1998/09/30 by A. Taruya, Atsushi Taruya, Jiro Soda +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Astrophysics #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #Galaxy #Kurtosis #Mathematics #Physics #Skewness #Statistical physics #Statistics #astro-ph
paper · pdf · doi:10.1086/307612
published as Astrophys.J. 522 (1999) 46-58 · 22 pages, 7 Encapusulated Postscript Figures, aastex, The title and the structure of the paper has been changed, Results and conclusions unchanged, Accepted for publication in ApJ
arxiv created 1999/04/01 · openalex publication_date 1999/09/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
It is believed that the biasing of galaxies plays an important role in understanding the large-scale structure of the universe. In general, the biasing of galaxy formation could be stochastic. Furthermore, future galaxy surveys might allow us to explore the time evolution of the galaxy distribution. In this paper the analytic study of the galaxy-mass density relation and its time evolution is presented within the framework of stochastic biasing. In the weakly nonlinear regime, we derive a general formula for the galaxy-mass density relation as a conditional mean using the Edgeworth expansion. The resulting expression contains the joint moments of the total mass and galaxy distributions. Using the perturbation theory, we investigate the time evolution of the joint moments and examine the influence of the initial stochasticity on the galaxy-mass density relation. The analysis shows that the galaxy-mass density relation could be well approximated by the linear relation. Compared with the skewness of the galaxy distribution, we find that the estimation of the higher order moments using the conditional mean could be affected by the stochasticity. Therefore, the galaxy-mass density relation as a conditional mean should be used with caution as a tool for estimating the skewness and the kurtosis.