Unfortunately, this question has an easy answer: not much. So far, no exoplanet has been confirmed to have a moon, even though scientists are detecting planets the size of the Jovians. Even though nothing has been confirmed, however, there have been some interesting potential discoveries. We say potential because again, the systems are so far away it is hard to confirm anything.
One astronomer from the University of Padua in Italy, Cecilia Lazzoni, claims she found two giant exomoons. In both cases, the planets are about 11 to 13 times as large as Jupiter, and their moons are around Jupiter size. The question is if these systems can even be understood as planets and their orbiting moons. Some say these planets could be classified as brown dwarfs, objects that can only complete half of the proton-proton chain and thus don’t achieve star status. Brown dwarfs are normally classified as 13 times as large as Jupiter, but the definition is completely clear. If the object is a brown dwarf, then the moon could actually be a planet. Another explanation for these systems could be calling them binary planets, similar to the idea of binary stars.
Other researchers from Columbia University claim to have evidence of an exomoon that is around Neptune size, orbiting around a planet several times as large as Jupiter.
This kind of discovery is exciting because, even if they aren’t called exomoons but end up being planets, they force us to expand how we classify and think of extrasolar systems. Additionally, similar to how astronomers consider Europa and other Jovian moons as possibilities for containing life, some consider exomoons as candidates for life outside our solar system. Dr. Phil Sutton from the University of Lincoln said,
“These moons can be internally heated by the gravitational pull of the planet they orbit, which can lead to them having liquid water well outside the normal narrow habitable zone for planets that we are currently trying to find Earth-like planets in…I believe that if we can find them, moons offer a more promising avenue to finding extra-terrestrial life.”
Exactly like our Jovian moons! So although exomoons might offer possibilities outside of what we know about our own solar system, we can still apply the knowledge we find in our solar neighborhood to other systems far, far away.