Models and theoretical spectrum for the free oscillations of Saturn

We constructed new models of Saturn with an allowance made for a helium mass fraction of ～0.18–0.25 in its atmosphere. Our modeling shows that the composition of Saturn differs markedly from the solar composition; more specifically, during its formation, the planet was ～11–15 planetary masses short of the hydrogen-helium component. Saturn, as well as the other giant planets, must have been formed according to Schmidt’s scenario, through the formation of embryonic nuclei, rather than according to Laplace’s scenario. The masses of the embryonic nuclei themselves lie within the range (3.5–8) M_⊕. We calculated a theoretical free-oscillation spectrum for our models of Saturn, each of which fits all of the available observational data. The results of our calculations are presented graphically and in tables. Of particular interest are the diagnostic potentialities of the discontinuity gravitational modes related to density jumps in the molecular envelope of Saturn and at the interface between its molecular and metallic envelopes. When observational data appear, our results can be used both to identify the observed modes and to improve the models themselves. We discuss some of the cosmogonical aspects associated with the formation of the giant planets.