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The planet orbits a supermassive gas giant, almost double the size of Jupiter. But the planet orbiting it is also supposed to have rather large rings in my story.
Question: Is it possible for a moon of a gas giant to have stable rings?
I expect the answer to be no, because of the gravity from the gas giant. Am I right in this assumption? And if I am right is there any way to make it possible for the planet to have rings? In a plausible / semi-plausible way.
The answer to your question is yes but.
It is certainly possible for a moon of a giant planet to have a ring, but the key word in your question is “stable”. What do you mean by stable? A year, a century, a millennia, 50 millennia, a million years? Any of these might be considered “stable” at some level.
The problem is that asking how long such a ring would last for is a very complex question. It would depend on the orbit of the moon, the mass of the moon relative to the planet, the presence of other moons, their sizes and orbits and many other factors.
But as a thought experiment to suggest that it should be possible, consider a series of cases starting with a Jupiter sized planet and a moon, could the moon have a large ring – debatable… now imagine increasing the mass of the planet in stages eventually the planet is so massive it becomes a brown dwarf and then a star, by the time it’s a star the moon is better considered to be a planet.
Could a planet have a ring in a binary system, I suggest yes it could. As the mass of the planet increase so does the stability of the moons ring, but how much mass is required to produce how much stability is very difficult to say.
The possible rings of Rhea have already been mentioned in the comments, but Iapetus is theorized to have once had rings. The moon has a huge equatorial ridge along its equator that could be the result of material from a ring system accumulating on the surface of the planet.
I think you could give your moon rings, but they would likely be thin, hard to see, and possibly unstable in the long run. However, since habitable gas giant moons are pretty theoretical, I think it's okay if you push the boundaries of realism.
General information here: https://en.wikipedia.org/wiki/Ring_system
It looks now like Saturn's rings are fairly long term stable.
A similar question came up on Astronomy SE: https://astronomy.stackexchange.com/questions/20514/what-stabilizes-rings-or-accretion-disks
And over in physics: https://physics.stackexchange.com/questions/26643/why-arent-saturns-rings-clumping-into-moons
The problem would be tides. Saturn has rings. It orbits the sun. The larger moons create and maintain the gaps in the rings that correspond to resonances with the moons.
Tidal forces go as the inverse cube of the distance. Put your moon far away.
Also give them shepherd moons to help keep them corralled.
Net conclusion: I think you are on solid enough ground to proceed with your story.
Stable is indeed the magic word here. The moon in your question has its own gravitational field, so if the ring particles are close enough to the planet, they could have a "stable" orbit. Loosely speaking, the moon's gravitational pull is able to overcome the planetary gravitational field for sufficiently small orbital distances between the moon and the ring particle.
The "sufficiently small orbital distance" here is called the "Hill radius". A ring particle orbiting well within this distance will have a reasonably stable orbit. Lots of weasel words there, but orbital stability is a sack full of weasels.
An approximation of the Hill radius for a moon in orbit around a larger planet is pretty straightforward to calculate, but I'll leave that to you.
