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 } \approx 0.31 and e _ { 2 } \approx 0.05 .
As seen in forced 3-body simulations , these lower eccentricities would persist during migration only for an eccentricity damping rate \dot { e } _ { 2 } / e _ { 2 } exceeding \approx 40 \dot { a } _ { 2 } / a _ { 2 } .
Previous theoretical and numerical analyses have found \dot { e } / e \sim \dot { a } / a or even eccentricity growth through disk-planet interactions .

In an attempt to find effects that could relax the excessive eccentricity damping requirement , we explore the evolution of the GJ 876 system using two-dimensional hydrodynamical simulations that include viscous heating and radiative cooling in some cases .
Before we evolve the whole system , the disk with just the outer planet embedded is brought into equilibrium .
We find that the relaxed disk remains circular in all models for low planet-to-star mass ratios q _ { 2 } , but becomes eccentric for high mass ratios for those models with fixed temperature structure .
The disk in models with full radiative thermodynamics remains circular for all q _ { 2 } considered due to the larger disk temperatures .
Given the small stellar mass , the mass ratio for the GJ 876 system is rather high ( with minimum q _ { 2 } = 5.65 \times 10 ^ { -3 } ) , and so the GJ 876 disk may have been slightly eccentric during the migration .

With a range of parameter values , 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 — similar to the three-body results .
The resonance corresponding to the resonant angle \theta _ { 1 } = 2 \lambda _ { 2 } - \lambda _ { 1 } - \varpi _ { 1 } ( involving the inner planet ’ s periapse longitude , \varpi _ { 1 } ) is always captured first .
There is no additional delay in capturing \theta _ { 2 } = 2 \lambda _ { 2 } - \lambda _ { 1 } - \varpi _ { 2 } into resonance that is attributable to the secular prograde contribution to the precession of \varpi _ { 2 } from the interaction with the disk , but an eccentric disk can induce a large outer planet eccentricity e _ { 2 } before capture and thereby further delay capture of \theta _ { 2 } for larger planetary masses .
The delay in capturing \theta _ { 2 } into libration , while delaying the resonance-induced growth of e _ { 2 } , has no effect on the forced eccentricities of both planets , which are uniquely determined by the resonance conditions , once both \theta _ { j } are librating .

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 .