The Most Massive Galaxies and Black Holes Allowed by $Λ$CDM

Peter Behroozi, Joseph Silk

Published 2016-09-14Version 1

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. While halo mass functions at $z<8$ are consistent with observed galaxy stellar masses, JWST and WFIRST will more than double the redshift range over which useful constraints are available. We calculate galaxy stellar masses as a function of redshift that, if they existed in sufficient numbers, would either require unusual baryonic physics or in extreme cases would rule out $\Lambda$CDM entirely. Extending the calculation to the entire observable Universe, we find that the existence of a single $10^{11}$ M$_\odot$ galaxy at $z=13$ would rule out Planck $\Lambda$CDM with >95% confidence. Similar arguments apply to black holes; using number density constraints alone, the most massive observed black holes at $z>5$ must lie above the median $z=0$ black hole mass - bulge mass relation. If their virial mass estimates are accurate, the quasars SDSS J1044$-$0125 and SDSS J010013.02$+$280225.8 must both have black hole mass - stellar mass ratios of at least 2%, equaling the recent $z=0$ record for central galaxies in NGC 1600.