Dynamical Mass of the Exoplanet Host Star HR 8799

TL;DR

This study determines the dynamical mass of the star HR 8799 using astrometry of its four giant planets, refining stellar and planetary parameters and providing insights into the system's age and formation history.

Contribution

It presents a new dynamical mass measurement of HR 8799 based on extensive astrometric data and Bayesian analysis, improving previous estimates and constraining system properties.

Findings

Dynamical mass of HR 8799 is approximately 1.46 solar masses.

System age estimated between 10-23 million years.

Planet masses consistent with hot start formation models.

Abstract

HR 8799 is a young A5/F0 star hosting four directly imaged giant planets at wide separations ($\sim$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 $\mu$m 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$^{+0.12}_{-0.17}$ \Msun assuming a uniform stellar mass prior, or 1.46$^{+0.11}_{-0.15}$ \Msun 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 is motivated by dynamical stability, our mass measurement improves to 1.43$^{+0.06}_{-0.07}$ \Msun. Our dynamical mass and other fundamental measured parameters of HR 8799 together with MESA Isochrones & Stellar Tracks grids yields a bulk metallicity most consistent with [Fe/H]$\sim$ -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 \Mjup for HR 8799 b and 4.1-7.0 \Mjup for HR 8799 c, d, and e, assuming they formed at the same time as the host star.