# A practical computational method for the anisotropic redshift-space three-point correlation function

## Abstract

Here, we present an algorithm enabling computation of the anisotropic redshift-space galaxy threepoint correlation function ( _{3}PCF) scaling as N ^{2}, with N the number of galaxies. Our previous work showed how to compute the isotropic _{3}PCF with this scaling by expanding the radially binned density field around each galaxy in the survey into spherical harmonics and combining these coefficients to form multipole moments. The N ^{2} scaling occurred because this approach never explicitly required the relative angle between a galaxy pair about the primary galaxy. Here, we generalize this work, demonstrating that in the presence of azimuthally symmetric anisotropy produced by redshift-space distortions (RSD), the _{3}PCF can be described by two triangle side lengths, two independent total angular momenta, and a spin. This basis for the anisotropic _{3}PCF allows its computation with negligible additional work over the isotropic _{3}PCF. We also present the covariance matrix of the anisotropic _{3}PCF measured in this basis. Our algorithm tracks the full _{5}D redshift-space _{3}PCF, uses an accurate line of sight to each triplet, is exact in angle, and easily handles edge correction. It will enable use of the anisotropic large-scale _{3}PCF as a probe of RSD in current and upcoming large-scale redshiftmore »

- Authors:

- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States)

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1480792

- Grant/Contract Number:
- AC02-05CH11231

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Monthly Notices of the Royal Astronomical Society

- Additional Journal Information:
- Journal Volume: 478; Journal Issue: 2; Journal ID: ISSN 0035-8711

- Publisher:
- Royal Astronomical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; cosmology: observations; distance scale; large-scale structure of Universe

### Citation Formats

```
Slepian, Zachary, and Eisenstein, Daniel J. A practical computational method for the anisotropic redshift-space three-point correlation function. United States: N. p., 2018.
Web. doi:10.1093/mnras/sty1063.
```

```
Slepian, Zachary, & Eisenstein, Daniel J. A practical computational method for the anisotropic redshift-space three-point correlation function. United States. doi:10.1093/mnras/sty1063.
```

```
Slepian, Zachary, and Eisenstein, Daniel J. Sat .
"A practical computational method for the anisotropic redshift-space three-point correlation function". United States. doi:10.1093/mnras/sty1063. https://www.osti.gov/servlets/purl/1480792.
```

```
@article{osti_1480792,
```

title = {A practical computational method for the anisotropic redshift-space three-point correlation function},

author = {Slepian, Zachary and Eisenstein, Daniel J.},

abstractNote = {Here, we present an algorithm enabling computation of the anisotropic redshift-space galaxy threepoint correlation function (3PCF) scaling as N2, with N the number of galaxies. Our previous work showed how to compute the isotropic 3PCF with this scaling by expanding the radially binned density field around each galaxy in the survey into spherical harmonics and combining these coefficients to form multipole moments. The N2 scaling occurred because this approach never explicitly required the relative angle between a galaxy pair about the primary galaxy. Here, we generalize this work, demonstrating that in the presence of azimuthally symmetric anisotropy produced by redshift-space distortions (RSD), the 3PCF can be described by two triangle side lengths, two independent total angular momenta, and a spin. This basis for the anisotropic 3PCF allows its computation with negligible additional work over the isotropic 3PCF. We also present the covariance matrix of the anisotropic 3PCF measured in this basis. Our algorithm tracks the full 5D redshift-space 3PCF, uses an accurate line of sight to each triplet, is exact in angle, and easily handles edge correction. It will enable use of the anisotropic large-scale 3PCF as a probe of RSD in current and upcoming large-scale redshift surveys.},

doi = {10.1093/mnras/sty1063},

journal = {Monthly Notices of the Royal Astronomical Society},

number = 2,

volume = 478,

place = {United States},

year = {2018},

month = {4}

}

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