The state of icy worlds during differentiation and accretion, and how they survive with their water

sno's answer gives a good account of why melted water doesn't evaporate in a water world. However, I think there is an implicit assumption in the question that needs a frame challenge.

Since the question is specifically about melted water in water worlds and not melted rock in rocky worlds, the implicit assumption is that liquid water evaporates – as we know from daily experience – but liquid rock doesn't.

The truth is that molten rock also evaporates. The vapor pressures of some molten minerals have been measured, and they are comparable or greater than that of liquid water.

According to Walter and Carron (1964) "this pressure is 190 ± 40 mm Hg at 1500°C, 450 ± 50 mm at 1800°C and 850 ± 70 mm at 2100° C" for some Philippine tektites, and other works give similar ranges. For comparison, the vapor pressure of water at its melting point is just 4.5 mm Hg, and, at its boiling point, it is 1 atm = 760 mm Hg.

Therefore, the problem of why an icy body that is hot enough to melt water and differentiate doesn't lose its water to evaporation isn't different from the problem of why a rocky body that is hot enough to melt rock and differentiate doesn't lose its rock to evaporation. And the answer is the same: the solid or frozen crust prevents the molten interior from evaporating.

And, in the end, the answer boils down to something that has been often said on this site: in the outer solar system, ice is just another kind of rock, and we could add that liquid water is just another kind of magma.

I think the answer is that, for example, Pluto is so far from the sun that it radiates away far more heat during formation than it receives from the sun, so the surface freezes, locking in the water in a sub-surface ocean. Water ice on the surface tends not to evaporate.

See also: Evidence supports ‘hot start’ scenario and early ocean formation on Pluto

Answer: they cooled too fast.

The fate of gasses in the atmosphere of a small hot planet depend on HOW small, HOW hot and how long you can wait around to watch.

In Jeans escape https://en.wikipedia.org/wiki/Atmospheric_escape a proportion of the gas molecules in the exosphere have thermal velocities above the planet’s escape velocity. If they happen to head off into the void without collision, gravity cannot return them and they are lost. The rate of loss depends on

• the body’s gravitational acceleration (escape velocity),
• -the molecular weight of the molecules/atoms in question, and
• -the exosphere temperature curve with time.

For instance, at the base of Earth’s exosphere, (roughly 900C), only 1:1000 hydrogen atoms have escape velocity, compared with 1:10^15 He atoms or 1:10^60 O atoms. H2O molecules would be even slower than these mono-atomic species.

The bodies you mention are small, so they have low escape velocity. But small bodies also cool much quicker than large bodies. They have less heat of gravitational collapse to begin with and also a higher surface-to-volume ratio. Since they are also further from the sun than inner planets, they receive less solar heating.

Basically, they cooled too fast to lose their water through thermal escape.

If these bodies had been closer to the sun, they would likely have lost their atmosphere through

• Thermal escape
• Loss of any magnetic field from core solidification would allow sputtering escape and photochemical escape