A Model-Independent Mass and Moderate Eccentricity for $β$ Pic b

We use a cross-calibration of Hipparcos and Gaia DR2 astrometry for $β$ Pic to measure the mass of the giant planet $β$ Pic b $(13\pm3$ $M_{\rm Jup})$ in a comprehensive joint orbit analysis that includes published relative astrometry and radial velocities. Our mass uncertainty is somewhat higher than previous work because our astrometry from the Hipparcos-Gaia Catalog of Accelerations accounts for the error inflation and systematic terms that are required to bring the two data sets onto a common astrometric reference frame, and because we fit freely for the host-star mass $(1.84\pm0.05$ $M_{\odot})$. This first model-independent mass for a directly imaged planet is inconsistent with cold-start models given the age of the $β$ Pic moving group $(22\pm6$ Myr) but consistent with hot- and warm-start models, concordant with past work. We find a higher eccentricity $(0.24\pm0.06)$ for $β$ Pic b compared to previous orbital fits. If confirmed by future observations, this eccentricity may help explain inner edge, scale height, and brightness asymmetry of $β$ Pic's disk. It could also potentially signal that $β$ Pic b has migrated inward to its current location, acquiring its eccentricity from interaction with the 3:1 outer Lindblad resonance in the disk.