Computing the Three-Point Correlation Function of Galaxies in $\mathcal{O}(N^2)$ Time

By Zachary Slepian, Daniel J. Eisenstein. 2015

67 citations recorded by the source corpus.

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 $90\;{\rm Mpc}/h$ 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.

Subfields: Astronomy and Astrophysics, Electrical and Electronic Engineering, Instrumentation

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Citations in the corpus

Learning to predict the cosmological structure formation (2018, background): “For higher multipoles, ζ` ∼ 1/(r2 1r(2) 2) + 1/(r2 1r(2) 3)+1/(r(2) 2r(2) 3), thus the amplitude is dominated by a small population of squeezed triangles where two sides are equal and the third side near 0 (63).”
nbodykit: An Open-source, Massively Parallel Toolkit for Large-scale Structure (2017, methodology): “Recently, we have seen faster power spectrum and 2PCF multipole estimators (Yamamoto et al. 2006; Scoccimarro 2015; Bianchi et al. 2015; Slepian & Eisenstein 2015a, 2016; Hand et al. 2017a) and improved FOF algorithms (Springel 2005; Behroozi et al. 2013; Feng & Modi 2017).”