The evolution of the size-mass relation at $z$=1-3 derived from the
  complete Hubble Frontier Fields data set
  We measure the size-mass relation and its evolution between redshifts
1$<z<$3, using galaxies lensed by six foreground Hubble Frontier Fields
clusters. The power afforded by strong gravitation lensing allows us to observe
galaxies with higher angular resolution beyond current facilities. We select a
stellar mass limited sample and divide them into star-forming or quiescent
classes based on their rest-frame UVJ colors from the ASTRODEEP catalogs.
Source reconstruction is carried out with the recently-released $lenstruction$
software, which is built on the multi-purpose gravitational lensing software
$lenstronomy$. We derive the empirical relation between size and mass for the
late-type galaxies with $M_{*}>3\times10^{9}M_{\odot}$ at 1$<z<$2.5 and $M_* >5
\times 10^{9} M_{\odot}$ at 2.5$<z<$3, and at a fixed stellar mass, we find
galaxy sizes evolve as $R_{eff}\propto (1+z)^{-1.05\pm0.37}$. The intrinsic
scatter is $<0.1$ dex at $z<1.5$ but increases to $\sim0.3$ dex at higher
redshift. The results are in good agreement with those obtained in blank
fields. We evaluate the uncertainties associated with the choice of lens model
by comparing size measurements using five different and publicly available
models, finding the choice of lens model leads to a 3.7 % uncertainty of the
median value, and $\sim 25$ % scatter for individual galaxies. Our work
demonstrates the use of strong lensing magnification to boost resolution does
not introduce significant uncertainties in this kind of work, and paves the way
for wholesale applications of the sophisticated lens reconstruction technique
to higher redshifts and larger samples.
