We study young star-forming clumps on physical scales of 10-500 pc in the Lyman-Alpha Reference Sample (LARS), a collection of low-redshift (z = 0.03-0.2) UV-selected star-forming galaxies. In each of the 14 galaxies of the sample, we detect clumps for which we derive sizes and magnitudes in 5 UV-optical filters. The final sample includes $sim$1400 clumps, of which $sim$600 have magnitude uncertainties below 0.3 in all filters. The UV luminosity function for the total sample of clumps is described by a power-law with slope $alpha = -2.03^{+0.11}_{-0.13}$. Clumps in the LARS galaxies have on average $Sigma_{SFR}$ values higher than what observed in HII regions of local galaxies and comparable to typical SFR densities of clumps in z = 1-3 galaxies. We derive the clumpiness as the relative contribution from clumps to the UV emission of each galaxy, and study it as a function of galactic-scale properties, i.e. $Sigma_{SFR}$ and the ratio between rotational and dispersion velocities of the gas ($v_s/sigma_0$). We find that in galaxies with higher $Sigma_{SFR}$ or lower $v_s/sigma_0$, clumps dominate the UV emission of their host systems. All LARS galaxies with Ly$alpha$ escape fractions larger than 10% have more than 50% of the UV luminosity from clumps. We tested the robustness of these results against the effect of different physical resolutions. At low resolution, the measured clumpiness appears more elevated than if we could resolve clumps down to single clusters. This effect is small in the redshift range covered by LARS, thus our results are not driven by the physical resolution.
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