✍ Scribed by Günther Wuchterl; Eike Guenther
No coin nor oath required. For personal study only.
In the extrasolar planetary system GJ 876 two planets orbit their central star with periods of approximately 30 and 60 days respectively, i.e. they are in a 2:1 mean motion resonance. Additionally, the periastrae are always fully aligned with very small libration. The masses of the two planets are M 1 = 0.56 and M 2 = 1.89 M Jup , with semi-major axis and eccentricities of a 1,2 = 0.13 and 0.21AU, and e 1,2 = 0.24 and 0.04. The stellar mass of only 0.32M leads to high mass ratios in this case. Theoretical attempts to model such a system typically assume a convergent migration scenario where an inwardly migrating outer planet, which is still in contact with an outer protoplanetary disk, catches up with a slower or stalled inner planet which orbits in the inner cavity of the disk (see eg. Kley et al. 2004). Depending on the migration rates, masses and eccentricities of the two planets capture can occur in different resonances. Utilizing simple N-body simulations applying additional damping forces mimicking the presence of a disk, i.e. specifying the damping rates of the semi-major axis (a/ ȧ) and eccentricity (e/ ė), it has been shown that the final observed eccentricities of GJ 876 can only be explained with models where the eccentricity damping rate is about 100 times faster than the migration rate (Lee & Peale 2002). We present full hydrodynamic simulation of this system to understand the formation process of resonant planetary systems in more detail.
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