The Correlation between Halo Mass and Stellar Mass for the Most Massive Galaxies in the Universe

We present measurements of the clustering of galaxies as a function of their stellar mass in the Baryon Oscillation Spectroscopic Survey. We compare the clustering of samples using 12 different methods for estimating stellar mass, isolating the method that has the smallest scatter at fixed halo mass. In this test, the stellar mass estimate with the smallest errors yields the highest amplitude of clustering at fixed number density. We find that the PCA stellar masses of Chen et al. clearly have the tightest correlation with halo mass. The PCA masses use the full galaxy spectrum, differentiating them from other estimates that only use optical photometric information. Using the PCA masses, we measure the large-scale bias as a function of $M_{\ast }$ for galaxies with $log{M}_{\ast }⩾11.4$, correcting for incompleteness at the low-mass end of our measurements. Using the abundance matching ansatz to connect dark matter halo mass to stellar mass, we construct theoretical models of $b\left(M_{\ast }\right)$ that match the same stellar mass function but have different amounts of scatter in stellar mass at fixed halo mass, ${\sigma }_{logM\ast }$. Using this approach, we find ${\sigma }_{logM\ast }={0.18}_{-0.02}^{+0.01}$. This value includes both intrinsic scatter as well as random errors in the stellar masses. To partially remove the latter, we use repeated spectra to estimate statistical errors on the stellar masses, yielding an upper limit to the intrinsic scatter of 0.16 dex.