Halo merger trees are constructed from ELUCID, a constrained $N$-body simulation in the Sloan Digital Sky Survey (SDSS) volume. These merger trees are used to populate dark matter halos with galaxies according to an empirical model of galaxy formation. Mock catalogs in the SDSS sky coverage are constructed, which can be used to study the spatial distribution of galaxies in the low-$z$ Universe. These mock catalogs are used to quantify the cosmic variance in the galaxy stellar mass function (GSMF) measured from the SDSS survey. The GSMF estimated from the SDSS magnitude-limited sample can be affected significantly by the presence of the under-dense region at $z<0.03$, so that the low-mass end of the function can be underestimated significantly. Several existing methods designed to deal with the effects of the cosmic variance in the estimate of GSMF are tested, and none is found to be able to fully account for the cosmic variance. We propose a method based on the conditional stellar mass functions in dark matter halos, which can provide an unbiased estimate of the global GSMF. The application of the method to the SDSS data shows that the GSMF has a significant upturn at $M_*< 10^{9.5} h^{-1}{\rm M}_\odot$, which has been missed in many earlier measurements of the local GSMF.
ELUCID - Exploring the Local Universe with reConstructed Initial Density field I: Hamiltonian Markov Chain Monte Carlo Method with Particle Mesh Dynamics
Multi-tracer mass bias in matched cosmic voids from SDSS DR7 and the ELUCID constrained simulation
Shanghai Astronomical Observatory（上海天文台）；Tsung-Dao Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院、汤忠道研究院）；Shanghai Key Laboratory for Particle Physics and Cosmology, and Key Laboratory for Particle Physics, Astrophysics and Cosmology Ministry of Education, Shanghai Jiao Tong University（上海交通大学粒子物理与宇宙学上海市重点实验室、粒子物理、天体物理与宇宙学教育部重点实验室）
Surveying the Universe in 4D: Beating Cosmic Variance with Wide-Field Slitless Spectroscopy from HST, JWST, Euclid, Roman, and Beyond
Space Telescope Science Institute（太空望远镜科学研究所）；School of Earth and Space Exploration, Arizona State University（亚利桑那州立大学地球与空间探索学院）；Beus Center for Cosmic Foundations, Arizona State University（亚利桑那州立大学宇宙基础布斯中心）；NASA/GSFC（美国国家航空航天局戈达德太空飞行中心）；Massachusetts Institute of Technology（麻省理工学院）
