I agree that, against a vacuum, particles can achieve very low temperatures. This could cause some particles (like Oxygen) to freeze. The problem is, even though it is frozen, it would be far more dense than gaseous oxygen. According to denpressure, the now frozen particle should plummet toward the surface.
This is assuming oxygen would be near the vacuum in the first place. Hydrogen, being much less dense, should be pushed upward at a much higher rate. Yet, to turn hydrogen into a solid that can form any kind of symmetrical shape, it needs to be at extremely high pressures (over 1 million atmospheres or 160 Gigapascals).
Hydrogen at low temperatures would become solid. If memory serves, the point at which the dome forms is almost at absolute zero (due to distance from the Sun), so hydrogen would definitely be solid then.
There are a few ways the rest could work. Hydrogen freezing/falling/evaporating/rising in which case you would end up with a dome, just one constantly replenished. Or you'd have the full arc of the dome frozen and so supporting itself, meaning it wouldn't fall.
Quick query for Scepti, though: what is it that decides whether an element/compound is a solid/liquid/gas? Is it strictly a matter of density (assuming not as some liquids can be heavier than some solids, though that might just be down to porousness. Mercury comes to mind) or is frequency a factor too?
Energy can certainly alter the state, but at a constant temperature, what decides that A would be solid, B would be a gas, etc?
Ok think of the dome. The very top would be frozen hydrogen//helium or whatever that has (like you mentioned) frozen. The outer skin is up against the true vacuum but the inner skin is still pushed into, albeit very weakly.
The thing is, weak at the top means nothing to us at the bottom.
the rest of the atmosphere is holding it up but as you say it's a replenishing system. It changes due to energy applied, as in the sun, as you say again.
Ok, so once that dome is expanded into again, we have the frozen gas to liquid gas or super fluid if you want.
Basically it can look like a sea up there and in truth, I believe there are many, just as I believe there are a few below our seas depending on where on Earth at depth they are.
So we're back to density build up. We have a drop off of ice through liquid or super fluid helium or hydrogen and a creating of a friction burn as the ice falls creating a gas which rises again unless it gets trapped enough to fall as a glowing ice ball or what we would term as a meteor.
I'm getting off track a bit there but it all ties in, in the end.
Obviously there's a lot more to it all.