Jovian coffee model (2)

Photo by Scott Liddell
Posted at morguefile.com
June 10, 2007

This is the background for modeling the precipitation of helium in Saturn's atmosphere as sugar in coffee. Tristan Guillot (2004) from the Observatoire de la Côte d'Azur in Nice, France, labels this model the "Gedanken Café."
...Let's assume you're sitting comfortably in the sun at a cafe' and you're served an espresso. I like it sweet, and, in any case, our gedanken experiment requires sugar...

Drop finely granulated sugar instead of cubes into the coffee. If the sugar is fine enough, it will dissolve before reaching the bottom, and very little stirring is needed. But that's only if the espresso is hot enough. If it's only lukewarm, the sugar has a hard time dissolving; it tends to sink to the bottom. Finally, after all this preparation, let a friend arrive at the table and try to guess, from his first sip, how much sugar there is in the cup.

For giant planets, the problem is similar, only more complex. If the coffee itself is a good analog for the hydrogen, the sugar is replaced by...helium, [it] could, for example, either be mixed with the hydrogen or sequestered in the deepest regions.

This illustrates nicely what is covered in the textbook used in Astronomy 10 (introductory astronomy) at Cuesta College, San Luis Obispo, CA, where John D. Fix (University of Alabama in Huntsville) writes:
At temperatures above 10,000 K, helium is dissolved in metallic hydrogen. At lower temperatures it isn't. Instead, helium slowly settles inward through the metallic hydrogen, converting gravitational energy to heat. This probably doesn't happen within Jupiter because Jupiter is hot enough to keep helium dissolved in its metallic hydrogen. The interior of Saturn may be cool enough, however, that helium condenses at the top of the metallic hydrogen core and falls toward the center. As time passed, the envelope and atmosphere of Saturn should have become depleted in helium. This is exactly what measurements of the helium to hydrogen ratio in Saturn's atmosphere have shown.

Clicker questions for peer-instruction exploring this model are covered in the previous post: Astronomy clicker question: jovian coffee model (1).

Tristan Guillot, "Probing the Giant Planets," Physics Today, vol. 57 no. 4, (April 2004), p. 63.

John D. Fix, Astronomy: Journey to the Cosmic Frontier, McGraw-Hill Higher Education, New York, NY, p. 279.

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