Forming ring systems

Did Saturn's rings form during the Late Heavy Bombardment ?

A hypothesis that attempts to explain why Saturn has a massive ring system and the other giant planets don't. Basic idea is that a Mimas-sized moon migrated inside the Roche limit and was destroyed by a large impact during the Late Heavy Bombardment. The alternative scenario, formation by disruption of large comets, suffers from the problem that Saturn is the giant planet expected to receive the least amount of such material, which is problematic in the light of the lack of massive ring systems around the other giant planets.

The reason the disrupted moon scenario works for Saturn and not for the other giant planets is that at Saturn, the synchronous orbit is below the Roche limit. This means the moon can survive in the Roche zone until the LHB without migrating inwards towards the planet. This would also be the case for Jupiter but the rings probably wouldn't have survived. The problem with this scenario is that there is the problem that Saturn's rings do not contain much silicate material, which means that an explanation is needed for why the satellite's core was not incorporated into the ring system.

...actually I'm not sure about some of the mathematics in there: for a start the quoted ratios for R_synchronous/R_Roche do not agree with the values they give.

If you work it out this ratio turns out to be independent of planetary mass, so the condition for R_synch/R_Roche<1 turns out to be an upper limit on rotation. For icy satellites (~1000 kg/m³) this turns out to mean requiring the planet has a rotation period less than 12 hours, for rocky satellites (~3000 kg/m³) the limit is less than 7 hours, which is faster than any of the planets in our solar system.