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arXiv 1009.3449astro-ph.CO
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用高斯随机场的峰值统计模拟重子声学标度上的标度相关偏置

Modeling scale-dependent bias on the baryonic acoustic scale with the statistics of peaks of Gaussian random fields

Vincent Desjacques, Martin Crocce, Roman Scoccimarro, Ravi K. Sheth

摘要:

星系和晕团的模型通常假设示踪剂可以被视为一个连续的场,相对于基本的质量分布局部偏置。在BBKS开创的峰值模型中,人们认为初始高斯质量密度场的密度最大值近似为维里化物体的形成位置。本文从两个方面对峰值模型进行了扩展,以提高其预测精度。首先,我们推导出两点关联函数的初始密度峰值到二阶,并证明了一个峰背景分裂的方法可以应用于获得k-独立和k-依赖的峰值偏置因子在所有的订单。其次,我们探讨了峰值关联函数在Zel'dovich近似下的引力演化。我们发现,当地(拉格朗日)偏差的方法出现作为一个特殊的情况下的峰值模型,其中所有的偏置参数是尺度无关的,没有统计速度偏差。我们应用我们的公式来研究如何拉格朗日峰值偏置,扩散由于大规模的流动和模式耦合由于非局域相互作用影响的规模依赖性的偏置从小分离的重子声学振荡(BAO)的规模。对于在z=0.3处塌陷的2-sigma密度峰,我们的模型预测了围绕声学尺度的约5%的残余尺度相关偏差,该偏差主要来自一阶拉格朗日峰值偏差(与二阶重力模式耦合相反)。我们还寻找一个规模依赖的偏见在大规模的自相关提取的大规模晕从一个非常大的N体模拟MICE合作。对于质量M>10^{14}Msun/h的晕,我们的测量表明,在BAO特征上存在尺度依赖的偏差,这可以通过基于峰值模型的预测很好地再现。

英文摘要:

Models of galaxy and halo clustering commonly assume that the tracers can be treated as a continuous field locally biased with respect to the underlying mass distribution. In the peak model pioneered by BBKS, one considers instead density maxima of the initial, Gaussian mass density field as an approximation to the formation site of virialized objects. In this paper, the peak model is extended in two ways to improve its predictive accuracy. Firstly, we derive the two-point correlation function of initial density peaks up to second order and demonstrate that a peak-background split approach can be applied to obtain the k-independent and k-dependent peak bias factors at all orders. Secondly, we explore the gravitational evolution of the peak correlation function within the Zel'dovich approximation. We show that the local (Lagrangian) bias approach emerges as a special case of the peak model, in which all bias parameters are scale-independent and there is no statistical velocity bias. We apply our formulae to study how the Lagrangian peak biasing, the diffusion due to large scale flows and the mode-coupling due to nonlocal interactions affect the scale dependence of bias from small separations up to the baryon acoustic oscillation (BAO) scale. For 2-sigma density peaks collapsing at z=0.3, our model predicts a ~ 5% residual scale-dependent bias around the acoustic scale that arises mostly from first-order Lagrangian peak biasing (as opposed to second-order gravity mode-coupling). We also search for a scale dependence of bias in the large scale auto-correlation of massive halos extracted from a very large N-body simulation provided by the MICE collaboration. For halos with mass M>10^{14}Msun/h, our measurements demonstrate a scale-dependent bias across the BAO feature which is very well reproduced by a prediction based on the peak model.

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