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Seismology of the gas giants holds the potential to resolve long-standingquestions about their internal structure and rotation state. We construct afamily of Saturn interior models constrained by the gravity field and computetheir adiabatic mode eigenfrequencies and corresponding Lindblad and verticalresonances in Saturn's C ring, where more than twenty waves with pattern speedsfaster than the ring mean motion have been detected and characterized usinghigh-resolution Cassini Visual and Infrared Mapping Spectrometer (VIMS) stellaroccultation data. We present identifications of the fundamental modes of Saturnthat appear to be the origin of these observed ring waves, and use theirobserved pattern speeds and azimuthal wavenumbers to estimate the bulk rotationperiod of Saturn's interior to be $10{\rm h}\, 33{\rm m}\, 38{\rm s}^{+1{\rmm}\, 52{\rm s}}_{-1{\rm m}\, 19{\rm s}}$ (median and 5%/95% quantiles),significantly faster than Voyager and Cassini measurements of periods inSaturn's kilometric radiation, the traditional proxy for Saturn's bulk rotationperiod. The global fit does not exhibit any clear systematics indicating strongdifferential rotation in Saturn's outer envelope.

Cassini Ring Seismology as a Probe of Saturn's Interior I: Rigid Rotation