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

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 2σ) 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 (L bol/ L ⊙) = -5 . 5 ±0 . 2 dex. Combining this luminosity with the 24 ± 3 Myr age of the β 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 kB baryon-1 at 97 per cent 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.