**34th Meeting of the AAS Division on Dynamical Astronomy, May 2003**

* 12 Migration and Others*

Oral, Wednesday, May 7, 2003, 10:50am-12:35pm,
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## [12.06] Diversity and Origin of 2:1 Orbital Resonances in Extrasolar Planetary Systems

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

The 2:1 orbital resonances of the two planets about GJ 876
can be easily established by the differential migration of
the orbits due to planet-disk interactions. A wide variety
of stable 2:1 resonance configurations can be reached by
differential migration of planets on initially coplanar and
nearly circular orbits. These include configurations with
librations of \theta_{1} = \lambda_{1} - 2\lambda_{2} + \varpi_{1}
(where \lambda_{i} and \varpi_{i} are the mean longitudes
and the longitudes of periapse) about 0^{\}circ and
\theta_{2} = \lambda_{1} - 2\lambda_{2} + \varpi_{2} about
180^{\}circ (as in the Io-Europa pair), configurations with
librations of both \theta_{1} and \theta_{2} about 0^{\}circ
(as in the GJ 876 system), and configurations with
asymmetric librations of \theta_{1} and \theta_{2} tens of
degrees from either 0^{\}circ or 180^{\}circ. There are
however stable resonance configurations with symmetric or
asymmetric librations that cannot be reached by capture into
resonances by coplanar differential migration. A particular
example is the \theta_{1} = 180^{\}circ and \theta_{2} =
0^{\}circ configuration with planets on intersecting orbits.
If real systems with these configurations are ever found,
their origin would require either a migration scenario
involving inclination resonances or multiple-planet
scattering in crowded planetary systems.

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Bulletin of the American Astronomical Society, **35** #4

© 2003. The American Astronomical Soceity.