http://arxiv.org/abs/2107.06918
We have developed a new analytic method to compute the galaxy two-point correlation functions (TPCFs) efficiently and accurately. We have derived precise formulas of the normalized random-random pair counts $RR(r)$ as functions of the survey area dimensions. We have also suggested algorithms to compute the normalized data-random pair counts $DR(r)$ analytically for a given data set and survey area. This method is applicable to survey areas with rectangular, cuboidal, circular, or spherical shapes. With all edge corrections fully considered analytically, our method computes $RR(r)$ and $DR(r)$ with perfect accuracy and zero variance in $O(1)$ and $O(N_g)$ time, respectively. Together with the data-data pair counts $DD(r)$, they can be used to compute TPCFs with any estimator at a speed 4 to 5 orders of magnitude faster than the traditional brute-force Monte Carlo method, which has $O(N_r^2)$ scaling. This method is favored over the Monte Carlo method whenever applicable. It is also directly applicable to galaxy angular TPCFs when the survey area is close to Euclidean.
C. He
Fri, 16 Jul 21
60/61
Comments: 15 pages, 3 figures, submitted to AAS Journals
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