Tidal dissipation modelling in gaseous giant planets at the time of space missions

Gaseous giant planets (Jupiter and Saturn in our solar system and hot Jupiters around other stars) are turbulent rotating magnetic objects that have strong and complex interactions with their environment (their moons in the case of Jupiter and Saturn and their host stars in the case of hot Jupiters/Saturns). In such systems, the dissipation of tidal waves excited by tidal forces shape the orbital architecture and the rotational dynamics of the planets.

During the last decade, a revolution has occurred for our understanding of tides in these systems. First, Lainey et al. (2009, 2012, 2017) have measured tidal dissipation stronger by one order of magnitude than expected in Jupiter and Saturn. Second, unexplained broad diversity of orbital architectures and large radius of some hot Jupiters are observed in exoplanetary systems. Finally, new constraints obtained thanks to Kepler/K2 and TESS indicate that tidal dissipation in gaseous giant exoplanets is weaker than in Jupiter and in Saturn (Ogilvie 2014, Van Eylen et al. 2018, Huber et al. 2019).

Furthermore, the space mission JUNO and the grand finale of the CASSINI mission have revolutionized our knowledge of the interiors of giant planets. We now know, for example, that Jupiter is a very complex planet: it is a stratified planet with, from the surface to the core, a differentially rotating convective envelope, a first mixing zone (with stratified convection), a uniformly rotating magnetised convective zone, a second magnetized mixing zone (the diluted core, potentially in stratified convection) and a solid core (Debras & Chabrier 2019). So far, tides in these planets have been studied by assuming a simplified internal structure with a stable rocky and icy core (Remus et al. 2012, 2015) and a deep convective envelope surrounded by a thin stable atmosphere (Ogilvie & Lin 2004) where mixing processes, differential rotation and magnetic field were completely neglected.

Our objective is thus to predict tidal dissipation using internal structure models, which agree with these last observational constrains. In this work, we build a new ab-initio model of tidal dissipation in giant planets that coherently takes into account the interactions of tidal waves with their complex stratification induced by the mixing of heavy elements, their zonal winds, and (dynamo) magnetic fields. This model is a semi-global model in the planetary equatorial plane. We study the linear excitation of tidal magneto-gravito-inertial progressive waves and standing modes. We take into account the buoyancy, the compressibility, the Coriolis acceleration (including differential rotation), and the Lorentz force. The tidal waves are submitted to the different potential dissipative processes: Ohmic, thermal, molecular diffusivities, and viscosity. We here present the general formalism and the potential regimes of parameters that should be explored. The quantities of interest such as tidal torque, dissipation, and heating are derived. This will pave the way for full 3D numerical simulations that will take into account complex internal structure and dynamics of gaseous giant (exo-)planets in spherical/spheroidal geometry.