They performed laboratory experiments to see which conditions could produce the silica particles. The result was alkaline water, with a pH of 8.5 to 10.5, heated to at least 194 degrees. The results fit in with findings last year by other scientists who suggested that Enceladus concealed not just pockets of water but a sea at least as large as Lake Superior.

The mystery is how the interior of Enceladus, just 313 miles wide, grows that hot. A moon that small probably does not have enough radioactive elements at its core to provide continued warmth. A chemical reaction between water and rock called serpentinization could also provide some heat, but the primary mechanism is probably the tidal forces that Saturn exerts on Enceladus.

“The amount of energy being dissipated currently, as well as the location of heating, is not well understood,” said Terry A. Hurford, a scientist at NASA’s Goddard Space Flight Center in Maryland. “So it is possible that heating can bring water to those temperatures locally.”

The earlier evidence for an ocean on Ganymede came from magnetic measurements during flybys by the Galileo probe, which suggested a conductive layer below the surface. Ice is not a good conductor. Saltwater is. But the readings could also be explained by oddities in Ganymede’s magnetic field.

In the new research, the Hubble telescope scrutinized Ganymede for seven hours. It could not see below the surface, but it observed the shimmering lights of Ganymede’s auroras. As Jupiter rotates, once every 10 hours, its changing magnetic field causes the auroras to sway. If Ganymede were frozen, computer simulations showed, its aurora would sway by 6 degrees. But the salts of an under-ice ocean would generate a counteracting magnetic field, and the auroras would sway by only 2 degrees.

The auroras swayed 2 degrees. “It was exactly like all our computer modeling and all our theory predicted,” Dr. Saur said. “It was right on.”

The scientists are now applying the approach to Io, a fiery world that certainly does not have an ocean of water. But it might have an underground ocean of magma that would similarly dampen the swaying of auroras. The technique could one day be used to explore planets around distant stars and see if they, too, might have oceans.