School of Mathematical Sciences, Monash University, Melbourne VIC 3800, Australia. Email: email@example.com
I report a model for the formation of Saturn's family of mid-sized icy moons to coincide with the first flypast of Rhea by the Cassini spacecraft on 2005 November 26. It is proposed that the moons had condensed from a concentric family of orbiting gas rings that were shed some 4.6 × 109 yr ago by the proto-Saturnian (hereafter p-Sat) cloud. The p-Sat cloud is made up of gas and residual grains of the gas ring that was shed by the proto-Solar cloud (hereafter PSC) at Saturn's orbit. The bulk of the condensate within this proto-Solar ring accumulates to form Saturn's central core of mass ∼10–20 M ⊕ (M ⊕ = Earth mass). The process of formation of Saturn's solid core thus provides an opportunity for the p-Sat cloud to become depleted in rock and water ice relative to the usual solar abundances of these materials. Nitrogen, which exists as uncondensing N2 in the PSC and as NH3 in the p-Sat cloud, retains its solar abundance relative to H2. If the depletion factor of solids relative to gas is ζ dep = 0.25, as suggested by the low mass of Rhea relative to solar abundance expectations, the mass-percent ratio of NH3 to H2O in the dense p-Sat cloud is 36:64. Numerical and structural models for Rhea are constructed on the basis of a ‘cosmogonic’ bulk chemical composition of hydrated rock (mass fraction 0.385), H2O ice (0.395), and NH3 ice (0.220). It is difficult to construct a chemically differentiated model of Rhea whose mean density matches the observed value ρ Rhea = 1.23 ± 0.02 g cm−3 for reasonable bounds of the controlling parameters. Chemically homogeneous models can, however, be constrained to match the observed Rhea density provided that the mass fraction of NH3 is permitted to exceed the cosmogonic value by a factor ζ NH3 = 1.20–1.35. A large proportion of NH3 in the ice mass inhibits the formation of the dense crystalline phase II of H2O ice at high pressure. This may explain the lack of compressional features on the surface of the satellite that are expected as a result of ice II formation in the cooling core. The favoured model of Rhea is chemically uniform and has mass proportions of rock (0.369), H2O ice (0.378), and NH3 ice (0.253). The enhancement factor of NH3 lies within the measured uncertainties of the solar abundance of nitrogen. The satellite is very cold and nearly isodense. The predicted axial moment-of-inertia coefficient is [C/MR 2]Rhea = 0.399 ± 0.004.
(Received November 30 2005)
(Accepted January 31 2006)