A Fast and Accurate Analytic Method of Calculating Galaxy Two-point Correlation Functions

We have developed a new analytic method to calculate the galaxy two-point correlation functions accurately and efficiently, applicable surveys with finite, regular, mask-free geometries. derived simple, accurate formulas of normalized random–random pair counts RR as survey area dimensions. also suggested algorithms compute data-random DR analytically. With all edge corrections fully accounted for analytically, our computes perfect accuracy zero variance in O(1) O(Ng) time, respectively. test on catalog from Evolution Assembly GaLaxies their Environments (EAGLE) simulation. Our calculates + at speed 3–6 orders magnitude faster than brute-force Monte Carlo 2.5 tree-based algorithms. For 10 million data points cube, this reduces computation time under 1 minute laptop. is favored over traditional whenever applicable. Some applications study power spectra cosmological simulations are discussed. However, we recognize that its applicability very limited realistic masks, irregular shapes, and/or weighted patterns.