Limits on the Mass and Initial Entropy of 51 Eri b from Gaia EDR3 Astrometry

TL;DR

This study constrains the mass and initial entropy of 51 Eri b using Gaia astrometry and luminosity measurements, indicating it likely did not form via cold-start scenarios and favoring warm or hot-start formation models.

Contribution

First observational constraint on the initial entropy of a potentially cold-start planet, combining astrometry, luminosity, and evolutionary models.

Findings

Mass of 51 Eri b is less than 11 Jupiter masses at 2σ confidence.

Luminosity of 51 Eri b is log(Lbol/Lsun) = -5.5 ± 0.2 dex.

Initial entropy of 51 Eri b is greater than 8 k_B/baryon at 97% confidence.

Abstract

51 Eri b is one of the only young planets consistent with a wide range of possible initial entropy states, including the cold-start scenario associated with some models of planet formation by core accretion. The most direct way to constrain the initial entropy of a planet is by measuring its luminosity and mass at a sufficiently young age that the initial conditions still matter. We present the tightest upper limit on 51 Eri b's mass yet (M < 11 Mjup at 2$\sigma$) using a cross-calibration of Hipparcos and Gaia EDR3 astrometry and the orbit-fitting code orvara. We also reassess its luminosity using a direct, photometric approach, finding log(Lbol/Lsun) = -5.5$\pm$0.2 dex. Combining this luminosity with the 24$\pm$3 Myr age of the $\beta$ Pic moving group, of which 51 Eri is a member, we derive mass distributions from a grid of evolutionary models that spans a wide range of initial entropies. We find that 51 Eri b is inconsistent with the coldest-start scenarios, requiring an initial entropy of >8 $k_B$/baryon at 97% confidence. This result represents the first observational constraint on the initial entropy of a potentially cold-start planet, and it continues the trend of dynamical masses for directly imaged planets pointing to warm- or hot-start formation scenarios.