The role of tidal torques on the evolution of the system of Saturn’s co-orbital satellites Janus and Epimetheus

This paper discusses the effect of tides raised by Saturn on its co-orbital satellites Janus and Epimetheus, and its consequences on the long-term evolution of the co-orbital horseshoe pattern of those moons. This tidal effect is found to produce a loosening of the co-orbital lock of Janus and Epimetheus. The increase of the difference D between their semi-major axes under this process is estimated as 2.77 km/Myear, regardless of whether the moons are composed of monolithic or fractured ice. On the other hand, assuming that the outer edge of Saturn’s A ring is permanently maintained by Janus and Epimetheus at their 7:6 resonance, Lissauer et al. [Lissauer, J.J., Goldreich, P., Tremaine S., 1985. Icarus 64, 425–434] have shown that the torques exerted on Janus and Epimetheus due to resonances with Saturn’s rings would produce a tightening of the co-orbital lock. The rate of decrease of orbital difference D under that latter process depends upon the precise relative radial location of the A-ring outer edge as compared with Janus’ lower orbit semi-major axis, which is quantified here by means of a parameter po characterizing the efficiency of the effect of Janus’ ring resonance. Under the combined effects of those two processes, depending on the value of po relative to a critical value po ≈ 19%, the system will evolve toward either a transition from horseshoe to tadpole orbit, or to a destruction of the co-orbital lock, after a few tens of Myears. Most recent observations of the A ring’s outer edge by Spitale and Porco [Spitale, J.N., Porco, C.C., 2009. The Astronomical Journal 138, 1520–1528] tend to indicate that the future evolution will be a net tightening of the co-orbital system, until a tadpole situation will be reached after about 15 Myears. From a study of the past history of the co-orbital system, it is shown that such a scenario is compatible with a capture from free orbits to co-orbital horseshoe pattern some 25 Myears ago.