Astronomy and Astrophysics – Astrophysics
Scientific paper
May 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009dda....40.1501g&link_type=abstract
American Astronomical Society, DDA meeting #40, #15.01; Bulletin of the American Astronomical Society, Vol. 41, p.908
Astronomy and Astrophysics
Astrophysics
Scientific paper
Values of the tidal parameter Q, and its frequency dependence, are often derived from estimates of internal energy dissipation when a satellite, planet, or star is physically distorted. Such estimates come from geophysical or astrophysical modeling, from seismic data, from ad hoc assumptions, or from constraints based on current spins and orbits. In a standard procedure, Q values are used to determine the lag in the response to each Fourier component of the tidal potential. The separate components are then co-added. The basis for this procedure is the analogy of the damped, driven, harmonic oscillator. However, this lag-and-add procedure would not be justifiable even for such a simple system, except for a very specific dependence of Q on frequency. There is no reason to expect the lag-and-add procedure to be relevant for a complex system. This type of model is a reasonable approximation only if the decomposed tidal potential involves a narrow range of frequencies, and thus may only be appropriate for analyses to low order in orbital eccentricity and inclination. Accordingly, models of the evolution of extra-solar planetary systems that require use of high-order terms should be regarded only as tentative representations of actual behavior at best. Similarly, the wide application to extra-solar planets of a standard value of Q that was derived for Jupiter is not appropriate. In addition to questions of whether dissipation mechanisms on such planets are similar to Jupiter, it should be recognized that current measurements of tidal heat and orbital evolution of Io show that there is no known upper limit to the value of Q for Jupiter.
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