Precise Dynamical Masses and Orbital Fits for β Pic b and β Pic c
Abstract
We present a comprehensive orbital analysis to the exoplanets β Pictoris b and c that resolves previously reported tensions between the dynamical and evolutionary mass constraints on β Pic b. We use the MCMC orbit code orvara to fit fifteen years of radial velocities and relative astrometry (including recent GRAVITY measurements), absolute astrometry from Hipparcos and Gaia, and a single relative radial velocity measurement between β Pic A and b. We measure model-independent masses of 9.3+2.6-2.5\, M Jup for β Pic b and 8.3 1.0\,M Jup for β Pic c. These masses are robust to modest changes to the input data selection. We find a well-constrained eccentricity of 0.119 0.008 for β Pic b, and an eccentricity of 0.21+0.16-0.09 for β Pic c, with the two orbital planes aligned to within 0.5. Both planets' masses are within 1σ of the predictions of hot-start evolutionary models and exclude cold starts. We validate our approach on N-body synthetic data integrated using REBOUND. We show that orvara can account for three-body effects in the β Pic system down to a level 5 times smaller than the GRAVITY uncertainties. Systematics in the masses and orbital parameters from orvara's approximate treatment of multiplanet orbits are a factor of 5 smaller than the uncertainties we derive here. Future GRAVITY observations will improve the constraints on β Pic c's mass and (especially) eccentricity, but improved constraints on the mass of β Pic b will likely require years of additional RV monitoring and improved precision from future Gaia data releases.