Your understanding of the Roche limit is not accurate. The International Space Station orbits well below the Roche limit of the Moon without being destroyed, for example, do you know why this is?
The Roche limit is simply the volume of space around a body where the tidal stress tends to destroy a body of a given density
This distinction is important. The Roche limit is dependent on the density of the other body, as you see here:
is the density of the primary, and ?_m
is the density of the secondary. Indeed several moons of Jupiter and Saturn orbit the planet close enough where they would be inside
the Roche limit if they had lower densities.
An unbound mass of gas is not governed by quite the same mechanics that governs tidal disintegration of rigid bodies.
You are correct that a gas disk close to the planet would be unstable, but not for the reason you think. The reason a gas disc very near a planetary body would be unstable is due to the disc's self-interaction - particles collide with each other causing them to trade orbital momentum around. Particles that surrender too much orbital momentum over the course of this find themselves falling onto the planet. If there were far fewer particles, then they could freely orbit the planet without having to worry about being accreted -- they would be in a normal orbit. The Roche limit is simply the distance from the primary that the secondary would be tidally disrupted.
(Note for obvious reasons I'm excluding effects of stellar radiation pressure and other external influences).
can you give us an example in the solar system or elsewhere ?
All the giant planets have rings within their Roche limits. But they are small particles, like a gas would be, and thus are free to orbit the planet without Roche limit -related tidal disruption.
Edit: These pictures are amazing, Cham
Cham wrote:I'm wondering if this effect could be used for something nice...
You could probably use it for Be stars