2022AJ....163...52S

HR 8799 is a young A5/F0 star hosting four directly imaged giant planets at wide separations (∼16-78 au), which are undergoing orbital motion and have been continuously monitored with adaptive optics imaging since their discovery over a decade ago. We present a dynamical mass of HR 8799 using 130 epochs of relative astrometry of its planets, which include both published measurements and new medium-band 3.1 µm observations that we acquired with NIRC2 at Keck Observatory. For the purpose of measuring the host-star mass, each orbiting planet is treated as a massless particle and is fit with a Keplerian orbit using Markov chain Monte Carlo. We then use a Bayesian framework to combine each independent total mass measurement into a cumulative dynamical mass using all four planets. The dynamical mass of HR 8799 is 1.47_–0.17^+0.12M_☉ assuming a uniform stellar mass prior, or 1.46_–0.15^+0.11M_☉ with a weakly informative prior based on spectroscopy. There is a strong covariance between the planets' eccentricities and the total system mass; when the constraint is limited to low-eccentricity solutions of e < 0.1, which are motivated by dynamical stability, our mass measurement improves to 1.43_–0.07^+0.06M_☉. Our dynamical mass and other fundamental measured parameters of HR 8799 together with Modules for Experiments in Stellar Astrophysics Isochrones and Stellar Tracks grids yields a bulk metallicity most consistent with [Fe/H] ∼ -0.25-0.00 dex and an age of 10-23 Myr for the system. This implies hot-start masses of 2.7-4.9 M_Jup for HR 8799 b and 4.1-7.0 M_Jup for HR 8799 c, d, and e, assuming they formed at the same time as the host star.