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Eccentricity Excitation and Apsidal Resonance Capture in the Planetary System υ Andromedae

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E. I. Chiang1 and N. Murray2

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The orbits of the outer two known planets orbiting υ Andromedae are remarkably eccentric. Planet C possesses an orbital eccentricity of e1 = 0.253. For the more distant planet D, e2 = 0.308. Previous dynamical analyses strongly suggest that the two orbits are nearly coplanar and are trapped in an apsidal resonance in which Δimg1.gif, the difference between their longitudes of periastron, undergoes a bounded oscillation about 0°. Here we elucidate the origin of these large eccentricities and of the apsidal alignment. Resonant interactions between a remnant circumstellar disk of gas lying exterior to the orbits of both planets can smoothly increase e2. Secular interactions between planets D and C can siphon off the eccentricity of the former to increase that of the latter. Externally amplifying e2 during the phase of the apsidal oscillation when e2/e1 is smallest drives the apsidal oscillation amplitude toward zero. Thus, the substantial eccentricity of planet C and the locking of orbital apsides are both consequences of externally pumping the eccentricity of planet D over timescales exceeding apsidal precession periods of order 104 yr. We explain why the recently detected stellar companion to υ And is largely dynamically decoupled from the planetary system.


Subject headings

celestial mechanics; planetary systems; stars: individual (υ Andromedae, HD 168443, 47 Ursa Majoris)


Dates

Issue 1 (2002 September 1)

Received 2002 April 14, accepted for publication 2002 May 8



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