# How to estimate the 3D power spectrum of the Lyman-α forest

## Abstract

Here, we derive and numerically implement an algorithm for estimating the 3D power spectrum of the Lyman-α (Lyα) forest flux fluctuations. The algorithm exploits the unique geometry of Lyα forest data to efficiently measure the cross-spectrum between lines of sight as a function of parallel wavenumber, transverse separation and redshift. We start by approximating the global covariance matrix as block-diagonal, where only pixels from the same spectrum are correlated. We then compute the eigenvectors of the derivative of the signal covariance with respect to cross-spectrum parameters, and project the inverse-covariance-weighted spectra onto them. This acts much like a radial Fourier transform over redshift windows. The resulting cross-spectrum inference is then converted into our final product, an approximation of the likelihood for the 3D power spectrum expressed as second order Taylor expansion around a fiducial model. We demonstrate the accuracy and scalability of the algorithm and comment on possible extensions. Our algorithm will allow efficient analysis of the upcoming Dark Energy Spectroscopic Instrument dataset.

- Authors:

- Univ. College London, Bloomsbury (United Kingdom). Dept. of Physics and Astronomy
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Brookhaven National Lab. (BNL), Upton, NY (United States)

- Publication Date:

- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Univ. College London, Bloomsbury (United Kingdom)

- OSTI Identifier:
- 1424960

- Report Number(s):
- BNL-200052-2018-JAAM

Journal ID: ISSN 1475-7516; TRN: US1801980

- Grant/Contract Number:
- SC0012704; ST/N003853/1; AC02-05CH11231

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2018; Journal Issue: 01; Journal ID: ISSN 1475-7516

- Publisher:
- Institute of Physics (IOP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS

### Citation Formats

```
Font-Ribera, Andreu, McDonald, Patrick, and Slosar, Anže.
```*How to estimate the 3D power spectrum of the Lyman-α forest*. United States: N. p., 2018.
Web. doi:10.1088/1475-7516/2018/01/003.

```
Font-Ribera, Andreu, McDonald, Patrick, & Slosar, Anže.
```*How to estimate the 3D power spectrum of the Lyman-α forest*. United States. doi:10.1088/1475-7516/2018/01/003.

```
Font-Ribera, Andreu, McDonald, Patrick, and Slosar, Anže. Tue .
"How to estimate the 3D power spectrum of the Lyman-α forest". United States.
doi:10.1088/1475-7516/2018/01/003.
```

```
@article{osti_1424960,
```

title = {How to estimate the 3D power spectrum of the Lyman-α forest},

author = {Font-Ribera, Andreu and McDonald, Patrick and Slosar, Anže},

abstractNote = {Here, we derive and numerically implement an algorithm for estimating the 3D power spectrum of the Lyman-α (Lyα) forest flux fluctuations. The algorithm exploits the unique geometry of Lyα forest data to efficiently measure the cross-spectrum between lines of sight as a function of parallel wavenumber, transverse separation and redshift. We start by approximating the global covariance matrix as block-diagonal, where only pixels from the same spectrum are correlated. We then compute the eigenvectors of the derivative of the signal covariance with respect to cross-spectrum parameters, and project the inverse-covariance-weighted spectra onto them. This acts much like a radial Fourier transform over redshift windows. The resulting cross-spectrum inference is then converted into our final product, an approximation of the likelihood for the 3D power spectrum expressed as second order Taylor expansion around a fiducial model. We demonstrate the accuracy and scalability of the algorithm and comment on possible extensions. Our algorithm will allow efficient analysis of the upcoming Dark Energy Spectroscopic Instrument dataset.},

doi = {10.1088/1475-7516/2018/01/003},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 01,

volume = 2018,

place = {United States},

year = {Tue Jan 02 00:00:00 EST 2018},

month = {Tue Jan 02 00:00:00 EST 2018}

}

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