The First Dynamical Mass Measurement in the HR 8799 System

HR 8799 hosts four directly imaged giant planets, but none has a mass measured from first principles. We present the first dynamical mass measurement in this planetary system, finding that the innermost planet HR 8799 e has a mass of ${9.6}_{-1.8}^{+1.9}\,{M}_{\mathrm{Jup}}$. This mass results from combining the well-characterized orbits of all four planets with a new astrometric acceleration detection (5σ) from the Gaia EDR3 version of the Hipparcos-Gaia Catalog of Accelerations. We find with 95% confidence that HR 8799 e is below 13 MJup, the deuterium-fusing mass limit. We derive a hot-start cooling age of ${42}_{-16}^{+24}$ Myr for HR 8799 e that agrees well with its hypothesized membership in the Columba association but is also consistent with an alternative suggested membership in the β Pictoris moving group. We exclude the presence of any additional ≳5 − MJup planets interior to HR 8799 e with semimajor axes between ≈3–16 au. We provide proper motion anomalies and a matrix equation to solve for the mass of any of the planets of HR 8799 using only mass ratios between the planets.