Could a moon of Epsilon Eridani b Have Surface Oceans of Liquid Water?

Question

Specifically, the gas giant Epsilon Eridani b, and a moon that has a mass of ≥0.25 M_e. If there's no feasible way the moon could have oceans at a distance of 3.52 AU from a star that emits 0.34 times the amount of light that the sun does.

Answer 1

The other answers are incorrect. There are two possible ways a moon of Epsilon Eridani b could have oceans.

One) Subsurface oceans beneath a thick shell of ice.

According to this list

Largest lakes and seas in the solar system

6 bodies in the outer solar system have global subsurface oceans of liquid water, and another 11 are suspected to. And I think there are probably more subsurface oceans in many larger Trans Neptunian Objects.

The question asked for surface oceans of liquid water, but for some types of stories, subsurface oceans might be good.

Two) Tidal interactions between the moon and its planet can cause sufficient tidal heating for liquid water oceans on the surface.

Theoretical studies of the possibiity of habitable exomoons of giant exoplanets show that the extent of tidal heating on those exomoons depends on their distance from their planets, among other factors. As a rule the closer to the planet, the greater the tidal heating on the moon.

If the moon orbits too close to the planet, the tidal heating will be enough to initate a runaway greenhouse effect, turning all the surface water into atmospheric water vapor. If the moon orbits even closer, the tidal heating will cause excesse vulcanism on the moon, making it a volcanic hell like Io.

Thus the phrase "habitable edge" for the inner limit of how close a moon can orbit to its planet while avoiding excessive tidal heating.

And it should be obvious that if the planet and moon orbit too far from their star for stellar radiation alone to warm the moon enough for liquid water, the moon could still be warm enough if it orbits outside the tidal edge but close enough for enough tidal heating for liquid water oceans.

Answer 2

Epsilon Eridani B has Mass of roughly 0.63 that of Jupiter (and is therefore not a brown dwarf star due to lack of mass), and a temperature of ~150 K (−123 °C; −190 °F).

This is too cold to have liquid water, and any moons of Epsilon Eridani B would have a similar temperature, and would therefore also not have surface oceans of liquid water.

Answer 3

It's too far away from the star and so cold for the surface of any ocean to be liquid.

Taking an example from the moons of Jupiter, Europa in particular, the possibility of a sub-surface ocean might be explored.

Internal heat generated by tidal flexing from the interaction with the orbits of other moons, and perhaps a slightly eccentric orbit might produce sufficient equivalent-to-tectonic stresses within the crust, could enable liquid water to exist.

Answer 4

Whoops, looking at the numbers, I've just realized it is kinda impossible. So nevermind!
Here's the math (I might've made an error somewhere): $$ f=\frac{L}{4\pi d^{2}} $$ L is the luminosity of Epsilon Eridani, which is 0.34 times that of the sun. d is the distance between Epsilon Eridani and Epsilon Eridani b, which is 3.54 AU
So plugging in the numbers gives us $$ \frac{0.34}{4\pi 3.52^{2}}\approx0.00218365349994 $$ The final value is the fraction of earth's solar flux, which is 1373W/m², so if we do a simple calculation: $$ 1373\left(0.00218365349994\right)=2.99815625542 $$ The final value we get is 2.99815625542W/m². Let me know if I got anything wrong!
Anyway, enough math, the final value (2.99815625542W/m²) is very small. Definitely not enough to raise the moon's temperature above 0C (which is the freezing point of water no matter the pressure). So this question answered itself with math!