Apparently we've known for a while that Saturn's upper atmosphere doesn't glow as brightly as expected. Solar wind hitting the molecules there should ionize some and make them glow; and they do--but not quite enough.
It was proposed some time back that water from the rings might quench the interactions that make the infrared glow, but it was hard to prove.
This team got a detailed look at the IR glow, and found banding that has some resemblance to the bands of the rings.
The team didn't actually detect water, but they modeled how ionized water (solar wind hits the ring material too) would stream from the rings down to the surface along magnetic field lines and make certain regions glow less, producing the patterns they see.
Of course this isn't "rain" in the sense of drops of water. In fact it would either have to be extremely rarefied or else there's some recycling mechanism that sends water back out to the rings somehow (and I haven't a clue how that would work).
The rings are supposed to be 3x10^22 g of ice (mostly), and the area being hit on Saturn is (conservatively) about 1x10^20 cm^2. A million years is about 3x10^13 seconds, so if the rings aren't going to evaporate in a million years then they can't lose more than 10^9 g/second. If they're flying at about 1000m/sec (to be very conservative) then the "rain" has to have a density less than 1x10^-16 g/cm^3.
Unfortunately I don't have the time to estimate how long water would stay present in the upper atmosphere or how much you need to produce the quenching they see. You could use those numbers to get a rough estimate of how much water they need falling in to produce the effect they see, and then we could see how much the rings would be losing each year, and whether this made sense.
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