The enormous Herschel Crater makes Mimas look rather like the Death Star space station from Star Wars
It has a tell-tale wobble that is twice as big as expected for a moon with a regular, solid structure.
The researchers offer two explanations: either it has a vast ocean beneath its surface, or a rocky core with a weird shape resembling a rugby ball. The study appears in Science Magazine.
Its authors are astronomers in the US, France and Belgium, who based their calculations on high-resolution photos of Mimas snapped by the Cassini spacecraft. Cassini was sent to Saturn in 1997 to explore the planet and its many moons, which so far number 62 (53 with names).
The researchers built a detailed 3D model of Mimas using images taken from various angles, and tracked the movement of hundreds of reference points on its pockmarked surface.
"After carefully examining Mimas, we found it librates - that is, it subtly wobbles - around the moon's polar axis," said lead author Dr Radwan Tajeddine, who works at Cornell University in the US.
Apart from these gentle "librations", Mimas otherwise presents the same face to Saturn throughout its orbit.
Our own moon has a similar motion, with a small wobble that offers us slightly different views of the satellite over time. But when Dr Tajeddine and his colleagues put all their measurements together, they found that the surface of Mimas swivels back and forth by 6km.
This is quite a wobble for a moon that measures less
than 400km across. In fact, it is twice as much movement as expected, based on
Mimas's size and its elliptical orbit.
"This is where we started thinking of more exotic interior models," Dr Tajeddine told BBC News.
First, the team tested whether the extra rotation could be explained by a deformity underneath the enormous Herschel Crater, one-third the size of Mimas itself, which gives the moon its signature appearance.
But even a "huge mass anomaly" created by the wallop that left the crater would not deliver the amount of movement that Dr Tajeddine's team had observed.
Instead, they wondered whether Mimas might be far from the simple, uniform sphere of ice and rock that most planetary scientists had previously assumed.
"Nature is essentially allowing us to do the same thing that a child does when she shakes a wrapped gift in hopes of figuring out what's hidden inside," Dr Tajeddine said. His team settled on two likely plot twists, wrapped beneath Mimas's icy crust.
Firstly, their calculations suggested that the wobbles could arise from a core that was squashed or elongated by 20-60km: a huge, central rugby ball of rock.
Alternatively, the moon could have a normal spherical core and crust, but separated by a "global ocean". That way, Dr Tajeddine explained, "the shell can wobble more easily, because it's not attached to another mass".
Of the two explanations, he favours the subterranean sea.
"When we saw this wobbling, the first thing we thought of was an ocean," Dr Tajeddine said.
Either possibility would make Mimas a much more interesting research subject: "This brings the spotlight back to this moon, which was a little bit ignored."
Prof Chris Lintott, an astrophysicist at the University of Oxford, was surprised to hear of the new results.
"If you'd asked me before now, I would have said that Mimas is a boring, icy moon.
"If the ocean is really there, we're getting to the point where it's just completely standard for icy moons to have substantial bodies of water inside - and that could have interesting implications for how many of these things could support life."
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