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We study the spatially resolved physical properties of the Cosmic Snake arcin MACS J1206.2-0847 and the arc in Abell 0521 (A521). These are two stronglylensed galaxies at redshifts $z=1.036$ and $z=1.044$. We used observations ofthe Hubble Space Telescope (HST) and the Atacama Large Millimeter/submillimeterArray (ALMA). The former gives access to the star formation rate (SFR) andstellar mass ($M_\star$), and the latter to the H$_2$ molecular gas mass($M_{\mathrm{mol}}$). HST and ALMA observations have similar angularresolutions of $0.15^{\prime \prime}-0.2^{\prime \prime}$, which with the helpof 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 ofnearby galaxies. We study the radial profiles of SFR, $M_\star$, and$M_{\mathrm{mol}}$ surface densities of these high-redshift galaxies andcompare the corresponding exponential scale lengths with those of localgalaxies. 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 inA521. This is a significant difference knowing that the two galaxies havecomparable integrated properties. These high-redshift scale lengths arenevertheless comparable to those of local galaxies, which cover a widedistribution. The particularity of our high-redshift radial profiles is thenormalisation of the $M_{\mathrm{mol}}$ surface density profiles ($\SigmaM_{\mathrm{mol}}$), which are offset by up to a factor of 20 with respect tothe profiles of $z=0$ counterparts. The SFR surface density profiles are alsooffset by the same factor as $\Sigma M_{\mathrm{mol}}$, as expected from theKennicutt-Schmidt law.

Radial profiles of lensed $z \sim 1$ galaxies on sub-kiloparsec scales