  The gas giant planets in the Solar System have a retinue of icy moons, and we
expect giant exoplanets to have similar satellite systems. If a Jupiter-like
planet were to migrate toward its parent star the icy moons orbiting it would
evaporate, creating atmospheres and possible habitable surface oceans. Here, we
examine how long the surface ice and possible oceans would last before being
hydrodynamically lost to space. The hydrodynamic loss rate from the moons is
determined, in large part, by the stellar flux available for absorption, which
increases as the giant planet and icy moons migrate closer to the star. At some
planet-star distance the stellar flux incident on the icy moons becomes so
great that they enter a runaway greenhouse state. This runaway greenhouse state
rapidly transfers all available surface water to the atmosphere as vapor, where
it is easily lost from the small moons. However, for icy moons of Ganymede's
size around a Sun-like star we found that surface water (either ice or liquid)
can persist indefinitely outside the runaway greenhouse orbital distance. In
contrast, the surface water on smaller moons of Europa's size will only persist
on timescales greater than 1 Gyr at distances ranging 1.49 to 0.74 AU around a
Sun-like star for Bond albedos of 0.2 and 0.8, where the lower albedo becomes
relevant if ice melts. Consequently, small moons can lose their icy shells,
which would create a torus of H atoms around their host planet that might be
detectable in future observations.
