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Star-forming clumps dominate the rest-frame ultraviolet morphology ofgalaxies at the peak of cosmic star formation. If turbulence drivenfragmentation is the mechanism responsible for their formation, we expect theirstellar mass function to follow a power-law of slope close to $-2$. We testthis hypothesis performing the first analysis of the stellar mass function ofclumps hosted in galaxies at $z\sim 1-3.5$. The clump sample is gathered fromthe literature with similar detection thresholds and stellar masses determinedin a homogeneous way. To overcome the small number statistics per galaxy (eachgalaxy hosts up to a few tens of clumps only), we combine all high-redshiftclumps. The resulting clump mass function follows a power-law of slope $\sim-1.7$ and flattens at masses below $2\times 10^7$ M$_{\odot}$. By means ofrandomly sampled clump populations, drawn out of a power-law mass function ofslope $-2$, we test the effect of combining small clump populations, detectionlimits of the surveys, and blending on the mass function. Our numericalexercise reproduces all the features observed in the real clump mass functionconfirming that it is consistent with a power-law of slope $\simeq -2$. Thisresult supports the high-redshift clump formation through fragmentation in asimilar fashion as in local galaxies, but under different gas conditions.

First constraints on the stellar mass function of star-forming clumps at the peak of cosmic star formation