# A Model-Independent Mass and Moderate Eccentricity for $\beta$ Pic b

## TL;DR

This study measures the mass and eccentricity of $eta$ Pic b using combined astrometric data, providing a model-independent mass estimate that challenges cold-start formation models and suggests possible orbital migration.

## Contribution

First model-independent mass measurement of a directly imaged exoplanet using combined Hipparcos and Gaia data, with implications for planet formation theories.

## Key findings

- Mass of $eta$ Pic b is $13\u00b1 3 M_{Jup}$.
- Eccentricity of $eta$ Pic b is $0.24\u00b1 0.06$, higher than previous estimates.
- Results are consistent with hot- and warm-start formation models.

## Abstract

We use a cross-calibration of Hipparcos and Gaia DR2 astrometry for $\beta$ Pic to measure the mass of the giant planet $\beta$ 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 $\beta$ 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 $\beta$ 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 $\beta$ Pic's disk. It could also potentially signal that $\beta$ Pic b has migrated inward to its current location, acquiring its eccentricity from interaction with the 3:1 outer Lindblad resonance in the disk.