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

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  • 30 July 2004
Abstract
Having studied the structure and properties of inertial-modes in a neutrally buoyant, uniformly rotating sphere (Wu 2004), we examine 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. We find that tidal dissipation by inertial-modes is three to five orders of magnitude stronger than that caused by the equilibrium tide. The uncertainty mostly arises from uncertainty in the tidal coupling, which depends on the density structure inside Jupiter. In the best-case scenario where hydrogen undergoes a first-order phase transition, the tidal quality factor Q ~ 10^7, approaching the empirically inferred Q value for Jupiter. The nominal value of Q is determined by intermediate-order inertial-modes that satisfy delta omega ~ gamma, where delta omega is the typical frequency off-resonance and gamma the turbulent damping rate. These modes can be excited to surface displacement amplitude of order 10^3 cm. Dissipation of inertial-modes occur very close to the surface in a narrow latitudinal zone (the 'singularity belt'). We 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, and compare our results with those by Ogilvie & Lin (2004). The inertial-mode theory can be applied to extra-solar jupiters, solar-type binaries and other objects where the mechanism for tidal dissipation is not well understood.

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