论文标题
随机对的快速分析计算，用于现实调查几何形状
Fast analytical calculation of the random pair counts for realistic survey geometry
论文作者
论文摘要
星系聚类是一种标准的宇宙学探针，通常通过两点统计进行分析。在观察中，对两点相关函数的估计至关重要地依赖于随机目录中的计数对。后者包含大量随机分布点，这说明了调查窗口功能。随机对计数也可以有利地用于建模观察到的功率谱中的窗口函数。由于对计数比例为$ \ Mathcal {o}（n^2）$，其中$ n $是点数，因此测量随机对计数的计算时间对于大型调查而言可能非常昂贵。在这项工作中，我们提出了一种替代方法，用于估计不依赖随机目录的使用的计数。我们得出了各向异性随机随机对计数的分析表达式，该对构成了星系径向距离分布，测量几何形状和可能的星系重量。 考虑到毒蛇和SDSS-Boss红移调查的情况，我们发现分析计算与从随机目录获得的对计数非常吻合。这种方法的主要优点是，单个CPU的主要计算仅需几分钟，并且不取决于随机点的数量。此外，它允许对单极的准确性，相当于我们在使用随机目录时与手头数据相比，我们原本将获得的精度。我们还描述并测试了数据随机计数的近似表达，该计数的准确性不如随机随机计数，但仍然提供了单极的次级精度。提出的形式主义在考虑下一代调查中的窗口函数方面应该非常有用，这将需要在庞大的观察到的宇宙学体积上进行准确的两点窗口函数估计。
Galaxy clustering is a standard cosmological probe that is commonly analysed through two-point statistics. In observations, the estimation of the two-point correlation function crucially relies on counting pairs in a random catalogue. The latter contains a large number of randomly distributed points, which accounts for the survey window function. Random pair counts can also be advantageously used for modelling the window function in the observed power spectrum. Since pair counting scales as $\mathcal{O}(N^2)$, where $N$ is the number of points, the computational time to measure random pair counts can be very expensive for large surveys. In this work, we present an alternative approach for estimating those counts that does not rely on the use of a random catalogue. We derived an analytical expression for the anisotropic random-random pair counts that accounts for the galaxy radial distance distribution, survey geometry, and possible galaxy weights. Considering the cases of the VIPERS and SDSS-BOSS redshift surveys, we find that the analytical calculation is in excellent agreement with the pair counts obtained from random catalogues. The main advantage of this approach is that the primary calculation only takes a few minutes on a single CPU and it does not depend on the number of random points. Furthermore, it allows for an accuracy on the monopole equivalent to what we would otherwise obtain when using a random catalogue with about 1500 times more points than in the data at hand. We also describe and test an approximate expression for data-random pair counts that is less accurate than for random-random counts, but still provides subpercent accuracy on the monopole. The presented formalism should be very useful in accounting for the window function in next-generation surveys, which will necessitate accurate two-point window function estimates over huge observed cosmological volumes.
