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

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Abstract
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 Δ, 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.
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