SCALES. I. Bridging Lensed Clump - Giant Clump Scales in Lensed Galaxies at z=1-4

Dense star-forming regions in z>1 galaxies, often termed 'clumps', have been studied across two distinct regimes of telescope resolution, each motivating interpretations in tension with the other. In the SCALES series (Star-Forming Clumps As Layered Emergent Structures), we aim to connect star-forming structures across scales, from the about100, pc clumps in lensed studies to the about kpc-scale ''giant'' clumps in unlensed surveys. In this first paper, we present a difference-of-Gaussian (DoG) decomposition that simultaneously models about100-300, pc (lensed) clumps and about kpc-scale component (the extended component, or EC), which would together constitute the giant clumps seen at lower resolution. Here the EC is treated as a scale-separated local background rather than a physical object, absorbing all light that is not a compact clump. Applying this to 23 moderately lensed (μ about 2-9) galaxies at z spec = 1-4 to evaluate clump properties (deferring ECs and giant clumps to the next work), we find their stellar mass to be capped at about 10 8.5,M. We measure clump stellar mass function slope of 2.19 plus or minus 0.06, which is higher than typical, and may reflect a physical truncation at the massive end. We also show that empirical correlations of clump surface densities and clump-to-host mass ratio with redshift are exaggerated by redshift-dependent detection bias, so about100-300, pc clumps are largely co-similar across our range (z = 1-4). Finally, combining clump mass, size and age estimates with literature gas-dispersion measurements at similar scales, we argue that about100, pc clumps are themselves composed of star-cluster-like sub-components at much smaller scales.