Origin of Tidal Dissipation in Jupiter: Ii. the Value of Q

Having studied the structure and properties of inertial-modes in a neutrally buoyant, uniformly rotating sphere (Wu 2004), we examine here their effect on tidal dissipation in Jupiter. The rate of tidal dissipation caused by resonantly excited inertial-modes depends on the following three parameters: how well coupled inertial-modesare to the tidal potential, how strongly dissipated inertial-modes are by the turbulent viscosity, and how densely distributed the inertial-modes are in frequency. Our analytical and numerical study based on realistic Jupiter models lead us to conclude that, tidal dissipation by inertial-modes is three to five orders of magnitude stronger than that caused by the equilibrium tide. The uncertainty in this result mostly arises from uncertainty in the tidal coupling, which depends on the density structure inside Jupiter. In the best-case scenario we have studied, where hydrogen undergoes a first-order molecular/metallic phase transition, the rate of tidal dissipation corresponds to a tidal quality factor Q ∼ 10, approaching the empirically inferred Q value for Jupiter. We find that as a function of tidal frequency, the tidal Q value exhibits large fluctuations, but its nominal value is determined by inertial-modes that satisfy δω ∼ γ, where δω is the typical frequency off-resonance and γ the turbulent damping rate. These are intermediate order inertial-modes with wavenumbers λ ∼ 60 and they can be excited to surface displacement amplitudes of order 10 cm. Dissipation of inertial-modes occur very close to the surface in a narrow latitudinal zone (the ’singularity belt’). We therefore expect the tidal luminosity to escapes easily from the planet. We discuss effects of the solid core, radiative atmosphere and prescription for turbulent viscosity on our conclusions. We also compare our results with those from a competing work by (Ogilvie & Lin 2004). We hope to apply the inertial-mode theory to extra-solar jupiters, solar-type binaries and other objects where the mechanism for tidal dissipation is not well understood. Subject headings: hydrodynamics — waves — planets and satellites: individual (Jupiter) — stars: oscillations — stars: rotation — turbulence