The Most Massive Galaxies and Black Holes Allowed by ΛCDM

Given a galaxy's stellar mass, its host halo mass has a lower limit from the cosmic baryon fraction and known baryonic physics. At z>4, galaxy stellar mass functions place lower limits on halo number densities that approach expected $\Lambda$CDM halo mass functions. High-redshift galaxy stellar mass functions can thus place interesting limits on number densities of massive haloes, which are otherwise very difficult to measure. Although halo mass functions at z<8 are consistent with observed galaxy stellar masses if galaxy baryonic conversion efficiencies increase with redshift, JWST and WFIRST will more than double the redshift range over which useful constraints are available. We calculate maximum galaxy stellar masses as a function of redshift given expected halo number densities from $\Lambda$CDM. We apply similar arguments to black holes. If their virial mass estimates are accurate, number density constraints alone suggest that the quasars SDSS J1044-0125 and SDSS J010013.02+280225.8 likely have black hole mass -- stellar mass ratios higher than the median z=0 relation, confirming the expectation from Lauer bias. Finally, we present a public code to evaluate the probability of an apparently $\Lambda$CDM-inconsistent high-mass halo being detected given the combined effects of multiple surveys and observational errors.