Constraining the depth of Saturn's zonal winds by measuring thermal and gravitational signals
Based on straightforward dynamical considerations, we show how available and upcoming measurements of Saturn's thermal and gravitational signals can be used to constrain the depth to which its zonal winds penetrate. The dynamical considerations issue from the facts that Saturn has a strong intrinsic heat flux, rotates rapidly, and has negligible atmospheric viscosity. As a result, convective motions align with surfaces of constant specific angular momentum, which are, away from the equator, approximately cylinders concentric with the planet's spin axis. Convective motions in the interior therefore tend to homogenize entropy in the direction of the spin axis, but not necessarily perpendicular to it. Using the assumption of interior entropy homogenization in the direction of the spin axis, we determine the zonal winds and their associated thermal and gravitational signals by combining thermal wind balance, the equation of state, the observed zonal winds at the cloud level, and estimates of the strength of the magnetohydrodynamic (MHD) drag that zonal winds experience in the deep interior. We find zonal winds likely extend deeply into Saturn, to a depth between about 0.630.63 and 0.83R_S(with Saturn's radius R_S), or to pressures between 1.4 and 0.3 Mbar. The equation of state of hydrogen constrains zonal winds with strengths similar to the cloud level winds to be confined within the outer few percent of Saturn's radius, with substantially weaker winds below, irrespective of where in the range of plausible estimates Saturn's imprecisely known rotation rate falls. Depending on the rotation rate and the precise depth to which zonal winds penetrate, we estimate that the meridional equator-to-pole temperature contrasts in thermal wind balance with the inferred zonal winds increase with depth and reach 1–2 K at 1 bar and 2–4 K at 5 bar. They would be much larger if the cutoff radii of the zonal winds were much shallower than we estimate, but thermal observations by the Cassini Composite Infrared Spectrometer (CIRS) already rule out very shallow flows: Zonal winds must extend deeper than 5000 bar (0.965R_S) because otherwise the associated equator-to-pole contrast would be inconsistent with Cassini CIRS retrievals of the temperature field. Upcoming Cassini gravitational measurements can further constrain the penetration depth of zonal winds, as gravitational zonal harmonics associated with deep zonal winds are much larger than those associated with shallow zonal winds. The even gravitational zonal harmonics associated with zonal winds that penetrate to megabar levels start to become distinguishable from the planetary solid body rotation at zonal harmonic degree n≳8n≳8. The low-order odd gravitational zonal harmonics, which do not depend on the planetary solid body rotation, will be detectable within likely Cassini measurement errors for cutoff radii r_c≲0.98R_S (≳1000 bar). Combining thermal and gravitational signals of the zonal winds, the penetration depths of the zonal winds relative to different rotation rates can thus be constrained.
© 2014 Elsevier Inc. Received 9 October 2013. Revised 6 March 2014. Accepted 23 May 2014. Available online 16 June 2014. This work was supported by the NASA Outer Planets Research Program (Grant NNX10AQ05G), by the National Science Foundation (Grant AGS-1049201), and by a Royal Society Fellowship at the University of Oxford.