Proper Elements and Secular Resonances for Irregular Satellites

Abstract

We present results of an analytical study of proper elements and secular resonances for the irregular satellites of the outer planets. In the case of the Jovian system we identify three satellite families, two of them previously known (Carme and Ananke), plus a new agglomeration of four bodies that includes Pasiphae as its largest member. While the distribution of proper elements for Saturn's moons seems to be more random, a small cluster was found for the direct moons formed by Albiorix, Erriapo, and 2004 S1, slightly different from the so-called Gaulish cluster. No significant families are detected in the present study for the Uranian or Neptunian satellite systems. For each satellite system we determine the location of several secular resonances in the proper element space. Apart from the well-known resonance locks of Pasiphae, Sinope, and Siarnaq, a comparison between the resonance locations and proper elements shows that Saturn's satellite Narvi also exhibits temporary librations in the - ⊙ resonance. However, unlike the resonant Jovian moons that are located in the same configuration, Narvi's critical argument librates alternately around values near 90° and 270°. Neither the Uranian nor Neptunian systems seem to have resonant moons. The resonant dynamics of the real satellites in the vicinity of - ⊙ = 0 is studied with a simple model for secular resonances based on the restricted three-body problem. Depending on the initial conditions, we show the existence of one or two modes of libration that can occur at different values of the critical angle, showing a good correspondence with the observed behavior of all the resonant moons. Finally, we discuss the global distribution of the real satellites with respect to the secular resonances, as compared with synthetic populations of bodies drawn solely from stability conditions. For Saturn, we find that the present satellite population appears compatible with simple random distributions. Although the same is noted for most of the retrograde moons at Jupiter, the existence of Pasiphae and Sinope so close to resonance lock seems statistically improbable. Thus, there is a strong indication that some kind of past smooth migration occurred in the Jupiter system (but not at Saturn), which may have caused a slow evolution of its satellite population toward their present sites.