Chaos and secondary resonances in the Mimas-Tethys system

We have investigated the role of the 200 yr period discovered by Vienne and Duriez (1992) on the tidal evolution of the Mimas-Tethys system through th e 2:4 ii' present resonance. Three terms are found to generate this period. We present a perturbed-pendulum model in which these terms bring about a p erturbation to the ideal ii' resonance pendulum, which is in a direct ratio to the eccentricity e' of Tethys. Although e' is now very small, it is sho wn that this quantity could have been much greater in the past. We also sho w, thanks to this model, that these terms may have brought about a stochast ic layer of noticeable width at the time of capture in the ii' resonance, w ith the consequence that the possible values of the inclination i(c) of Mim as before capture range from 0.4 degrees to 0.6 degrees (these uncertaintie s arise from the present uncertainties on e'). The role of each one of the three terms is examined in the appearance of chaos. A capture into the 1/1 secondary resonance (between the libration period of the primary ii' resona nce and the period of about 200 yr) is found possible. It means that the sy stem could have experienced several captures in the primary resonance, inst ead of a single one, and that i(c) could have been, with this assumption, m uch lower than 0.4 degrees. A probability of capture into this secondary re sonance as a function of the eccentricity of Tethys on encounter is derived , using Malhotra's method (Malhotra, 1990). Allan's values of i(c) = 0.42 d egrees and e' approximate to 0 (Allan, 1969) are therefore called into ques tion, and taking e' not equal 0 is shown to be absolutely necessary if we w ant to understand the phenomena at work in the Mimas-Tethys system.