First constraints on the stellar mass function of star-forming clumps at
  the peak of cosmic star formation
  Star-forming clumps dominate the rest-frame ultraviolet morphology of
galaxies at the peak of cosmic star formation. If turbulence driven
fragmentation is the mechanism responsible for their formation, we expect their
stellar mass function to follow a power-law of slope close to $-2$. We test
this hypothesis performing the first analysis of the stellar mass function of
clumps hosted in galaxies at $z\sim 1-3.5$. The clump sample is gathered from
the literature with similar detection thresholds and stellar masses determined
in a homogeneous way. To overcome the small number statistics per galaxy (each
galaxy hosts up to a few tens of clumps only), we combine all high-redshift
clumps. 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 of
randomly sampled clump populations, drawn out of a power-law mass function of
slope $-2$, we test the effect of combining small clump populations, detection
limits of the surveys, and blending on the mass function. Our numerical
exercise reproduces all the features observed in the real clump mass function
confirming that it is consistent with a power-law of slope $\simeq -2$. This
result supports the high-redshift clump formation through fragmentation in a
similar fashion as in local galaxies, but under different gas conditions.
