Saturn's Seismic Rotation Revisited

Abstract

Normal mode seismology is a promising means of measuring rotation in gas giant interiors, and ring seismology presents a singular opportunity to do so at Saturn. We calculate Saturn’s normal modes of oscillation and zonal gravity field, using nonperturbative methods for normal modes in the rigidly rotating approximation, and perturbative methods for the shifts that Saturn’s deep winds induce in the mode frequencies and zonal gravity harmonics. The latter are calculated by solving the thermogravitational wind equation in an oblate geometry. Comparing many such models to gravity data and the frequencies of ring patterns excited by Saturn’s normal modes, we use statistical methods to estimate that Saturn’s cloud-level winds extend inward along cylinders before decaying at a depth 0.125–0.138 times Saturn’s equatorial radius, or 7530–8320 km, consistent with analyses of Cassini’s gravity and magnetic field data. The seismology is especially useful for pinning down Saturn’s poorly constrained deep rotation period, which we estimate at 2π/ΩS = 634.7 minutes (median) with a 5/95% quantile range of 633.8–635.5 minutes. Outstanding residuals in mode frequencies at low angular degree suggest a more complicated deep interior than has been considered to date. Smaller but still significant residuals at high angular degrees also show that our picture for the thermal, composition, and/or rotation profile in Saturn’s envelope is not yet complete.

Depth Dependent Dynamics Explain the Equatorial Jet Difference Between Jupiter and Saturn

“…Note that the wind profile of Saturn is shown according to the latest estimate for the rotation rate (Mankovich et al, 2023). This estimate aligns with findings from the past two decades, indicating Saturn's rotation period to be approximately between 10 hr 32 min and 10 hr 34 min (Anderson & Schubert, 2007;Helled et al, 2015;Mankovich et al, 2019Mankovich et al, , 2023Read et al, 2009). Closer to the tangent cylinder there are strong retrograde flows reaching ∼30 m s 1 on Jupiter (Tollefson et al, 2017) and ∼90 m s 1 on Saturn (Garcia-Melendo et al, 2011) (Figures 1a and 1b).…”

“…At the equatorial region, corresponding to outside from the tangent cylinder, both planets have a strong prograde flow (in the direction of rotation), which is superrotating within ∼6°(∼10°) latitude of the equator (Imamura et al, 2020) and reaching ∼100 m s 1 (∼300 m s 1 ) on Jupiter (Saturn) (Garcia-Melendo et al, 2011;Tollefson et al, 2017) (Figures 1a and 1b). Note that the wind profile of Saturn is shown according to the latest estimate for the rotation rate (Mankovich et al, 2023). This estimate aligns with findings from the past two decades, indicating Saturn's rotation period to be approximately between 10 hr 32 min and 10 hr 34 min (Anderson & Schubert, 2007;Helled et al, 2015;Mankovich et al, 2019Mankovich et al, , 2023Read et al, 2009).…”

The Origin of Jupiter’s Obliquity

“…The moments of inertia found in Wisdom et al (2022) used very different methods, but were found to be in remarkable agreement with one another. They are supported by more recent independent determinations (Mankovich et al 2023). The determination by Jacobson (2022) has larger estimated uncertainties, but is also compatible.…”