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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.

By means of three-dimensional hydrodynamical simulations, we investigate the formation of second generation (SG) stars in young globular clusters of different masses. We consider clusters with a first generation of asymptotic giant branch (AGB) stars with mass 10^5 and 10^6 Msun moving at constant velocity through a uniform gas with density 10^(-24) and 10^(-23) g cm^(-3). Our setup is designed to reproduce the encounter of a young cluster with a reservoir of dense gas, e. g. during its orbital motion in the host galaxy. In the low-density models, as a result of the cooling AGB ejecta which collect in the centre, weakly perturbed by the external ram pressure, a compact central He-rich SG stellar component is formed on a timescale which decreases with increasing initial cluster mass. Our high-density models are subject to stronger ram pressure, which prevents the accumulation of the most He-rich AGB ejecta in the cluster centre. As a result, the SG is more extended and less He-enhanced than in the low-density models. By combining our results with previous simulations, we are able to study relevant, cluster-related scaling relations across a dynamical range of two orders of magnitude in mass (from 10^5 Msun to 10^7 Msun). In agreement with current observationally-based estimates, we find positive correlations between the SG-to-total number ratio and maximum He enhancement in SG stars as a function of the initial cluster mass., 18 pages, 8 figures, MNRAS, accepted for publication

We empirically test the relation between the SFR(LIR) derived from the infrared luminosity, LIR, and the SFR(Ha) derived from the Ha emission line luminosity using simple conversion relations. We use a sample of 474 galaxies at z = 0.06 - 0.46 with both Ha detection (from 20k zCOSMOS survey) and new far-IR Herschel data (100 and 160 {\mu}m). We derive SFR(Ha) from the Ha extinction corrected emission line luminosity. We find a very clear trend between E(B - V) and LIR that allows to estimate extinction values for each galaxy even if the Ha emission line measurement is not reliable. We calculate the LIR by integrating from 8 up to 1000 {\mu}m the SED that is best fitting our data. We compare SFR(Ha) with the SFR(LIR). We find a very good agreement between the two SFR estimates, with a slope of m = 1.01 \pm 0.03 in the SFR(LIR) vs SFR(Ha) diagram, a normalization constant of a = -0.08 \pm 0.03 and a dispersion of sigma = 0.28 dex.We study the effect of some intrinsic properties of the galaxies in the SFR(LIR)-SFR(Ha) relation, such as the redshift, the mass, the SSFR or the metallicity. The metallicity is the parameter that affects most the SFR comparison. The mean ratio of the two SFR estimators log[SFR(LIR)/SFR(Ha)] varies by approx. 0.6 dex from metal-poor to metal-rich galaxies (8.1 < log(O/H) + 12 < 9.2). This effect is consistent with the prediction of a theoretical model for the dust evolution in spiral galaxies. Considering different morphological types, we find a very good agreement between the two SFR indicators for the Sa, Sb and Sc morphologically classified galaxies, both in slope and normalization. For the Sd, irregular sample (Sd/Irr), the formal best-fit slope becomes much steeper (m = 1.62 \pm 0.43), but it is still consistent with 1 at the 1.5 sigma level, because of the reduced statistics of this sub-sample.