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Could a moon or planet with otherwise no atmosphere maintain gas pockets in sufficiently deep craters, and could it be habitable by humans without pressure or space suits?
I found this similar question Would oxygen pool in sink holes if the upper atmosphere was helium, hydrogen and methane? but it focusses on a planet with a full atmosphere, I want to know if it would be realistic for a planet without enough gas to maintain a breathable atmosphere beyond depressions to exist.
Yes, it could (or at least reasonably enough for a story).
For life to develop or be habitable by colonists, the gasses would have to be continually be replenished from some source because it will eventually dissipate for the same reason that our atmosphere continuously leaks into space.
https://en.wikipedia.org/wiki/Atmospheric_escape
One classical thermal escape mechanism is Jeans escape.[2] In a quantity of gas, the average velocity of any one molecule is measured by the gas's temperature, but the velocities of individual molecules change as they collide with one another, gaining and losing kinetic energy. The variation in kinetic energy among the molecules is described by the Maxwell distribution. The kinetic energy and mass of a molecule determine its velocity by $E_{kin}=$$1 \over 2 $$\cdot mv^2$
Individual molecules in the high tail of the distribution may reach escape velocity, at a level in the atmosphere where the mean free path is comparable to the scale height, and leave the atmosphere.
The more massive the molecule of a gas is, the lower the average velocity of molecules of that gas at a given temperature, and the less likely it is that any of them reach escape velocity.
If you look at Mars, you will find that the atmosphere in the deeper craters is different to that on the high surface. There's no need to ask if it could exist - because it does.
https://en.wikipedia.org/wiki/Atmosphere_of_Mars
"It ranges from a low of 30 pascals (0.0044 psi; 0.30 mbar) on Olympus Mons's peak to over 1,155 pascals (0.1675 psi; 11.55 mbar) in the depths of Hellas Planitia"
The only question left to ask is "could this atmosphere sustain life" - and while the answer for Mars is no; there's no reason why, if the chemical composition of it was different, it wouldn't.
Kind of, if it doesn't need to be a crater
Here is a very long article talking about helium production: https://www.chemistryworld.com/news/scientists-unearth-one-of-worlds-largest-helium-gas-deposits/1010122.article
The interesting tidbit: after the helium is produced (by radioactive decay; beta radiation is basically a helium nucleus expelled at high speed), in the right spots it gets trapped because it can't penetrate the rock layers above it. Whereas when helium gets into the atmosphere, it's so light it just drifts up through the atmosphere and leaks into outer space.
If your settlement does not need to have an open roof, then this will work just fine. Craters typically have denser material from whatever impact created them. It could easily trap enough gas to hold a pocket of livable atmosphere.
Yes, it is possible. Consider that at the bottom of a valley one is closer to the center of mass of the planet, thus gravity can be relatively stronger, and this could reflect on the local atmospheric pressure.
On Earth we don't have valleys deep enough to experience dramatic difference, but we have such feature on Mars: Valles Marineris.
Up to 7 km deep, the pressure at its bottom is about 0.168 psi, while the average atmospheric pressure on Mars is 0.087 psi. About double, as you see.
Still not high enough to take a walk in T-shirt, but if the atmosphere on Mars would be more dense, it would be first spot to achieve habitable conditions.
It is absolutely possible for a body to have breathable atmospheres in some places but not others. Earth already has that actually. Look at Mount Everest, you cannot survive at the peak for an extended period of time without supplemental oxygen. Now imagine if Earth's atmosphere was 1/10th as dense as it really is. You would then have that same low pressure 1/10th of the way up Everest. This would mean places as low as Denver, Colorado would not have enough air to breathe. Push it further, and you'll get isolated low areas with breathable atmospheres with barren wastelands between them. Places like Death Valley, New Mexico, or the Great Rift Valley in Africa would be breathable.
One problem is that if the air really is so thin the only breathable areas are deep in valleys or craters is that it will slowly bleed off into space. Every atmosphere, even our own, loses atoms to space. As the sun heats the atmosphere, some atoms gain enough energy to reach escape velocity. Some of these are stopped by running into other atoms, but some escape. With so much less atmosphere above these craters, this proportion will probably be a lot higher. The craters will not have a breathable atmosphere for long, at least not on geologic timescales.
Factor in life. A natural evolved or genetically engineered amoeba like entity (ALE) which has adapted to living on the edge of a pocket of gas in colonies. The ALE secretes an airtight liquid which hardens into an airtight shell at the edge of the colony. As the colony expands, it expands the shell, sealing a larger and larger pocket. Inside or under this pocket more complex life prospers.
Yes and no.
As the question is asked in the title the answer is yes--you can perfectly well have a body whose atmosphere is only dense enough at the lowest altitudes.
As the question is asked in the body, however, the answer is no. You simply need too much distance between the airless surface and the habitable pocket--more distance than the strength of the rocks of which your planet is made. Any pocket deep enough to hold a breathable atmosphere collapses.
