SIMBAD references

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 Markov Chain Monte Carlo orbit code orvara to fit 15 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_–2.5^+2.6M_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_–0.09^+0.16 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 radial velocity monitoring and improved precision from future Gaia data releases.