Breaking degeneracies in the first galaxies with clustering

The high-redshift galaxy UV luminosity function (UVLF) has become essential for understanding the formation and evolution of the first galaxies. Yet, UVLFs only measure galaxy abundances, giving rise to a degeneracy between the mean galaxy luminosity and its stochasticity. Here, we show that upcoming clustering measurements with the James Webb Space Telescope (JWST), as well as with Roman, will be able to break this degeneracy, even at redshifts $z \gtrsim 10$. First, we demonstrate that current Subaru Hyper Suprime-Cam (HSC) measurements of the galaxy bias at $z\sim 4-6$ point to a relatively tight halo-galaxy connection, with low stochasticity. Then, we show that the larger UVLFs observed by JWST at $z\gtrsim 10$ can be explained with either a boosted average UV emission or an enhanced stochasticity. These two models, however, predict different galaxy biases, which are potentially distinguishable in JWST and Roman surveys. Galaxy-clustering measurements, therefore, will provide crucial insights into the connection between the first galaxies and their dark-matter halos, and identify the root cause of the enhanced abundance of $z \gtrsim 10$ galaxies revealed with JWST during its first year of operations.