Radial profiles of lensed $z \sim 1$ galaxies on sub-kiloparsec scales
  We study the spatially resolved physical properties of the Cosmic Snake arc
in MACS J1206.2-0847 and the arc in Abell 0521 (A521). These are two strongly
lensed galaxies at redshifts $z=1.036$ and $z=1.044$. We used observations of
the Hubble Space Telescope (HST) and the Atacama Large Millimeter/submillimeter
Array (ALMA). The former gives access to the star formation rate (SFR) and
stellar mass ($M_\star$), and the latter to the H$_2$ molecular gas mass
($M_{\mathrm{mol}}$). HST and ALMA observations have similar angular
resolutions of $0.15^{\prime \prime}-0.2^{\prime \prime}$, which with the help
of strong gravitational lensing enable us to reach spatial resolutions down to
$\sim 30\,\mathrm{pc}$ and $\sim 100\,\mathrm{pc}$ in these two galaxies,
respectively. These resolutions are close to the resolution of observations of
nearby galaxies. We study the radial profiles of SFR, $M_\star$, and
$M_{\mathrm{mol}}$ surface densities of these high-redshift galaxies and
compare the corresponding exponential scale lengths with those of local
galaxies. We find that the scale lengths in the Cosmic Snake are about
$0.5\,\mathrm{kpc}-1.5\,\mathrm{kpc}$, and they are 3 to 10 times larger in
A521. This is a significant difference knowing that the two galaxies have
comparable integrated properties. These high-redshift scale lengths are
nevertheless comparable to those of local galaxies, which cover a wide
distribution. The particularity of our high-redshift radial profiles is the
normalisation of the $M_{\mathrm{mol}}$ surface density profiles ($\Sigma
M_{\mathrm{mol}}$), which are offset by up to a factor of 20 with respect to
the profiles of $z=0$ counterparts. The SFR surface density profiles are also
offset by the same factor as $\Sigma M_{\mathrm{mol}}$, as expected from the
Kennicutt-Schmidt law.
