Dynamical Mass Estimates of the β Pictoris Planetary System through Gaussian Process Stellar Activity Modeling

Nearly 15 yr of radial velocity (RV) monitoring and direct imaging enabled the detection of two giant planets orbiting the young, nearby star β Pictoris. The δ Scuti pulsations of the star, which overwhelm planetary signals, need to be carefully suppressed. In this work, we independently revisit the analysis of the RV data following a different approach than available in the literature to model the activity of the star. We show that a Gaussian process (GP) with a stochastically driven damped harmonic oscillator kernel can model the δ Scuti pulsations. It provides similar results to parametric models but with a simpler framework, using only three hyperparameters. It also enables us to model poorly sampled RV data that were excluded from previous analyses, hence extending the RV baseline by nearly five years. Altogether, the orbit and mass of both planets can be constrained from RV only, which was not possible with the parametric modeling. To characterize the system more accurately, we also perform a joint fit of all available relative astrometry and RV data. Our orbital solutions for $\beta \ \mathrm{Pic}$ b favor a low eccentricity of ${0.029}_{-0.024}^{+0.061}$ and a relatively short period of ${21.1}_{-0.8}^{+2.0}$ yr. The orbit of $\beta \ \mathrm{Pic}$ c is eccentric with ${0.206}_{-0.063}^{+0.074}$ with a period of 3.36 ± 0.03 yr. We find model-independent masses of 11.7 ± 1.4 and 8.5 ± 0.5 ${M}_{\mathrm{Jup}}$ for $\beta \ \mathrm{Pic}$ b and c, respectively, assuming coplanarity. The mass of $\beta \ \mathrm{Pic}$ b is consistent with the hottest start evolutionary models, at an age of 25 ± 3 Myr. A direct detection of $\beta \ \mathrm{Pic}$ c would provide a second calibration measurement in a coeval system.