Frequency Dependence of Tidal Q

For studies of tidal evolution, values of the key 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, because the relationship between dissipation rates and tidal lags is unknown. This widely applied 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.