Saturn

Here we draw heavily from the review by L. Spilker (14 June 2019) titled, Cassini-Huygens' exploration of the Saturn system: 13 years of discovery that has appeared in Science, Vol. 364, Issue 6445, pp. 1046 - 1051. This review reminds us to emphasize that, although virtually all of the chapters of our H_Book have been written from the standpoint of analyzing the structure, stability, and dynamics of stars, much of our discussion is applicable in a fairly straightforward manner to studies of planets — especially the gas giants — because they are also self-gravitating fluids.

Structure and Stability

Excerpt from the first paragraph on p. 1050 of L. Spilker (2019):

Saturn's ring system acts like a seismograph, providing a measure of Saturn's internal oscillations (or normal modes) that directly probe the interior of the planet … and provide a means for measuring its deep rotation rate. These vibrations, determined by Saturn's nonuniform internal structure, are probably driven by convection inside the planet, which cause oscillations in Saturn's gravity field … Preliminary modeling of the propagation behavior of this collection of waves provides an interior rotation rate for Saturn of ∼ 10.6 hours …

Excerpts from the article by L. Iess et al. (2019), Science, Vol. 364, Issue 6445, p. 1052 titled, Measurement and implications of Saturn's gravity field and ring mass:

… the mass distribution inside a fluid and rapidly rotating planet like Saturn is largely driven by the ratio between centrifugal and gravitational forces. In static conditions, the planet should rotate uniformly and its gravity field should be axially and hemispherically symmetric and thus described by zonal harmonics.

In its final 22 orbits, the Cassini spacecraft passed between the rings and the atmosphere of Saturn. In six of these orbits, while the spacecraft was in free fall under the combined attraction of Saturn and its rings, radio tracking from an antenna on Earth was established to measure the radial velocity of the spacecraft with [high accuracy, which] … allowed us to determine the separate signatures from each zonal harmonic and the ring mass … We found that the measured values of <math>~J_6, J_8</math> and <math>~J_{10}</math> are so large that they cannot be matched with interior models relying on uniform rotation and plausible compositions, but they are in agreement with interior models that assume deep differential rotations extending from the equtor into the interior up to distances of 0.7 to 0.8 Saturn radii from the spin axis.

Hexagon Storm

Image on the Right: obtained from this NASA/JPL site; image on the Left: obtained from this NASA Newsletter. See also the wikipedia page titled, Saturn's hexagon.

FIGURE 1	FIGURE 2

Post Cassini

Binary Mass-Transfer

Several key references:

[Paper DMTF (2006)] M. C. R. D'Souza, P. M. Motl, J. E. Tohline & J. Frank (2006), ApJ, 643, p. 381: Numerical Simulations of the Onset and Stability of dynamical Mass Transfer in Binaries
[Paper MFTD (2007)] P. M. Motl, J. Frank, J. E. Tohline & M. C. R. D'Souza (2007), ApJ, 670, p. 1314: The Stability of Double White Dwarf Binaries Undergoing Direct-Impact Accretion
[Paper MFSCFEDT (2017)] P. M. Motl, J. Frank, J. Staff, G. C. Clayton, C. L. Fryer, W. Even, S. Diehl & J. E. Tohline (2017), ApJSuppl., Vol. 229, Issue 2, article id. 27, 41 pp.: A Comparison of Grid-based and SPH Binary Mass-transfer and Merger Simulations

FIGURE 3: Nonlinear-Amplitude Distortions that Develop in Three Separate Model Evolutions
Evolution A	Evolution B	Evolution C
MFTD (2007) Model Q0.4D Animation: video4.mpg (link is in caption of their Figure 3)	MFSCFEDT (2017) Model Q0.4P_S1 Animation: apjsaa5bdef26_video.mpg (link is in caption of their Figure 26)	MFSCFEDT (2017) ^†Model Q0.5P_G1 Animation: apjsaa5bdef21_video.mpg (link is in caption of their Figure 21)



^†The evolution identified here as Model Q0.5P_G1 was first discussed in §5.2 of DMTF (2006), wherein it was identified as Model Q0.5-Da; the caption to Figure 7 of that paper contains a link to an (mpeg_file = video3-2.mpg) animation that presents a 3D rendering of this model's evolution.

The following discussion has largely been extracted from §3.1.4 of MFSCFEDT (2017):

In §4 of their paper, MFTD (2007) point out that in the vicinity of the accretor some of the models developed nonlinear-amplitude "equatorial distortions with [azimuthal mode numbers] <math>~6 \ge m \ge 3</math>." As is illustrated by the trio of images displayed in the bottom row of Figure 3, above, at a certain point (or points) in each of these binary mass-transfer evolutions … the disk surrounding the accretor has a triangular shape … This trio of triangular shaped images come from, respectively, evolutionary times: (A, B, C) = (15.3, 17.50, 24.33), as measured in terms of initial orbital periods.

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