Monday, April 22, 2002, 8:40-10:30am

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*S. J. Peale, M. H. Lee (Dept. of Physics, UCSB)*

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, \theta_{1} =
\lambda_{1}-2\lambda_{2}+\varpi_{1} and \theta_{2} =
\lambda_{1}-2\lambda_{2}+\varpi_{2}, and the secular resonance
variable, \theta_{3} = \varpi_{1}-\varpi_{2} (\lambda_{i} and
\varpi_{i} are the mean longitudes and the longitudes of
periapse), about 0^{\}circ in the GJ 876 system differs from
the geometry of the Io-Europa pair, where \theta_{2} and
\theta_{3} librate about 180^{\}circ. The large
eccentricities, e_{i}, 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 e_{1} 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 (m_{1}+m_{2})/m_{0} \la 10^{-3} (m_{0}, m_{1}, and m_{2} are
the masses of the primary, inner and outer planets
respectively) and very small initial e_{i}, the system is
captured automatically into all resonances as the orbits are
forced together, with \theta_{1} librating about 0^{\}circ
and \theta_{2} and \theta_{3} librating about 180^{\}circ
--- like the Io-Europa pair. Continued migration forces the
e_{i} to larger values until the system passes smoothly over
to the GJ 876 configuration with all \theta_{i} librating
about 0^{\}circ. For m_{1}\la m_{2}, the e_{i} continue to
grow with continued migration with libration amplitudes
about 0^{\}circ remaining very small until instability
ensues at very large e_{i}. The e_{i} at which the system
becomes unstable decrease with increasing planetary masses.
For m_{1} \ga m_{2}, the passage through the Io-Europa
configuration is as above, but when the increasing e_{1}
reaches ~0.1--0.2 (depending on m_{1}/m_{2}), the
libration centers depart by tens of degrees from 0^{\}circ
leading to stable libration of the \theta_{i} far from
either 0^{\}circ or 180^{\}circ. As eccentricities continue
to grow, the libration centers return to 0^{\}circ and
remain there until instability is induced. If (m_{1}+m_{2})/m_{0}
\ga 10^{-3}, which forces large e_{i} before resonance
encounter, then the system passes directly into the GJ 876
configuration upon resonance capture. The libration of both
\theta_{1} and \theta_{2} forces the \varpi_{i} to precess
at the same rate normally in a retrograde sense, but this
changes to prograde above some large value of e_{1} while
librations of the \theta_{i} are maintained. Within each
type of evolution, the details of the path depend only on
m_{1}/m_{2} and not on the total planetary mass, provided
m_{i} are not too large. Support for this work is NASA PG&G
Grant NAG5-3646.

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Bulletin of the American Astronomical Society, **34**, #3

© 2002. The American Astronomical Society.