The extrasolar planet ∈ Eridani b:: Orbit and mass

Hubble Space Telescope (HST) observations of the nearby (3.22 pc) K2 V star epsilon Eridani have been combined with ground-based astrometric and radial velocity data to determine the mass of its known companion. We model the astrometric and radial velocity measurements simultaneously to obtain the parallax, proper motion, perturbation period, perturbation inclination, and perturbation size. Because of the long period of the companion, epsilon Eri b, we extend our astrometric coverage to a total of 14.94 yr (including the 3 yr span of the HST data) by including lower precision ground-based astrometry from the Allegheny Multichannel Astrometric Photometer. Radial velocities now span 1980.8-2006.3. We obtain a perturbation period, P = 6.85 +/- 0.03 yr, semimajor axis alpha = 1.88 +/- 0.20 mas, and inclination i = 30 degrees.1 +/- 3 degrees.8. This inclination is consistent with a previously measured dust disk inclination, suggesting coplanarity. Assuming a primary mass M-* = 0.83 M-circle dot, we obtain a companion mass M = 1.55M(J) +/- 0.24M(J). Given the relatively young age of epsilon Eri (similar to 800 Myr), this accurate exoplanet mass and orbit can usefully inform future direct-imaging attempts. We predict the next periastron at 2007.3 with a total separation rho = 0".3 at position angle P.A = -27 degrees. Orbit orientation and geometry dictate that epsilon Eri b will appear brightest in reflected light very nearly at periastron. Radial velocities spanning over 25 yr indicate an acceleration consistent with a Jupiter-mass object with a period in excess of 50 yr, possibly responsible for one feature of the dust morphology, the inner cavity.