Tidal Dissipation in a Homogeneous Spherical Body. 2. Three Examples: Mercury, IO, and Kepler-10 b
NAVAL OBSERVATORY WASHINGTON DC
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In Efroimsky Makarov Paper I, we derived from the first principles a formula for the tidal heating rate in a homogeneous sphere, compared it with the previously used formulae, and noted the differences. Now we present case studies Mercury, Kepler-10 b, and a triaxial Io. A sharp frequency dependence of k sub2 Q near spin orbit resonances yields a sharp dependence of k sub2 Q and, therefore, of tidal heating upon the spin rate. Thereby physical libration plays a major role in tidal heating of synchronously rotating planets. The magnitude of libration in the spin rate being defined by the planet s triaxiality, the latter becomes a factor determining the dissipation rate. Other parameters equal, a strongly triaxial synchronized body generates more heat than a similar body of a more symmetrical shape. After an initially triaxial object melts and loses its triaxiality, dissipation becomes less intensive the body can solidify, with the tidal bulge becoming a new figure with triaxiality lower than the original. We derive approximate expressions for the dissipation rate in a Maxwell planet with the Maxwell time longer than the inverse tidal frequency. The expressions derived pertain to the 11 and 32 resonances and a nonresonant case so they are applicable to most close-in super-Earths detected. In these planets, the heating outside synchronism is weakly dependent on the eccentricity and obliquity, provided both these parameters s values are moderate. According to our calculation, Kepler-10 b could hardly survive the intensive tidal heating without being synchronized, circularized, and reshaped through a complete or partial melt-down.
- Celestial Mechanics