2023A&A...678A.183N

We study the star formation rate (SFR) vs. molecular gas mass (M_mol) scaling relation from hundreds to thousands of parsec in two strongly lensed galaxies at redshift z ∼ 1, the Cosmic Snake and A521. We trace the SFR using extinction-corrected rest-frame UV observations with the Hubble Space Telescope (HST), and M_mol using detections of the CO(4-3) line with the Atacama Large Millimeter/submillimeter Array (ALMA). The similar angular resolutions of our HST and ALMA observations of 0.15 - 0.2″ combined with magnifications reaching μ > 20 enable us to resolve structures in the galaxies of sizes lower than 100 pc. These resolutions are close to those of studies of nearby galaxies. This allows us to investigate for the first time the Kennicutt-Schmidt (KS) law (SFR-M_mol surface densities) at different spatial scales, from galactic scales to ∼100 pc scales, in galaxies at z ∼ 1. At integrated scales we find that both galaxies satisfy the KS law defined by galaxies at redshifts between 1 and 2.5. We test the resolved KS (rKS) law in cells of sizes down to 200 pc in the two galaxies. We observe that this relationship generally holds in these z ∼ 1 galaxies, although its scatter increases significantly with decreasing spatial scales. We check the scale dependence of the spatial correlation between the surface densities of SFR and M_mol by focusing on apertures centred on individual star-forming regions and molecular clouds. We conclude that star-forming regions and molecular clouds become spatially de-correlated at ≲1 kpc in the Cosmic Snake, whereas they appear de-correlated at all spatial scales (from 400 pc to 6 kpc) in A521.