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

(Abridged) Hubble Space Telescope (HST) 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 data to determine the mass of the outermost of two previously known companions. Our new radial velocities obtained with the Hobby-Eberly Telescope and velocities from the Carnegie-California group now span over eleven years. With these data we obtain improved RV orbital elements for both the inner companion, HD 38529 b and the outer companion, HD 38529 c. We identify a rotational period of HD 38529 (P_{rot}=31.65 +/- 0.17 d) with FGS photometry. We model the combined astrometric and RV measurements to obtain the parallax, proper motion, perturbation period, perturbation inclination, and perturbation size due to HD 38529 c. For HD 38529 c we find P = 2136.1 +/- 0.3 d, perturbation semi-major axis α=1.05 +/-0.06$ mas, and inclination $i$ = 48.3 deg +/- 4 deg. Assuming a primary mass M_* = 1.48 M_{sun}, we obtain a companion mass M_c = 17.6 ^{+1.5}_{-1.2} M_{Jup}, 3-sigma above a 13 M_{Jup} deuterium burning, brown dwarf lower limit. Dynamical simulations incorporating this accurate mass for HD 38529 c 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. Additional observations (radial velocities and/or Gaia astrometry) are required to validate an interpretation of HD 38529 d as a planetary-mass companion. If confirmed, the resulting HD 38529 planetary system may be an example of a "Packed Planetary System".