Computing the Three-Point Correlation Function of Galaxies in $\mathcal{O}(N^2)$ Time
Abstract
We present an algorithm that computes the multipole coefficients of the galaxy three-point correlation function (3PCF) without explicitly considering triplets of galaxies. Rather, centering on each galaxy in the survey, it expands the radially-binned density field in spherical harmonics and combines these to form the multipoles without ever requiring the relative angle between a pair about the central. This approach scales with number and number density in the same way as the two-point correlation function, allowing runtimes that are comparable, and 500 times faster than a naive triplet count. It is exact in angle and easily handles edge correction. We demonstrate the algorithm on the LasDamas SDSS-DR7 mock catalogs, computing an edge corrected 3PCF out to in under an hour on modest computing resources. We expect this algorithm will render it possible to obtain the large-scale 3PCF for upcoming surveys such as Euclid, LSST, and DESI.
Keywords
Cite
@article{arxiv.1506.02040,
title = {Computing the Three-Point Correlation Function of Galaxies in $\mathcal{O}(N^2)$ Time},
author = {Zachary Slepian and Daniel J. Eisenstein},
journal= {arXiv preprint arXiv:1506.02040},
year = {2015}
}
Comments
21 pages, 12 figures, accepted MNRAS with minor revisions; v2 matches accepted version