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The Stripe 82 Massive Galaxy Project II: Stellar Mass Completeness of Spectroscopic Galaxy Samples from the Baryon Oscillation Spectroscopic Survey

The Baryon Oscillation Spectroscopic Survey (BOSS) has collected spectra for over one million galaxies at $0.15<z<0.7$ over a volume of 15.3 Gpc$^3$ (9,376 deg$^2$) -- providing us an opportunity to study the most massive galaxy populations with vanishing sample variance. However, BOSS samples are selected via complex color cuts that are optimized for cosmology studies, not galaxy science. In this paper, we supplement BOSS samples with photometric redshifts from the Stripe 82 Massive Galaxy Catalog and measure the total galaxy stellar mass function (SMF) at $z\sim0.3$ and $z\sim0.55$. With the total SMF in hand, we characterize the stellar mass completeness of BOSS samples. The high-redshift CMASS ("constant mass") sample is significantly impacted by mass incompleteness and is 80% complete at $\log_{10}(M_*/M_{\odot}) >11.6$ only in the narrow redshift range $z=[0.51,0.61]$. The low redshift LOWZ sample is 80% complete at $\log_{10}(M_*/M_{\odot}) >11.6$ for $z=[0.15,0.43]$. To construct mass complete samples at lower masses, spectroscopic samples need to be significantly supplemented by photometric redshifts. This work will enable future studies to better utilize the BOSS samples for galaxy-formation science.