Astronomy and Astrophysics – Astronomy
Scientific paper
Sep 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002dda....33.0102p&link_type=abstract
American Astronomical Society, DDA Meeting #33, #01.02; Bulletin of the American Astronomical Society, Vol. 34, p.933
Astronomy and Astrophysics
Astronomy
1
Scientific paper
Ease of capture into low-order mean-motion resonances from nebula induced differential migration means that such resonances are likely to be ubiquitous among extrasolar planetary systems. The libration of the lowest order 2:1 mean-motion resonance variables, θ 1 = λ 1-2λ2 +ϖ_1 and θ 2 = λ 1-2&lambda2 +ϖ_2, and the secular resonance variable, θ 3 = ϖ1-ϖ_2 (λ i and ϖi are the mean longitudes and the longitudes of periapse), about 0o in the GJ 876 system differs from the geometry of the Io-Europa pair, where θ 2 and θ 3 librate about 180o. The large eccentricities, ei, of the GJ 876 system cause its libration geometry to differ from that of Io and Europa, and, remarkably, the GJ 876 geometry is stable for e1 up to 0.86 (Lee and Peale 2002). Following a differentially migrating, coplanar two-planet system through capture into the 2:1 resonances for a selection of parameter values reveals the conditions for a wide variety of unusual 2:1 resonance configurations. For (m1+m_2)/m_0 ⪉ 10-3 (m0, m1, and m2 are the masses of the primary, inner and outer planets respectively) and very small initial ei, the system is captured automatically into all resonances as the orbits are forced together, with θ 1 librating about 0o and θ 2 and θ 3 librating about 180o --- like the Io-Europa pair. Continued migration forces the ei to larger values until the system passes smoothly over to the GJ 876 configuration with all θ i librating about 0o. For m1⪉ m2, the ei continue to grow with continued migration with libration amplitudes about 0o remaining very small until instability ensues at very large ei. The ei at which the system becomes unstable decrease with increasing planetary masses. For m1 ⪆ m2, the passage through the Io-Europa configuration is as above, but when the increasing e1 reaches ~ 0.1--0.2 (depending on m1/m_2), the libration centers depart by tens of degrees from 0o leading to stable libration of the θ i far from either 0o or 180o. As eccentricities continue to grow, the libration centers return to 0o and remain there until instability is induced. If (m1+m_2)/m_0 ⪆ 10-3, which forces large ei before resonance encounter, then the system passes directly into the GJ 876 configuration upon resonance capture. The libration of both θ 1 and θ 2 forces the ϖi to precess at the same rate normally in a retrograde sense, but this changes to prograde above some large value of e1 while librations of the θ i are maintained. Within each type of evolution, the details of the path depend only on m1/m_2 and not on the total planetary mass, provided mi are not too large. Support for this work is NASA PG&G Grant NAG5-3646.
Lee Michael H.
Peale Stanton J.
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