Understanding Saturn’s Hexagon

Students at the University of Manchester have been investigating the formation and persistence of Saturn’s Hexagon: a hexagonal wind pattern, 3 times the size of earth, near the north pole in the atmosphere of Saturn.

Saturn’s Hexagon first caught my attention when I saw a picture of the Gas Giant on twitter (shown below) taken by Cassini. As I stared at the Rings of Saturn in all their beauty and noted Saturn’s highly ellipsoidal shape my eyes became fixated on the northern tip of the planet. Surely that wasn’t a hexagon? A quick Google later convinced me otherwise. But how can a regular polygon form in a fluid? Fluids by their nature are turbulent; polygons have straight sides. More recently I discovered that this curious feature inspired legendary singer-songwriter Paul Weller’s latest Album Saturn’s Pattern, but how can we understand more about the cause of this natural phenomenon?

Saturn’s North Polar Hexagon and Rings (credit: NASA JPL)

Final year students Harriet Challen and Barney Wareing investigated The Hexagon under my supervision using a numerical model written in MATLAB. In order to model polygon structures near the north pole of the planet they needed to input Saturn’s average wind into the model using measurements of the east-west wind taken from the Voyager flybys in the 1980s. The polygons that the model produced were short-lived and rotated prograde with a slow period of around 100 hours. However, observations from Voyager and Cassini have shown that The Hexagon appears to be stable over at least 30 years, which suggests that it may be a permanent structure.

These initial model calculations used a time period of 10 h and 39 minutes for the spin period of Saturn, which has been determined from the Saturn Kilometric Radio (SKR) rotation period. The SKR refers to periodic radio waves that emanate from Saturn’s interior (this rotation period has been labelled System III). This raises an interesting question: how is the spin period of a Gas Giant even defined? unlike rocky planets, e.g. Earth, there are no surface structures to track on a Gas Giant so it is not easy to determine the spin.

Part way through the project an article was published in Nature (Helled et al., 2015) which argued that the spin period of Saturn is slightly shorter than that of System III, at 10 h 32 minutes. The paper provides compelling evidence that System III’s spin does not correspond to the true spin period of Saturn because it shows small variations in time: in-fact the spin period of a body as large as Saturn should hardly vary at all – as Newton’s principle of conservation of angular momentum quite clearly tells us.

The implication of this faster spin period is that it strongly affects our estimates of the east-west wind: think about it, Voyager determined the wind by measuring the speed of cloud features on Saturn as they whizzed past and, using knowledge of the spin period derived from the SKR, scientists converted these measured speeds to a wind speed that is measured relative to Saturn’s spin. The latest evidence is that Saturn is actually spinning faster than the SKR and hence the east-west wind has to be reduced so that the speed of the cloud features does not change.

It turned out that the faster spin of Saturn made all the difference to the persistence of The Hexagon: the model was now able to produce a very stable hexagon wind pattern. Using the model Harriet and Barney were able to propose a conceptual model for how The Hexagon is formed:

Current hypothesis for how The Hexagon is formed

Current hypothesis for how The Hexagon is formed

(1) They started with the assumption of a jet, which is a region of air moving faster than the air either north or south of it; (2) a small kink in the location of the jet can be amplified in this situation; (3) the Coriolis effect leads to air moving in the northern hemisphere being deflected to the right, so as air moves south it develops a clockwise movement, which then forms a closed circulation: this happens at regular positions along the jet and forms a so-called vortex street. However, as the jet moves south its vorticity is maintained, so down wind of the clockwise circulation an anti-clockwise rotation is formed (a.k.a. Rossby wave motion). (4) both of these motions develop into closed circulations, which help to straighten the sides of The Hexagon.

Furthermore with the new spin period The Hexagon is almost stationary with respect to the spin of the planet (see animation below). Although at first glance this result seemed to be in agreement with observations, which state that The Hexagon does not rotate relative to Saturn’s spin, we now recognise that the previous literature assumed Saturn’s spin period was equal to that of System III. In fact it is faster; hence, because The Hexagon is observed rotate in sync with System III, we should observe that The Hexagon rotates retrograde relative to the true Saturnian spin – this aspect is still left unanswered. So there is still some work to do in explaining this exquisite structure that some have labelled “the Jewel of the Solar System”.

animation of The Hexagon simulated in the model over ~ 1 earth year. Left: orthographic plot of vorticity; Right: same but looking down on the north pole.

animation of The Hexagon simulated in the model over ~ 1 earth year. Left: orthographic plot of vorticity; Right: same but looking down on the north pole.

Reference: Ravit Helled, Eli Galanti, Yohai Kaspi. Saturn’s fast spin determined from its gravitational field and oblateness. Nature, 2015; DOI: 10.1038/nature14278

Link to Cassini website

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About Paul J. Connolly

Atmospheric Scientist at The University of Manchester. Botherer of clouds and tinkerer with computer code.
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