Exploring the physical properties of lensed star-forming clumps at 2 ≲ z ≲ 6

We study the physical properties (size, stellar mass, luminosity, starformation rate) and scaling relations for a sample of 166 star-forming clumpswith redshift $z \sim 2-6.2$. They are magnified by the Hubble Frontier Fieldgalaxy cluster MACS~J0416 and have robust lensing magnification ($2\lesssim \mu\lesssim 82$) computed by using our high-precision lens model, based on 182multiple images. Our sample extends by $\sim 3$ times the number ofspectroscopically-confirmed lensed clumps at $z \gtrsim 2$. We identify clumpsin ultraviolet continuum images and find that, whenever the effective spatialresolution (enhanced by gravitational lensing) increases, they fragment intosmaller entities, likely reflecting the hierarchically-organized nature of starformation. Kpc-scale clumps, most commonly observed in field, are not found inour sample. The physical properties of our sample extend the parameter spacetypically probed by $z \gtrsim 1$ field observations and simulations, bypopulating the low mass (M$_\star \lesssim 10^7$ M$_\odot$), low star formationrate (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 theregime of compact stellar complexes and star clusters. In the mass-size plane,our sample spans the region between galaxies and globular clusters, with a fewclumps in the region populated by young star clusters and globular-clusters.For the bulk of our sample, we measure star-formation rates which are higherthan those observed locally in compact stellar systems, indicating differentconditions for star formation at high redshift than in the local Universe