Exploring the physical properties of lensed star-forming clumps at $2\lesssim z \lesssim6$

We study the physical properties (size, stellar mass, luminosity, star formation rate) and scaling relations for a sample of 166 star-forming clumps with redshift $z \sim 2-6.2$. They are magnified by the Hubble Frontier Field galaxy cluster MACS~J0416 and have robust lensing magnification ($2\lesssim \mu \lesssim 82$) computed by using our high-precision lens model, based on 182 multiple images. Our sample extends by $\sim 3$ times the number of spectroscopically-confirmed lensed clumps at $z \gtrsim 2$. We identify clumps in ultraviolet continuum images and find that, whenever the effective spatial resolution (enhanced by gravitational lensing) increases, they fragment into smaller entities, likely reflecting the hierarchically-organized nature of star formation. Kpc-scale clumps, most commonly observed in field, are not found in our sample. The physical properties of our sample extend the parameter space typically probed by $z \gtrsim 1$ field observations and simulations, by populating the low mass (M$_\star \lesssim 10^7$ M$_\odot$), low star formation rate (SFR $\lesssim 0.5$ M$_\odot$ yr$^{-1}$), and small size (R$_\mathrm{eff} \lesssim 100$ pc) regime. The new domain probed by our study approaches the regime of compact stellar complexes and star clusters. In the mass-size plane, our sample spans the region between galaxies and globular clusters, with a few clumps in the region populated by young star clusters and globular-clusters. For the bulk of our sample, we measure star-formation rates which are higher than those observed locally in compact stellar systems, indicating different conditions for star formation at high redshift than in the local Universe.