Yhyjyk

I want to create a planet with a deep gravity well, say about 12G at the surface. At first I wanted the planet to have either no atmosphere or a very thin one. But I want this to be as close to realistic as possible. So, would a planet be guaranteed to have a thick atmosphere with a gravity well that deep?

You ask a tricky question because the case you describe -- a rocky planet with 12G surface gravity -- is extremely unlikely. If the planet is defined as being rocky, then it's made of normal matter (not neutron star or white dwarf stuff) and to have 12G surface gravity, it would have to be quite large.

For a constant density sphere, the surface gravity increases proportional to the sphere's radius, so to have 12G surface gravity it would have to be around 12 times the diameter of the Earth. (The surface gravity is proportional to the planet's mass which is proportional to the cube of the radius. And surface gravity is also inversely proportional to the square of the radius (because the surface in further from the center and the inverse square law). The net effect is a proportionality to radius.)

Even rocks compress, so 12x is somewhat of an overestimate. Say it's "only" 10x the diameter of the Earth. It's still very difficult to see how a rocky planet 10x the diameter of Earth (meaning a mass of 1000 Earths -- greater than Jupiter!) could avoid picking up a huge atmosphere of gasses and being a typical Super Jupiter or even a small star.

About the only way I can think of is if the star it circles went through a very high luminosity phase and stripped away nearly all the atmosphere. (Since hot Jupiters are common, it seems unlikely that a planet that massive even one forming near a star could avoid a big atmosphere. It pretty much has to have had its atmosphere stripped later.) Not so clear that life would survive on it then.

Likely, but not guaranteed. Consider a large rocky planet very close to its star. There is certainly a possibility that the atmosphere would be boiled off / stripped away by the star.

This would be the case if, for instance, Mercury were orders of magnitude more massive. If your large rocky planet is close enough to its star to make this case true, you will have to deal with strange conditions for your character. One example is the planet is likely to be tidally locked, with an extremely hot side always facing the star and an extremely cold side always facing away from the star.

Whether humans have actually discovered a planet that meets these criteria is probably up for debate. Most inquiries into exoplanet atmospheres make the assumption that the existence or lack of atmosphere is unknown until the presence of an atmosphere is proven definitively.

Heavy metal world.

1. 12G planet. You could ramp up the gravity by making the core more dense. Our planet has an iron / nickel core under the rocks, and those have atomic weights of 55 and 58. Uranium has an atomic weight of 238. So if you made the core out of uranium and other heavy friends your density is 5x that of earth. Those elements are rarer than iron but not crazy rare. Now your planet only needs to be 2.4x as big as earth to have your 12G. If you want your planet even smaller, you can invoke the stable superheavy elements from the undiscovered far reaches of the periodic table - the island of stability
   

There could be other cool things about the uranium planet. Maybe natural fission goes on deep inside, which would make for rocking volcanoes. Could you take advantage of this to get off planet? Hmm... Also, the atmosphere would have a lot of radon, which would give everyone very low voices among other things.

2. My understanding of atmosphere is that you need a magnetosphere to keep it in, gravity notwithstanding. Otherwise the solar wind will strip it away. Mars lost its magnetosphere and then lost its atmosphere because of that. No reason to think that the heavy planet would not have a magnetosphere.

I think I see a scenario that could produce your world. Note that this is cataclysmic on an interstellar scale--life on nearby stars would have been eradicated.

We need a system that starts out with three stars, two of which are a close binary and each star exceeds (but not by too much) 8 solar masses. The third star is more distant and somewhat smaller.

The two big stars burn through their fuel and supernova, leaving behind neutron stars. The third is abused by these detonations but survives. The neutron stars are like their parents--a close binary. In time they spiral in and go splat--but enough mass is thrown off in the process to make your high-G world, from which a planet is born. (Note that I'm not sure it's possible for it to end up in a planet. The process is extremely energetic, it might be ejected too fast.)

Now you have a neutron star or black hole, a super-planet and an ordinary star. Now it's time for our third star to die--this time more peacefully, to a white dwarf.

This collection of debris encounters another star which ends up captured, the super-planet ending up in the life zone of the new star. The white dwarf sucks in matter from this fourth star, eventually you get a nova. This scours the atmosphere off the super-planet.

You're now left with a super-planet with no atmosphere. It's going to be an incredibly dense world as much of the stuff thrown off from the neutron star impact is from the lower part of the periodic table.

While you didn't ask for it this is going to be an immensely valuable source of heavy metals. (This is assuming it's worthwhile to ship such stuff. If you have a brute-force stardrive it probably isn't.)

Note that this is a very dangerous star system to be in, the white dwarf will periodically nova (although a sufficiently advanced science should be able to predict the detonations) and if it sucks down enough matter it will be even worse when it collapses down to a neutron star. You also have the jets from the other neutron star or black hole, although they could be aimed in a safe direction.