The First Dynamical Mass Measurement in the HR 8799 System
G. Mirek Brandt, Timothy D. Brandt, Trent J. Dupuy, Daniel Michalik, Gabriel-Dominique Marleau
Abstract
Abstract 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>9.6</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1.8</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1.9</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>Jup</mml:mi> </mml:mrow> </mml:msub> </mml:math> . This mass results from combining the well-characterized orbits of all four planets with a new astrometric acceleration detection (5 σ ) from the Gaia EDR3 version of the Hipparcos-Gaia Catalog of Accelerations. We find with 95% confidence that HR 8799 e is below 13 M Jup , the deuterium-fusing mass limit. We derive a hot-start cooling age of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>42</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>16</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>24</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> 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 − M Jup 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.