Constraints on Planets in Nearby Young Moving Groups Detectable by
  High-Contrast Imaging and Gaia Astrometry
  The formation of giant planets is best studied through direct imaging by
observing planets both during and after formation. Giant planets are expected
to form either by core accretion, which is typically associated with low
initial entropy (cold-start models) or by gravitational instability, which
corresponds to a high initial entropy of the gas (hot-start models). Thus,
constraining the initial entropy provides insight into the planet formation
mechanism and determines the resultant brightness evolution. We find that, by
observing planets in nearby moving groups of known age both through direct
imaging and astrometry with Gaia, it will be possible to constrain the initial
entropy of giant planets. We simulate a set of planetary systems in stars in
nearby moving groups identified by BANYAN $\Sigma$ and assume a model for
planet distribution consistent with radial velocity detections. We find that
Gaia should be able to detect approximately 50% of planets in nearby moving
groups greater than ~0.3 M$_\text{J}$. Using 5$\sigma$ contrast limits of
current and future instruments, we calculate the flux uncertainty, and using
models for the evolution of the planet brightness, we convert this to an
initial entropy uncertainty. We find that, for future instruments such as
MICADO and METIS on E-ELT and VIKiNG with VLTI, the entropy uncertainty is less
than 0.5 $k_{B}$/baryon, showing that these instruments should be able to
distinguish between hot and cold-start models.
