  Regarding tidal dissipation in Saturn, usually parameterized by Saturn's
quality factor Q, there remains a discrepancy between conventional estimates
and the latest determination that has been derived from astrometric
observations of Saturn's inner satellites. If dissipation in Saturn is as large
as the astrometric observations suggest, conventional models predict that
Mimas' initial orbit should be located inside Saturn's synchronous orbit or
even inside its Roche limit. Using simple structure models and assuming
Saturn's core to be viscoelastic, we look for dissipation models which are
consistent with both the latest astrometric observations and with Mimas'
orbital migration. Firstly, using a two-layer model of Saturn's interior
structure, we constrain the ranges of rigidity and viscosity of Saturn's core
which are consistent with Saturn's dissipation derived from astrometric
observations at the tidal frequencies of Enceladus, Tethys, and Dione. Next,
within the constrained viscosity and rigidity ranges, we calculate Mimas'
semi-major axis considering the frequency dependence of viscoelastic
dissipation in Saturn's core. By the two calculations, we evaluate (1)
Saturnian models which can explain the astrometrically determined Saturnian
dissipation, and (2) whether Mimas' initial semi-major axis is larger than the
synchronous orbit. We show that if the core is assumed to be solid with a
viscosity of 10^{13}-10^{14} Pa s, the lower boundary of the observed Saturnian
dissipation at tidal frequencies of Enceladus, Tethys, and Dione can be
explained by our model. In this viscosity range, Mimas can stay outside the
synchronous orbit and the Roche limit for 4.5 billion years of evolution. In
the case of a frequency dependent viscoelastic dissipative core, the lower
boundary of the observed Saturnian dissipation can be consistent with the
orbital expansion of Mimas.
