new era in giant exoplanet characterisation
• Nonlinear tides in a homogeneous rotating planet or star: global modes and elliptical instability
• The Radius and Entropy of a Magnetized, Rotating Fully-convective Star: Analysis With Depth-dependent Mixing Length Theories
• Dynamical tides in Jupiter and the role of interior structure
• Wave propagation in semi-convective regions of giant planets
• The effects of nonlinearities on tidal flows in the convective envelopes of rotating stars and planets in exoplanetary systems
• Layered semi-convection and tides in giant planet interiors - II. Tidal dissipation
• Magnetic effect on equilibrium tides and its influence on the orbital evolution of binary systems
• Tidal dissipation in stratified and semi-convective regions of giant planets
• Magnetic quenching of the inverse cascade in rapidly rotating convective turbulence
• The interactions of the elliptical instability and convection

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