Modeling the resonant planetary system GJ876
  The two planets about the star GJ 876 appear to have undergone extensive migration from their point of origin in the protoplanetary disk -- both because of their close proximity to the star (30 and 60 day orbital periods) and because of their occupying three stable orbital resonances at the 2:1 mean-motion commensurability. The resonances were most likely established by converging differential migration of the planets leading to capture into the resonances. A problem with this scenario is that continued migration of the system while it is trapped in the resonances leads to orbital eccentricities that rapidly exceed the observational upper limits of e_1 = 0.31 and e_2 = 0.05. As seen in forced 3-body simulations, lower eccentricities would persist during migration only for an applied eccentricity damping.   Here we explore the evolution of the GJ 876 system using two-dimensional hydrodynamical simulations that include viscous heating and radiative effects. We find that a hydrodynamic evolution within the resonance, where only the outer planet interacts with the disk, always rapidly leads to large values of eccentricities that exceed those observed.   Only if mass is removed from the disk on a time scale of the order of the migration time scale (before there has been extensive migration after capture), as might occur for photoevaporation in the late phases of planet formation, can we end up with eccentricities that are consistent with the observations. 
Willy Kley (1), Man-Hoi Lee (2), Norman Murray (3), Stan Peale (2)   ((1) Tuebingen, (2) Santa Barbara, (3) Toronto)