Which one is the right number for Saturn's spin period? 10.8, 10.7, 10.6 hours? The radio-derived numbers vary with time, so it's tempting to say this newly-derived number is the right answer. But it's not time to update the textbooks just yet. This paper hasn't been published yet; it still needs to be picked at by other scientists who may find faults with it. It would be nice to see another independent measure of the spin rate that found a result in agreement with this paper, too.

As with any physics paper, there are simplifying assumptions. One major assumption as to do with the planet's rotation. As the title of the paper suggests, the work assumed that all of Saturn rotates at the same rate -- that it's rotating as a rigid body. Obviously this isn't true at the very topmost levels of the clouds, but it's hard to know how deep Saturn's winds go. (I wrote about this issue on Jupiter last year.) In fact, later on in the paper, the authors show that there are some waves in the C ring that they still can't explain. These not-yet-explained waves very likely have to do with differential rotation, where Saturn's uppermost envelope may be rotating at a slightly faster speed than its interior. I asked Mankovich on Twitter how it would likely affect their derivation of the rotation rate if Saturn did have differential rotation; he replied that "if Saturn rotates on cylinders with a speedup toward the surface, then we've under-predicted the bulk rotation period. [We are w]orking on differential rotation now; it seems that the median background rotation period is only likely to get longer by 2 minutes, not enough to square with radio periods."

Another set of assumptions had to do with the interior structure of Saturn, something they had to assume in order to calculate its gravity. A cool aspect of this work is that they were able to fine-tune their interior model of Saturn to match the C ring waves observed in Cassini images -- that is, they let the ring waves inform them about where Saturn's internal layers are. They assumed a three-layered interior: a dense rock/ice core, an inner envelope with a mixture of hydrogen/helium and rock/ice, and an outer hydrogen/helium envelope. They allowed the proportion of materials in the inner envelope to vary, as well as the partitioning of helium between the outer and inner envelopes. (Helium is heavier than hydrogen, so it sinks; there'll be proportionally less helium in the outer envelope and more in the inner envelope.)

The observed ring waves pretty much require Saturn to have a substantial rocky core with a radius about 25% of Saturn's width, or about 15,000 kilometers. That would make its core about 15 to 20 Earth masses, and it's consistent with the larger end of other workers' estimates of Saturn's core size. That's quite large -- Saturn's rocky core is about as massive as the whole of planet Neptune! The boundary between outer and inner envelopes isn't as well constrained; there may be no sharp boundary anyway. Later on in our Twitter conversation, Mankovich mentioned that Saturn might actually have a deep layer, several thousand kilometers thick, right above the core, of nearly pure helium that has rained out of the gassy envelope. That wasn't included in their model, and might be important. (Weirdly, the ice/rock core might have started dissolving into this helium-rich layer.)

So work remains to be done, but I think it's pretty neat that the beautiful waves in Saturn's rings can tell us something about what the deep interior of the planet is doing.