标题： 弱非线性状态下星系-质量密度的关系与随机偏向 显示英文标题

标题： Stochastic Biasing and Galaxy-Mass Density Relation in the Weakly Non-linear Regime

摘要： 人们认为星系的偏倚在理解宇宙的大尺度结构中起着重要作用。一般来说，星系形成的偏倚可能是随机的。此外，未来的星系巡天可能会使我们能够探索星系分布的时间演化。本文在随机偏倚框架内研究了星系-质量密度关系及其时间演化。在弱非线性区域，我们利用埃奇沃思展开式导出了星系-质量密度关系的一般公式作为条件均值。所得表达式包含了总质量和星系分布的联合矩。通过扰动理论，我们研究了联合矩的时间演化，并考察了初始随机性对星系-质量密度关系的影响。分析表明，星系-质量密度关系可以很好地用线性关系来近似。与星系分布的偏度相比，我们发现使用条件均值估计高阶矩可能会受到随机性的影响。因此，作为估算偏度和峰度工具的星系-质量密度关系作为条件均值应该谨慎使用。 显示英文摘要

摘要： It is believed that the biasing of the galaxies plays an important role for understanding the large-scale structure of the universe. In general, the biasing of galaxy formation could be stochastic. Furthermore, the future galaxy survey 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 the stochastic biasing. In the weakly non-linear 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 a caution as a tool for estimating the skewness and the kurtosis.