In the article that @thistle linked to, it cites Prof Björn Benneke's paper which goes through all of the reasoning his team used to determine that it might be a water world. They talk about "sub-Neptune worlds" a lot but these run from 1.5-2.5 times Earth mass so I am not sure you could have one of these "supercritical" oceans at 1 Earth mass.
I realised that because Benneke cites another paper which talks about "what happens if essentially your entire planet is made of water, and it is impossible to "run out" of ocean to evaporate?" And what happens is it will boil and boil and boil until the pressure of the gas (that just boiled off) increases to the point the pressure and temperature combo (p-T for short) hits the "critical point" of water. At that point you essentially have an ocean that is all "supercritical water" so the water is no longer boiling or condensing between a water ocean and a steam atmosphere, it's just one very deep "ocean" of this weird phase of water called "superfluid." The critical point happens when the temperature is very high but the pressure stops it from boiling.
This... thing... which is neither ocean or atmosphere... is nonetheless the top layer of the planet and it is the thing that tails off into interplanetary space, so you can call it an atmosphere for now. If you keep adding heat to the bottom of it (via vulcanism) and the middle of it (via solar radiation) there is a point where the top of it has got as hot as it's going to get and it's losing heat to space as fast as it ever will. At that point the next bunch o' kilowatts from the star are just going to turn straight into heat which causes the entire thing to expand, and because it's expanded now there's more room for things to radiate off again.
So in short
- the ocean boils
- the ocean stops boiling because the pressure is now too high
- the liquid ocean gets superhot
- the ocean and the "steam" atmosphere will effectively "merge" into one superfluid thing once water hits 646K (373C) and 220 atmos. (Note Venus is about 90 atmos.)
So it's a race between whether the atmosphere can leak off fast enough at the top versus whether it can get tall enough to be 220 atmos at the bottom, or whether the top leaks heat faster so it never hits supercritical.
But before that point...
If the temp never hits 646K and the pressure never hits 220 atmos you can have any equilibrium you like provided you have enough water to expand the atmosphere so the rate it's leaking heat matches the rate the sun and vulcanism are heating it. For a planet which is at 500K there will be some pressure where it boils awhile and then the pressure of the conventional steam atmosphere is enough to stop it boiling, and it leaks heat out to space at the top, and it will sit there forever, provided there was enough water to allow the atmosphere to expand to that point.
There's a thing called a phase diagram which will tell you which phase water wants to be in for a given temperature and pressure, so you can look at that and figure out what pressure the atmosphere would have to be to keep a 150C or 200C ocean stable. And then you could work out how deep the steam atmosphere needs to be to achieve that on a 1g ELW that is x distance from the sun(s). (Bear in mind though that assumes a pure steam atmosphere, if it's a mix then you have to use "partial pressures" and I for one need pencil and paper at that point)
I found this quite readable but you do need high school physical chemistry (partial pressures and the gas laws)
