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

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.