Empirical estimates of how massive galaxies can be in {\Lambda}CDM

Using Extreme Value Statistics applied to the observed galaxy stellar mass and the UV luminosity functions, we empirically estimate masses and luminosities of the most extreme galaxies in cosmological surveys, including the full sky. We incorporate uncertainties in stellar mass measurements (Eddington bias) and the scatter in the stellar-halo mass relation to derive empirical limits for galaxies residing in the most massive halos. The maximum observed $M_\ast$ strongly depends on survey area and redshift, ranging from $M_\ast \sim 7 \times 10^{12} M_\odot$ for full-sky surveys at $z\sim0$ to $M_\ast \sim 10^{10}M_\odot$ at $z\sim16$. Massive galaxies, particularly at high redshift, approach the theoretical maximum baryonic mass available in halos $M_\ast \sim 0.16 \times M_{\mathrm{vir}}$, consistent with previous claims. Accounting for measurement uncertainties significantly reduces the inferred maximum $M_\ast$ by up to $\sim1$ dex at $z\gtrsim10$, yielding stellar masses consistent with $M_\ast < 0.16$ at all redshifts. Assuming a perfect rank-order correspondence between the most massive halos and galaxies would guarantee this inequality at all redshifts. At 2 $\lesssim$ z $\lesssim$ 6, the most massive galaxies have stellar masses comparable to the total cold gas reservoir from cold and cooling flows, suggesting near-maximal star formation efficiencies, SFEs. At higher redshifts, halos are predicted to host galaxies undergoing starburst phases. When accounting for dust attenuation and adopting empirically inferred SFEs, we find good agreement between the model and the brightest observed UV galaxies at high redshifts. At lower redshifts, however, observed UV galaxies are too bright. Overall, our results indicate that current observations remain broadly consistent with $\Lambda$CDM once statistical and observational effects are properly accounted for.