Hubble Space Telescope ( HSTÂ ) Fine Guidance Sensor astrometric observations of the G4 IV star HDÂ 38529Â 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 , HDÂ 38529b and the outer companion , HDÂ 38529c .
We identify a rotational period of HDÂ 38529Â ( P _ { rot } = 31.65 \pm 0.17 ^ { d } ) with FGS 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 HDÂ 38529c .
For HDÂ 38529c we find P = 2136.1 \pm 0.3 d , perturbation semi-major axis \alpha = 1.05 \pm 0.06 mas , and inclination i = 48.3 \fdg 0 \pm 4 \fdg 0 .
Assuming a primary mass M _ { * } = 1.48 M _ { \sun } , we obtain a companion mass { \it M } _ { c } = 17.6 ^ { +1.5 } _ { -1.2 } { \it M } _ { Jup } , 3 \sigma above a 13 M _ { Jup } ~ { } deuterium burning , brown dwarf lower limit .
Dynamical simulations incorporating this accurate mass for HDÂ 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 ( \sim 0.17 M _ { Jup } ) companion at P \sim 194 days .
Including this component in our modeling lowers the error of the mass determined for HDÂ 38529c .
Additional observations ( radial velocities and/or Gaia astrometry ) are required to validate an interpretation of HDÂ 38529d as a planetary-mass companion .
If confirmed , the resulting HDÂ 38529Â planetary system may be an example of a “ Packed Planetary System ” .