The Mass of HD 38529c from Hubble Space Telescope Astrometry and High-precision Radial Velocities

Hubble Space Telescope Fine Guidance Sensor astrometric observations of the G4 IV star HD 38529 are combined with the results of the analysis of extensive ground-based radial velocity (RV) data to determine the mass of the outermost of two previously known companions. Our new RVs obtained with the Hobby-Eberly Telescope and velocities from the Carnegie-California group now span over 11 yr. With these data we obtain improved RV orbital elements for both the inner companion, HD 38529b, and the outer companion, HD 38529c. We identify a rotational period of HD 38529 (P rot = 31.65 ? 017) with Fine Guidance Sensor photometry. The inferred star spot fraction is consistent with the remaining scatter in velocities being caused by spot-related stellar activity. We then model the combined astrometric and RV measurements to obtain the parallax, proper motion, perturbation period, perturbation inclination, and perturbation size due to HD 38529c. For HD 38529c we find P = 2136.1 ? 0.3 d, perturbation semimajor axis Delta *a = 1.05 ? 0.06 mas, and inclination i = 483 ? 37. Assuming a primary mass M * = 1.48 M , we obtain a companion mass Mc = 17.6+1.5 --1.2 M Jup, 3 Delta *s above a 13 M Jup deuterium burning, brown dwarf lower limit. Dynamical simulations incorporating this accurate mass for HD 38529c indicate that a near-Saturn mass planet could exist between the two known companions. We find weak evidence of an additional low amplitude signal that can be modeled as a planetary-mass (~0.17 M Jup) companion at P ~194 days. Including this component in our modeling lowers the error of the mass determined for HD 38529c. Additional observations (RVs and/or Gaia astrometry) are required to validate an interpretation of HD 38529d as a planetary-mass companion. If confirmed, the resulting HD 38529 planetary system may be an example of a 'Packed Planetary System.'