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Could it be possible for Earth-like rogue planet to maintain large bodies of liquid water on the surface without a sun by relying mostly on tidal forces of a moon (or multiple moons). How big/far/fast would the moon have to be?

What about a binary planet instead of planet and a moon?

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    $\begingroup$ A binary planet system - yes. A single rogue planet, no, because you need a near by large near by body to have tides. $\endgroup$
    – userLTK
    Commented Aug 12, 2015 at 0:11
  • $\begingroup$ userLTK: Then ofc there would be the question if this configuration is stable over Gyrs, what I guess OP's question aims at. Tidal heat in the end is converted orbital angular momentum. $\endgroup$
    – AtmosphericPrisonEscape
    Commented Aug 12, 2015 at 1:27
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    $\begingroup$ Binary planet systems like Pluto+Charon have the problem with getting mutually tidally locked, in both rotation and orbit. There shouldn't be much tidal forces going on there (but everyone is surprised by their active geology, I'm hoping for some conclusions soon). The Galilean moons pull each other to eccentric orbits which in turn is what causes their tidal forces relative to Jupiter. Maybe a multi-moon rogue planet could have an atmosphere on one of its moons? $\endgroup$
    – LocalFluff
    Commented Aug 12, 2015 at 5:54

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Do you need tidal heat? What about core heat?

Ice is a fair insulator. Put enough ice on top and the heat flux from the core can keep the bottom of the oceans liquid, no tides required.

If you need the water on the surface, I don't think it's possible. Even a huge amount of interior heat (whether from tides, radiation, or primordial) wouldn't be sufficient to hold the surface liquid. The Earth possibly had periods where there was no surface water (snowball earth), and that was with the advantages of an atmosphere and solar input.

The lack of a sun is going to make having an Earth-like atmosphere difficult. In an interstellar environment, any thin atmosphere will freeze out. Without an atmospheric blanket, the surface temperature plummets.

So I think you could have an ocean, but not with surface water.

One more thing. Assuming the current heat production of the earth, and its size, I calculate that something around 5.6km of ice is sufficient insulation. Water below that depth with average heat flow would be liquid (ignoring pressure effects and only assuming temperature and heat flow issues). That's a lot of ice, but not implausible.

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