Constraints on the size and dynamics of the J1407b ring system

Context. J1407 (1SWASP J140747.93-394542.6 in full) is a young star in the Scorpius-Centaurus OB association that underwent a series of complex eclipses over 56 days in 2007. To explain these, it was hypothesised that a secondary substellar companion, J1407b, has a giant ring system filling a large fraction of the Hill sphere, causing the eclipses. Observations have not successfully detected J1407b, but do rule out circular orbits for the companion around the primary star.
Aims: We test to what degree the ring model of J1407b could survive in an eccentric orbit required to fit the observations.
Methods: We run N-body simulations under the AMUSE framework to test the stability of Hill radius-filling systems where the companion is on an eccentric orbit.
Results: We strongly rule out prograde ring systems and find that a secondary of 60 to 100 M_Jup with an 11 yr orbital period and retrograde orbiting material can survive for at least 10⁴ orbits and produce eclipses with similar durations as the observed one.