The sizes of $z\sim6-8$ lensed galaxies from the Hubble Frontier Fields
  Abell 2744 data
  We investigate sizes of $z\sim6-8$ dropout galaxies using the complete data
of the Abell 2744 cluster and parallel fields in the Hubble Frontier Fields
program. By directly fitting light profiles of observed galaxies with
lensing-distorted S\'ersic profiles on the image plane with the \texttt{glafic}
software, we accurately measure intrinsic sizes of 31 $z\sim6-7$ and eight
$z\sim8$ galaxies, including those as faint as $M_{\mathrm{UV}}\simeq-16.6$. We
find that half-light radii $r_\mathrm{e}$ positively correlates with UV
luminosity at each redshift, although the correlation is not very tight.
Largest ($r_\mathrm{e}>0.8$ kpc) galaxies are mostly red in UV color while
smallest ($r_\mathrm{e} < 0.08$ kpc) ones tend to be blue. We also find that
galaxies with multiple cores tend to be brighter. Combined with previous
results at $2.5\lesssim z\lesssim12$, our result confirms that the average
$r_{\mathrm{e}}$ of bright ($(0.3-1)L^\star_{z=3}$) galaxies scales as
$r_{\mathrm{e}}\propto(1+z)^{-m}$ with $m=1.24\pm0.1$. We find that the ratio
of $r_\mathrm{e}$ to virial radius is virtually constant at $3.3\pm0.1\%$ over
a wide redshift range, where the virial radii of hosting dark matter halos are
derived based on the abundance matching. This constant ratio is consistent with
the disk formation model by Mo et al. (1998) with $j_\mathrm{d}\sim
m_\mathrm{d}$, where $j_\mathrm{d}$ and $m_\mathrm{d}$ are the fractions of the
angular momentum and mass within halos confined in the disks. A comparison with
various types of local galaxies indicates that our galaxies are most similar to
circumnuclear star-forming regions of barred galaxies in the sense that a
sizable amount of stars are forming in a very small area.
