Apsidal Alignment in υ Andromedae

One of the parameters fitted by Doppler radial velocity measurements of extrasolar planetary systems is ω, the argument of pericenter of a given planet's orbit referenced to the plane of the sky. Curiously, the ω's of the outer two planets orbiting υ Andromedae are presently nearly identical: Δω ≡ ω_D - ω_C = 48 ± 48 (1 σ). This observation is least surprising if planets C and D occupy orbits that are seen close to edge-on (sin i_C, sin i_D ≳ 0.5) and whose mutual inclination Θ does not exceed 20°. In this case, planets C and D inhabit a secular resonance in which Δω librates about 0° with an amplitude of ∼30° and a period of ∼4 × 10³ yr. The resonant configuration spends about one-third of its time with |Δω| ≤ 10°. If Θ ≳ 40°, either Δω circulates or the system is unstable. This instability is driven by the Kozai mechanism, which couples the eccentricity of planet C to Θ to drive the former quantity to values approaching unity. Our expectation that Θ ≲ 20° suggests that planets C and D formed in a flattened, circumstellar disk, and this may be tested by upcoming astrometric measurements with the FAME satellite.