On the clumpy nature of super-early galaxies

JWST has revealed that galaxies during the Epoch of Reionization are composed of compact stellar clumps spanning more than two orders of magnitude in mass and size. We present an analytical framework that connects the global properties of high-redshift galactic disks to the formation, dynamical evolution and visibility of these systems. Starting from the classical Toomre instability, we derive analytical mass-size and surface density-size relations together with, for the first time, the intrinsic clump mass spectrum obtained by integrating over the entire unstable branch of the dispersion relation. The observed clumps are naturally reproduced for turbulent velocity dispersions σ 10-80, km,s-1, while their location along the mass-size relation is determined by the compactness of the parent disk. The intrinsic spectrum extends over nearly two decades in mass, 5.5 (M cl/M) 7.3, and is transformed by gas dynamical friction, which suppresses the high-mass tail (t df proportional to M cl-1) and reproduces the observed clump mass-function slope, dN/dM proportional to M-1.89. Supernova feedback is insufficient to clear the dense natal gas, whereas radiation pressure provides a robust clearing mechanism: Ly α trapping dominates in dust-poor clumps and infrared trapping takes over as they become enriched. The results provide the first self-consistent analytical framework connecting the formation, statistical properties and visibility of stellar clumps in super-early galaxies.