关于星系团超过高质量阈值的过剩的模拟
On the modelling of the excesses of galaxy clusters over high-mass thresholds
摘要：
在这项工作中，我们提出了第一次的帕累托方法的建模超过高质量阈值的星系团的过剩的应用。这些过剩的分布可以用广义帕累托分布（GPD）来描述，它与广义极值分布（GEV）密切相关。在介绍了形式主义之后，我们研究了不同的阈值和红移范围对分布的影响，以及调查区域对高于给定质量阈值的平均超额的影响。我们还表明，GPD和GEV的方法导致相同的结果罕见的，因此高质量和高红移，集群。作为一个例子，我们应用帕累托方法ACT-CL J 0102 -4915和SPT-CL J2106-5844，并推导出不同质量阈值的累积分布函数。我们还研究了使用GPD作为宇宙学探测器的可能性。由于在分布参数的极大似然估计中使用了来自质量阈值以上的聚类的所有信息，因此GPD可能提供一种有趣的替代方案，以替代仅使用补丁中的最大值的基于GEV的方法。当比较的准确性，可以估计的参数，事实证明，基于补丁的建模的最大值是优于帕累托方法。在理想的情况下，GEV方法能够估计位置参数的百分比级精度小于100块。这一结果使得GEV为基础的方法可能也有趣的聚类调查与较小的面积。
英文摘要：
In this work we present for the first time an application of the Pareto approach to the modelling of the excesses of galaxy clusters over high-mass thresholds. The distribution of those excesses can be described by the generalized Pareto distribution (GPD), which is closely related to the generalized extreme value (GEV) distribution. After introducing the formalism, we study the impact of different thresholds and redshift ranges on the distributions, as well as the influence of the survey area on the mean excess above a given mass threshold. We also show that both the GPD and the GEV approach lead to identical results for rare, thus high-mass and high-redshift, clusters. As an example, we apply the Pareto approach to ACT-CL J0102-4915 and SPT-CL J2106-5844 and derive the respective cumulative distribution functions of the exceedance over different mass thresholds. We also study the possibility to use the GPD as a cosmological probe. Since in the maximum likelihood estimation of the distribution parameters all the information from clusters above the mass threshold is used, the GPD might offer an interesting alternative to GEV-based methods that use only the maxima in patches. When comparing the accuracy with which the parameters can be estimated, it turns out that the patch-based modelling of maxima is superior to the Pareto approach. In an ideal case, the GEV approach is capable to estimate the location parameter with a percent level precision for less than 100 patches. This result makes the GEV based approach potentially also interesting for cluster surveys with a smaller area.
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