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R. Malhotra (U. Arizona)
Orbital eccentricities in exo-planetary systems discovered thus far are often surprisingly large and have proven to be a major puzzle in understanding these systems. In multiple-planet systems, there is also a tendency for near-alignment of the arguments of periapse of two planets, and secular apsidal resonance is strongly indicated in one case, Upsilon Andromedae. Apsidal resonance is the phenomenon of phase-locking of the apsidal longitudes of two orbits, such that the two planets have a common average rate of apsidal precession and the angular difference of their apsidal longitudes librates around 0. We describe a dynamical mechanism for establishing apsidal resonance in a pair of planets that are initially on nearly circular orbits. We show that in such a system, a perturbation that imparts a finite eccentricity to one planet's orbit causes the other planet's orbit to become eccentric as well, and also leads to a libration of their relative apsidal longitudes for a wide range of initial conditions. Such a mechanism may explain orbital eccentricities and apsidal alignment in some exo-planetary systems. The eccentricity perturbation could be caused by the ejection of a planet from these systems or by torques from a primordial gas disk. The amplitude of secular variations provides a constraint on the dynamical history of such systems.
We acknowledge research support from NASA.
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Bulletin of the American Astronomical Society, 34, #3< br> © 2002. The American Astronomical Soceity.