The Sizes of Candidate $z\sim9-10$ Galaxies: confirmation of the bright
  CANDELS sample and relation with luminosity and mass
  Recently, a small sample of six $z\sim9-10$ candidates was discovered in
CANDELS that are $\sim10-20\times$ more luminous than any of the previous
$z\sim9-10$ galaxies identified over the HUDF/XDF and CLASH fields. We measure
the sizes of these candidates to map out the size evolution of galaxies from
the earliest observable times. Their sizes are also used to provide a valuable
constraint on whether these unusual galaxy candidates are at high redshift.
Using galfit to derive sizes from the CANDELS F160W images of these candidates,
we find a mean size of 0.13$\pm$0.02" (or 0.5$\pm$0.1 kpc at $z\sim9-10$). This
handsomely matches the 0.6 kpc size expected extrapolating lower redshift
measurements to $z\sim9-10$, while being much smaller than the 0.59" mean size
for lower-redshift interlopers to $z\sim9-10$ photometric selections lacking
the blue IRAC color criterion. This suggests that source size may be an
effective constraint on contaminants from $z\sim9-10$ selections lacking IRAC
data. Assuming on the basis of the strong photometric evidence that the Oesch
et al. 2014 sample is entirely at $z\sim9-10$, we can use this sample to extend
current constraints on the size-luminosity, size-mass relation, and size
evolution of galaxies to $z\sim10$. We find that the $z\sim9-10$ candidate
galaxies have broadly similar sizes and luminosities as $z\sim6$-8 counterparts
with star-formation-rate surface densities in the range of $\rm
\Sigma_{SFR}=1-20\, M_\odot~ yr^{-1}\, kpc^{-2}$. The stellar mass-size
relation is uncertain, but shallower than those inferred for lower-redshift
galaxies. In combination with previous size measurements at z=4-7, we find a
size evolution of $(1+z)^{-m}$ with $m=1.0\pm0.1$ for $>0.3L^*_{z=3}$ galaxies,
consistent with the evolution previously derived from $2 < z < 8$ galaxies.
