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If it does exist, the numbers indicate the Neptune-sized moon would be up to 1.5 per cent the mass of its planet.
While it might be a supersized system, the mass ratio and the distance between the two bodies would be on par with the Earth and our moon, Dr Horner said.
But it is a mystery how such a moon — which is bigger than any satellite in our solar system — could form.
Unlike Earth, planet 1625b is a gas giant, so a moon could not be formed from an impact in the same way as our moon.
One possible explanation put forward by the research team is that the moon and planet formed from the same disc, like Jupiter's moons Io, Europa, Callisto and Ganymede.
"We don't really know how this would have formed, but this doesn't mean it couldn't have," Dr Horner said.
"When we found the first planets around other stars — the hot Jupiters — everyone said this doesn't make sense because it's not how we expect planets to form.
"The problem was we'd built all our ideas about how planets formed on one planetary system — the solar system."
Chris Tinney, who heads up the exoplanetary science group at the University of New South Wales, said finding exomoons was an extremely difficult feat.
"The problem is that moons are very small in general compared to planets and finding planets itself is incredibly hard," said Professor Tinney, who was not involved in the research.
Add trying to catch the orbit of a moon at the right time as it goes around the planet and sun, and it becomes a very complicated picture.
"There is a lot of statistical analysis to try and determine whether … [1625b's] got an exomoon," he said.
"I don't think it's completely proven one way or the other. There's clearly something else going on in this system.
"But whether it's an exomoon or not, we've probably got to wait for yet another year."
That's how long it takes for 1625b to orbit its sun and astronomers will be able to see it transit again.
The next opportunity to do this will be in May 2019.
Mr Teachey and Dr Kipping have put in for more Hubble time, but there are no guarantees.
"If we don't get the time, maybe someone else will get the time. That would be just fine with us," Mr Teachey said.
"It would be more convincing … if somebody else came along and got the same answer."
That was really interesting!
I love that there are no certainties in our understanding of the universe.
It looks like a billiard ball!
Maybe if life is there, it's making sure we can't interfere!!
Rogue planets are the drifters of the galaxy, wandering interstellar space alone. Now it turns out they could have company in the form of moons — and perhaps even sustain life that hitched a ride on them.
New simulations show giant planets kicked out of their solar system could hang onto nearly half their moons during the ejection process, and potentially maintain conditions for life for billions of years.
The work, which will be published in the Monthly Notices of the Royal Astronomical Society, suggests that life might be more widespread through the galaxy than we thought, said astrophysicist and study co-author Jason Steffen from the University of Nevada, Las Vegas.
"Say there's one out of every million stars that ejects a planet that's like Jupiter, with its conditions.
"That's 300,000 rogue planets [in our galaxy] that could have life on their moons."
That's a conservative estimate, he added: "We suspect it's closer to 1 per cent, rather than one in a million."
When it comes to looking for life as we know it, it's hard to go past a solar system's "Goldilocks zone", a region around a star where it's not too hot and not too cold for liquid water to exist.
But in recent years, astrobiologists have turned their gaze to less intuitive targets: giant planets way out in the frozen reaches of a solar system — or, rather, their moons.
There, far from the warming rays of the sun, water stays liquid thanks to heat generated from friction, when a moon is warped by its planet's gravitational pull, as well as that of other moons.
We see this "tidal flexing" in our solar system with Jupiter's suite of moons, Dr Steffen said.
The three innermost moons, Io, Europa and Ganymede, traipse around Jupiter in what's called a resonant frequency: in the time it takes Ganymede to orbit once, Europa orbits twice, and Io makes it around four times.
When Europa is directly between Jupiter and Ganymede, for instance, it's pulled in two directions.
But when Ganymede is around the other side of Jupiter, Europa's tugged more strongly in one direction.
All this regular stretching and squashing causes enough heat to build up inside Europa and, planetary scientists suspect, sustain a liquid ocean beneath its icy crust — an ingredient for life.
And with the relatively recent discovery of rogue planets — huge, gas Jupiter-like objects that wander the galaxy, untethered to a star — Dr Steffen and his student Ian Rabago asked: could they also host and sustain life on their moons?
To find out if moons might survive a planetary ejection — or if they'd be stripped off their planet — Mr Rabago and Dr Steffen ran 77 simulations of a planetary system with three Jupiter-like gas giants, each with moons.
To their surprise, they saw that almost half the moons survived.
"My gut feeling was that it would be less than that, maybe 10 per cent," Dr Steffen said.
"I certainly didn't expect to have that many systems that could keep any moons."
Around 22 per cent of moons were left behind in the solar system, while the remainder were slung out into space, free from any star or planet.
The most gratifying result, Dr Steffen said, was that simulated moon systems with the same orbital resonance as Io, Europa and Ganymede were among those that survived.
"You could take Jupiter, you can kick it out of the solar system through natural processes, and those resonance conditions, and potential for life, can survive."
Aditya Chopra, an astrobiologist at the Australian National University who was not involved with the study, said life on a rogue planet's moon would probably find it a lot tougher to survive than if it remained in a solar system.
"Even though Europa is so far away, UV radiation from the sun is breaking down chemicals on its surface, which might be useful for life," he said.
"Rogue planets don't get a whole lot of photons.
"And in the solar system you have this constant influx of material, like comets, but you don't have that so much with rogue planets."
And while detecting rogue planets is no easy feat at the moment — let alone any life that may linger on their moons — there is an upside.
"The great thing about rogue planets and their moons is they may visit us," Dr Chopra said.
He pointed to 'Oumuamua, a comet from interstellar space that zipped through our solar system last year.