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Gravitational clustering of galaxies: Derivation of two-point galaxy correlation function using statistical mechanics of cosmological many-body problem

机译:星系引力聚类:使用宇宙多体问题的统计力学推导两点星系相关函数

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We derive the spatial pair correlation function in gravitational clustering for extended structure of galaxies (e.g. galaxies with halos) by using statistical mechanics of cosmological many-body problem. Our results indicate that in the limit of point masses (epsilon = 0) the two-point correlation function varies as inverse square of relative separation of two galaxies. The effect of softening parameter 'epsilon' on the pair correlation function is also studied and results indicate that two-point correlation function is affected by the softening parameter when the distance between galaxies is small. However, for larger distance between galaxies, the two-point correlation function is not affected at all. The correlation length r(0) derived by our method depends on the random dispersion velocities < v(2)>(1/2) and mean number density (n) over bar, which is in agreement with N-body simulations and observations. Further, our results are applicable to the clusters of galaxies for their correlation functions and we apply our results to obtain the correlation length r(0) for such systems which again agrees with the data of N-body simulations and observations.
机译:我们使用宇宙学多体问题的统计力学方法,得出了引力聚类中星系扩展结构(例如具有光晕的星系)的空间对相关函数。我们的结果表明,在点质量的极限(ε= 0)中,两点相关函数随着两个星系的相对分离的平方成反比而变化。还研究了软化参数“ε”对对相关函数的影响,结果表明,当星系之间的距离较小时,两点相关函数会受到软化参数的影响。但是,对于较大的星系之间的距离,两点相关函数完全不受影响。通过我们的方法得出的相关长度r(0)取决于随机色散速度(1/2)和条形图上的平均数密度(n),这与N体模拟和观察结果一致。此外,我们的结果适用于星系团的相关函数,我们将结果应用到此类系统的相关长度r(0),这再次与N体模拟和观测的数据相符。

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