Apsidal Alignment in Upsilon Andromedae
Abstract
One of the parameters fitted by Doppler radial velocity measurements of extrasolar planetary systems is omega, the argument of pericenter of a given planet's orbit referenced to the plane of the sky. Curiously, the omega's of the outer two planets orbiting Upsilon Andromedae are presently nearly identical: Delta-omega = omegaD - omegaC = 4.8 deg +/- 4.8 deg (1 sigma). This observation is least surprising if planets C and D occupy orbits that are seen close to edge-on (sin iC, sin iD > 0.5) and whose mutual inclination Theta does not exceed 20 deg. In this case, planets C and D inhabit a secular resonance in which Delta-omega librates about 0 deg with an amplitude of 30 deg and a period of 4000 yr. The resonant configuration spends about one-third of its time with |Delta-omega| < 10 deg. If Theta > 40 deg, either Delta-omega circulates or the system is unstable. This instability is driven by the Kozai mechanism which couples the eccentricity of planet C to Theta to drive the former quantity to values approaching unity. Our expectation that Theta < 20 deg suggests that planets C and D formed in a flattened, circumstellar disk, and may be tested by upcoming astrometric measurements with the FAME satellite.
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