Helium rain inside metallic hydrogen within Jupiter, conditions and experiments? In response to today being pi day (also see http://www.piday.org/), NASA has published it's fifth annual pi in the sky day 5 activity set (see also NASA goes the distance and Celebrate Pi Day with NASA).

This year's NASA activity includes the problem set Helium Heist: A 'Pi in the Sky' Math Challenge. Below is a cropped screen shot of the illustration from this PDF version.

The part of the text that I found most striking is:


  It has been hypothesized that the helium was depleted out of the upper atmosphere and transported deeper inside the planet. The extreme pressure inside Jupiter condenses helium into droplets that form inside a liquid metallic hydrogen layer below. Because the helium is denser than the surrounding hydrogen, the helium droplets fall like rain through the liquid metallic hydrogen.


Question: Roughly what are the pressure and temperature thought to be at this depth in Jupiter? Is this regime at all accessible experimentally on Earth to confirm that these two fluids are immiscible, or is this behavior purely theoretical?



below: cropped screen shot from here (NASA). Click for full size.
Different sources give significantly different values for the conditions under which hydrogen shifts from molecular to metallic. See the discussion in the comments associated with this question. Pressures from about 20 to 300 GPa and temperatures very broadly around 10 000 K seem to be the most common.  

Experiments can only just reach these pressures, at lower temperatures, for tiny volumes of material, and the question of whether anyone has made metallic hydrogen at all remains controversial. Certainly no one can make it repeatably. (wikipedia has a reasonable summary of the history) or make enough of it and keep it for long enough to check to what extent, if any, helium is soluble in it.

That said, analysing from theory whether it will be soluble shouldn't be that hard, since both hydrogen and helium are relatively simple atoms. An early paper concludes that the hydrogen would be at or close to the limit of how much helium could be dissolved. I'm sure there is more accurate recent work, but I couldn't find it quickly.