Fig. 1: Limits on the abundance of galaxies as a function of redshift.

Curves show the relationship between M_⋆ and z at fixed cumulative halo abundance (left) and fixed ρ_b (>M_halo), or equivalently fixed peak height ν (right). The most extreme L23 galaxy candidates are shown as blue stars, with uncertainties indicating 68% intervals (symmetric about the median) of the posterior probability distribution. The existence of a galaxy with M_⋆ at redshift z requires that such galaxies have a cumulative co-moving number density that is, at most, the number density shown in the left panel, as those galaxies must reside in host halo of mass M_halo = M_⋆/(f_bϵ). The cumulative co-moving number density corresponding to an observed M_⋆ will probably be (much) smaller than is indicated here, as the curves are placed on the plot by assuming the physically maximal ϵ = 1.0. For smaller values of ϵ, the curves in each panel move down relative to the points by a factor of ϵ (as indicated by the black downward-facing arrows). The right panel demonstrates that even for the most conservative assumption of ϵ = 1.0, the data points correspond to very rare peaks in the density field, implying a limited baryonic reservoir that is in tension with the measured stellar masses of the galaxies.