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*Ignoring external factors such as Jupiter's magnetosphere blowing this new atmosphere off. I'm not sure where to begin the maths for that

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  • $\begingroup$ For surface liquid water you need not only a temperature above 0.01 °C, you also need a surface pressure of more than 0.006 bar. But the surface pressure of Europa is much lower, about 100 nPa or 1 pbar (yes 1 picobar). $\endgroup$
    – Uwe
    Aug 14, 2023 at 20:20
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    $\begingroup$ @Uwe my engineering final project in uni was a Europa lander (DORRA the Europa Explorer, the paper is out in the wild) and every time someone said Europa has an atmosphere I reminded them that there's more atmosphere in a light bulb $\endgroup$
    – Erin Anne
    Aug 14, 2023 at 23:14
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    $\begingroup$ @ErinAnne An Ultra High Vacuum (UHV) with 1 µbar is ten times the surface pressure of Europa. $\endgroup$
    – Uwe
    Aug 15, 2023 at 12:56

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A very rough starting point is how much this atmosphere would differ from a perfect blackbody.

The melting point of water is roughly 270 kelvin for a wide range of pressures, so with that as a surface temperature, an object would radiate 300 W/m^2

Compare that to the solar energy flux of 50 W/m^2, and keeping in mind that the cross section area of a sphere receiving light is four times smaller than the total surface area, that means the atmosphere must reduce the thermal radiation to 1/24th of a blackbody.

For comparison, for well insulated Venus, the same numbers are 2600 W/m^2 emitted and 2600 W/m^2 received for a blackbody with the same temperature. Factoring in the area difference again, the heavy atmosphere of Venus is only improving upon a blackbody by a factor of 4. (The equality of the two numbers is a coincidence).

So probably we need a stronger greenhouse effect than Venus, but I stress that this is only a very approximate estimate.

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