The Incomplete Conditional Stellar Mass Function: Unveiling the Stellar Mass Functions of Galaxies at 0.1 < Z < 0.8 from BOSS Observations

We propose a novel method to constrain the missing fraction of galaxies using galaxy clustering measurements in the galaxy conditional stellar mass function (CSMF) framework, which is applicable to surveys that suffer significantly from sample selection effects. The clustering measurements, which are not sensitive to the random sampling (missing fraction) of galaxies, are widely used to constrain the stellar-halo mass relation (SHMR). By incorporating a missing fraction (incompleteness) component into the CSMF model (ICSMF), we use the incomplete stellar mass function and galaxy clustering to simultaneously constrain the missing fractions and the SHMRs. Tests based on mock galaxy catalogs with a few typical missing fraction models show that this method can accurately recover the missing fraction and the galaxy SHMR, and hence provides us reliable measurements of the galaxy stellar mass functions. We then apply it to the Baryon Oscillation Spectroscopic Survey (BOSS) over the redshift range of 0.1<z<0.8 for galaxies of $M_*>10^{11}M_\odot$. We find the sample completeness for BOSS is over 80% at z<0.6, but decreases at higher redshifts to about 30%. After taking these completeness factors into account, we provide accurate measurements of the stellar mass functions for galaxies with $10^{11}M_\odot<M_*<10^{12}M_\odot$, as well as the SHMRs, over the redshift range 0.1<z<0.8 in this largest galaxy redshift survey.