Tidal dissipation and spin-orbit alignment due to the precessional instability in convection zones in rotating giant planets and stars

Abstract

Tidal dissipation in star-planet systems occurs through various mechanisms, including the precessional instability. This is an instability of laminar flows (``Poincar\'{e} flows") forced by axial precession of a rotating, oblate, spin-orbit misaligned fluid planet or star, which excites inertial waves in convective regions if the dimensionless precession rate (``Poincar\'{e} number" $\mathrm{Po}$) is sufficiently large. We constrain the contribution of the precessional instability to tidal dissipation and heat transport, using Cartesian hydrodynamical simulations in a small patch of a planet, and study its interaction with turbulent convection, modelled as rotating Rayleigh-B\'{e}nard convection. The precessional instability without convection results in laminar flow at low values and turbulent flow at sufficiently high values of $\mathrm{Po}$. The associated tidal dissipation rate scales as $\mathrm{Po}^2$ and $\mathrm{Po}^3$ in each regime, respectively. With convection, the Poincar\'e number at which turbulent flow is achieved shifts to lower values for stronger convective driving. Convective motions also act on large-scale tidal flows like an effective viscosity, resulting in continuous tidal dissipation (scaling as $\mathrm{Po}^2$), which obfuscates or suppresses tidal dissipation due to precessional instability. The effective viscosities obtained agree with scaling laws previously derived using (rotating) mixing-length theory. By evaluating our scaling laws using interior models of Hot Jupiters, we find that the precessional instability is significantly more efficient than the effective viscosity of convection. The former drives alignment in 1 Gyr for a Jupiter-like planet orbiting within 23 days. Linearly excited inertial waves can be even more effective for wider orbits, aligning spins for orbits within 53-142 days.