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M.H. Lee, S.J. Peale (UCSB)
The origin of Hyperion in the 4:3 mean-motion resonance with Titan poses special problems because of Titan's large mass and distance from Saturn. A tidal origin of the resonance, with the capture of Hyperion into the resonance as the orbit of Titan was expanded by tides, suffers from the requirement that the dissipation parameter Q of Saturn for Titan induced tides must be much less than the lower bound set by the proximity of Mimas to Saturn if Titan's orbit was to expand significantly. We investigate the formation of Hyperion through the accretion of satellitesimals using N-body simulations. We are able to form Hyperion and leave it in the 4:3 resonance with essentially its current orbital properties if (1) the gradient of the surface mass density of the disk of particles and gas is relatively steep (\propto r-3), (2) the time over which the mass and eccentricity of Titan grow to their current values is relatively long (~8 \times 105 Titan orbital periods), and (3) no particles are added to the outside of the disk. These conditions may be real constraints on the properties of the disk that formed the Saturnian satellite system.
The simulations are performed using the symplectic integrator SyMBA, with different imposed rates of growth of Titan's mass and eccentricity and gas drag from an accompanying gas disk (the total composition of the particle and gas disk being solar). There are initially \approx 1100 particles in an annulus from approximately 1.1 to 1.45 Titan orbital radius, with the surface mass density \propto r-n, where 1 \le n \le 3. The surface density of the disk at Hyperion's current orbital radius specifies the total initial disk mass. Although gas drag can bring more satellitesimals into the vicinity of resonances, accretion does not generally occur within any of the resonances because satellitesimal interaction is sufficiently strong to scatter particles out of the resonances. However, gas drag seems to be a necessary process in the scenario to allow orbital decay and capture into the resonance after most of the accretion is complete. Scenarios with an initial surface density in the disk that varies as r-1 and/or the addition of particles near the outer edge of the initial disk to simulate particles migrating from further distances through gas drag lead to the last large embryo(s) ending up in a resonance outside the 4:3 resonance, with the 3:2 resonance being strongly preferred.