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

In Efroimsky and 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 {sub 2}/Q near spin-orbit resonances yields a sharp dependence of k {sub 2}/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 1:1 and 3:2 resonances and a nonresonant case; somore » 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.« less
Authors:
;  [1]
  1. US Naval Observatory, 3450 Massachusetts Avenue NW, Washington, DC 20392 (United States)
Publication Date:
OSTI Identifier:
22370357
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 795; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; APPROXIMATIONS; COMPARATIVE EVALUATIONS; EVOLUTION; HEATING RATE; MERCURY; ORBITS; PLANETS; RESONANCE; SATELLITES; SPHERICAL CONFIGURATION; SPIN; STABILITY