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
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.
