Low-Surface-Brightness Galaxies are missing in the observed Stellar Mass Function

We investigate the impact of the surface brightness (SB) limit on the galaxy stellar mass functions (GSMFs) using mock surveys generated from the Horizon Run 5 (HR5) simulation. We compare the stellar-to-halo-mass relation, GSMF, and size-stellar mass relation of the HR5 galaxies with empirical data and other cosmological simulations. The mean SB of simulated galaxies are computed using their effective radii, luminosities, and colors. To examine the cosmic SB dimming effect, we compute $k$-corrections from the spectral energy distributions of individual simulated galaxy at each redshift, apply the $k$-corrections to the galaxies, and conduct mock surveys based on the various SB limits. We find that the GSMFs are significantly affected by the SB limits at a low-mass end. This approach can ease the discrepancy between the GSMFs obtained from simulations and observations at $0.625\le z\le 2$. We also find that a redshift survey with a SB selection limit of $\left<\mu_r\right>^e =$ 28 mag arcsec${}^{-2}$ will miss 20% of galaxies with $M_\star^g=10^{9}~{\rm M_\odot}$ at $z=0.625$. The missing fraction of low-surface-brightness galaxies increases to 50%, 70%, and 98% at $z=0.9$, 1.1, and 1.9, respectively, at the SB limit.