The 14 Her Planetary System: Companion Masses and Architecture from Radial Velocities and Astrometry

We combine Hubble Space Telescope (HST) Fine Guidance Sensor, Hipparcos, and Gaia DR3 astrometric observations of the K0 V star 14 Her with the results of an analysis of extensive ground-based radial velocity data to determine perturbation orbits and masses for two previously known companions, 14 Her b and c. Radial velocities obtained with the Hobby-Eberly Telescope and from the literature now span over twenty five years. With these data we obtain improved RV orbital elements for both the inner companion, 14 Her b and the long-period outer companion, 14 Her c. We also find evidence of an additional RV signal with P $/sim$ 3789d. We then model astrometry from Hipparcos, HST, and Gaia with RV results to obtain system parallax and proper motion, perturbation periods, inclinations, and sizes due to 14 Her b and c. We find P_b = 1767.6 +/- 0.2 d, perturbation semi-major axis {\alpha}_b = 1.3 +/- 0.1 mas, and inclination i_b = 36 +/- 3 degrees, P_c = 52160 +/- 1028 d, perturbation semi-major axis {\alpha}_c = 10.3 +/- 0.7 mas, and inclination i_c = 82 +/- 14 degrees. In agreement with a past investigation, the 14 Her b, c orbits exhibit significant mutual inclination. Assuming a primary mass M = 0.98 +/- 0.04Msun, we obtain companion masses M_b = 8.5 +/- 1.0Mjup and M_c = 7.1 +/- 1.0Mjup.