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Free-floating planets (FFPs) can result from dynamical scattering processeshappening in the first few million years of a planetary system's life. Severalmodels predict the possibility, for these isolated planetary-mass objects, toretain exomoons after their ejection. The tidal heating mechanism and thepresence of an atmosphere with a relatively high optical thickness may supportthe formation and maintenance of oceans of liquid water on the surface of thesesatellites. In order to study the timescales over which liquid water can bemaintained, we perform dynamical simulations of the ejection process and inferthe resulting statistics of the population of surviving exomoons aroundfree-floating planets. The subsequent tidal evolution of the moons' orbitalparameters is a pivotal step to determine when the orbits will circularize,with a consequential decay of the tidal heating. We find that close-in ($a\lesssim 25 $R$_{\rm J}$) Earth-mass moons with CO$_2$-dominated atmospherescould retain liquid water on their surfaces for long timescales, depending onthe mass of the atmospheric envelope and the surface pressure assumed. Massiveatmospheres are needed to trap the heat produced by tidal friction that makesthese moons habitable. For Earth-like pressure conditions ($p_0$ = 1 bar),satellites could sustain liquid water on their surfaces up to 52 Myr. Forhigher surface pressures (10 and 100 bar), moons could be habitable up to 276Myr and 1.6 Gyr, respectively. Close-in satellites experience habitableconditions for long timescales, and during the ejection of the FFP remain boundwith the escaping planet, being less affected by the close encounter.

Presence of liquid water during the evolution of exomoons orbiting ejected free-floating planets