Tidal dissipation in a homogeneous spherical body. II. Three examples: Mercury, Io, and Kepler-10 b

Abstract

In Efroimsky & Makarov (2014), we derived from the first principles a formula for the tidal heating rate in a tidally perturbed homogeneous sphere. We compared it with the formulae used in the literature, and pointed out the differences. Using this result, we now present three case studies - Mercury, Kepler-10b, and a triaxial Io. A very sharp frequency-dependence of k2/Q near spin-orbit resonances yields a similarly sharp dependence of k2/Q on the spin rate. This indicates that physical libration may play a major role in tidal heating of synchronously rotating bodies. The magnitude of libration in the spin rate being defined by the planet's triaxiality, the latter should be a factor determining the dissipation rate. Other parameters equal, a synchronously rotating body with a stronger triaxiality should generate more heat than a similar body of a more symmetrical shape. Further in the paper, we discuss scenarios where initially triaxial objects melt and lose their triaxiality. Thereafter, dissipation in them becomes less intensive; so the bodies freeze. The tidal bulge becomes a new permanent figure, with a new triaxiality lower than the original. In the paper, we also derive simplified, approximate expressions for dissipation rate in a rocky planet of the Maxwell rheology, with a not too small Maxwell time. The three expressions derived pertain to the cases of a synchronous spin, a 3:2 resonance, and a nonresonant rotation; so they can be applied to most close-in super-Earth exoplanets detected thus far. In such bodies, the rate of tidal heating outside of synchronous rotation is weakly dependent on the eccentricity and obliquity, provided both these parameters are small or moderate. According to our calculation, Kepler-10b could hardly survive the great amount of tidal heating without being synchronised, circularised and also reshaped through a complete or partial melt-down.

References in corpus (7)

• KEPLER's First Rocky Planet: Kepler-10b
• Long-term tidal evolution of short-period planets with companions
• Tidal Heating of Extra-Solar Planets
• The Kepler-10 planetary system revisited by HARPS-N: A hot rocky world and a solid Neptune-mass planet
• Dynamical evolution and spin-orbit resonances of potentially habitable exoplanets. The case of GJ 581d
• Mercury's capture into the 3/2 spin-orbit resonance including the effect of core-mantle friction
• Bodily tides near the 1:1 spin-orbit resonance. Correction to Goldreich's dynamical model

Cited by in corpus (5)

• Exomoons in the habitable zones of M dwarfs
• Prolonged sub-luminous state of the new transitional pulsar candidate CXOU J110926.4-650224
• The Short Rotation Period of Hi'iaka, Haumea's Largest Satellite
• Tidally Heated Exomoons around $\epsilon$ Eridani b: Observability and prospects for characterization
• Initial conditions for tidal synchronisation of a planet by its moon