Strong Tidal Dissipation in Saturn and Constraints on Enceladus' Thermal State from Astrometry
Abstract
Tidal interactions between Saturn and its satellites play a crucial role in both the orbital migration of the satellites and the heating of their interiors. Therefore, constraining the tidal dissipation of Saturn (here the ratio k _{2}/Q) opens the door to the past evolution of the whole system. If Saturn's tidal ratio can be determined at different frequencies, it may also be possible to constrain the giant planet's interior structure, which is still uncertain. Here, we try to determine Saturn's tidal ratio through its current effect on the orbits of the main moons, using astrometric data spanning more than a century. We find an intense tidal dissipation (k _{2}/Q = (2.3 ± 0.7) × 10^{4}), which is about 10 times higher than the usual value estimated from theoretical arguments. As a consequence, eccentricity equilibrium for Enceladus can now account for the huge heat emitted from Enceladus' south pole. Moreover, the measured k _{2}/Q is found to be poorly sensitive to the tidal frequency, on the short frequency interval considered. This suggests that Saturn's dissipation may not be controlled by turbulent friction in the fluid envelope as commonly believed. If correct, the large tidal expansion of the moon orbits due to this strong Saturnian dissipation would be inconsistent with the moon formations 4.5 Byr ago above the synchronous orbit in the Saturnian subnebulae. But it would be compatible with a new model of satellite formation in which the Saturnian satellites formed possibly over a longer timescale at the outer edge of the main rings. In an attempt to take into account possible significant torques exerted by the rings on Mimas, we fitted a constant rate da/dt on Mimas' semimajor axis as well. We obtained an unexpected large acceleration related to a negative value of da/dt = (15.7 ± 4.4) × 10^{15} AU day^{1}. Such acceleration is about an order of magnitude larger than the tidal deceleration rates observed for the other moons. If not coming from an astrometric artifact associated with the proximity of Saturn's halo, such orbital decay may have significant implications on the Saturn's rings.
 Publication:

The Astrophysical Journal
 Pub Date:
 June 2012
 DOI:
 10.1088/0004637X/752/1/14
 arXiv:
 arXiv:1204.0895
 Bibcode:
 2012ApJ...752...14L
 Keywords:

 astrometry;
 celestial mechanics;
 ephemerides;
 Planets and satellites: dynamical evolution and stability;
 Planets and satellites: interiors;
 Astrophysics  Earth and Planetary Astrophysics
 EPrint:
 doi:10.1088/0004637X/752/1/14