Monday, April 12, 2010

Saturn's Enigmatic Hexagon

One of our planets has a hex on it. Seriously.

Perhaps I should back up and explain. Back in 1988, scientists analyzing images of Saturn sent back by Voyager 2 noticed an odd structure in the cloud banding circling Saturn's North Pole. One of the cloud bands was shaped like a hexagon! [Godfrey, D. A., 1988: A hexagonal feature around Saturn's North Pole. Icarus (ISSN 0019-1035), vol. 76, Nov. 1988, p. 335-356., doi:10.1016/0019-1035(88)90075-9.]

The public was dazzled and puzzled by the images. Atmospheric scientists looked at them and said "Oh, a standing Rossby wave. Interesting." Some of these scientists went on to work out the hydrodynamic calculations of how this structure might have been formed as a side effect of a cyclone near the boundary of the hexagon. [Allison, M., D.A Godfrey, and R.F. Beebe, 1990: A wave dynamical interpretation of Saturn's polar hexagon. Science, 247, 1061-1063, doi:10.1126/science.247.4946.1061.]

When the Cassini probe reached Saturn in 2006, the northern polar region was shrouded in winter darkness, but the Cassini VIMS team was nevertheless able to image the region in infrared. (See image to the right.) Sure enough, the hexagonal shape was still there, although the vortex that had been swirling about one of its sides was gone, which was verified in the visible spectrum as daylight began to creep back into the polar region in early 2009.

Keep in mind that the absense the cyclone on the periphery of the hexagon does not automatically render the analysis by Allison, Godfrey, and Beebe incorrect. The sinusoidal "wobble" of the polar jet stream could easily persist long after whatever triggered the initial perturbation goes away. Such persistant structures in the atmospheres of the gas giants is not unprecedented. In the Jovian atmosphere, a cyclone known as the Great Red Spot has persisted for centuries. The only real mystery is whether the cyclone observed adjacent to the hexagon by Voyager 2 was actually what triggered the oscillation, or if something else was the culprit. Scientists continue to dig into the issue. Some have even speculated that the driving force might be convective currents of hotter gasses upwelling from deep within Saturn's atmosphere. [Fletcher LN, Irwin PG, Orton GS, Teanby NA, Achterberg RK, Bjoraker GL, Read PL, Simon-Miller AA, Howett C, de Kok R, Bowles N, Calcutt SB, Hesman B, Flasar FM. Temperature and composition of Saturn's polar hot spots and hexagon. Science. 2008 Jan 4;319(5859):79-81.]

Just this month, it was announced that Oxford physicists Ana Claudia Barbosa Aguiar and Peter Read had managed to duplicate this hexagon structure in the lab in a tank of swirling fluid. [Ana C. Barbosa Aguiar, Peter L. Read, Robin D. Wordsworth, Tara Salter, Y. Hiro Yamazaki, A laboratory model of Saturn's North Polar Hexagon, Icarus, Volume 206, Issue 2, Cassini at Saturn, April 2010, Pages 755-763, ISSN 0019-1035, DOI: 10.1016/j.icarus.2009.10.022.]

This experiment provided confirmation of an earlier experiment. In 2005, researchers at the Technical University of Denmark had achieved similar results with a similar apparatus. [Jansson, T. R. N., et al, 2006. Polygons on a Rotating Fluid Surface. Phys. Rev. Lett., 96. 174502.]

So, the science on this topic is humming along nicely. That having been said, some in the general public still seem puzzled and bewildered by all of this. A hexagon formed by clouds? It seems counterintuitive that such a structure could possibly exist. However, a closer examination of the images reveals that the sides of the hexagon are not perfectly straight, nor do the polar winds of Saturn make abrupt, crisp 120 degree turns at each of the hexagon's vertices.

Consider the graph below illustrating the simple expression (in polar coordinates) r = 2 + 0.07 * sin(6*Θ). Keep in mind that this is not even remotely intended to serve as an analysis of the dynamics of the Saturn hexagon. Heady hydrodynamic equations involving vector fields would be required for that. What I am attempting to qualitatively demonstrate here is how a stationary Rossby wave could conceivably resemble a regular polygon.

With the amplitude of the sinusoidal component set to be sufficiently shallow, and the angular component being multiplied by 6 (forcing the resulting figure to possess the six-fold radial symmetry of the D6 dihedral group, a property shared with true hexagons), the resulting figure (composed of nothing more than curves) appears at a glance to have the form of a hexagon.

So, a hex upon Saturn!

1 comment:

Riccardo Manzotti said...