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

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:
 [1] ;  [2] ;  [3]
  1. Univ. College London, Bloomsbury (United Kingdom). Dept. of Physics and Astronomy
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  3. Brookhaven National Lab. (BNL), Upton, NY (United States)
Publication Date:
Report Number(s):
BNL-200052-2018-JAAM
Journal ID: ISSN 1475-7516; TRN: US1801980
Grant/Contract Number:
SC0012704; ST/N003853/1; AC02-05CH11231
Type:
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)
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)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS
OSTI Identifier:
1424960

Font-Ribera, Andreu, McDonald, Patrick, and Slosar, Anže. How to estimate the 3D power spectrum of the Lyman-α forest. United States: N. p., 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. 2018. "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 = {2018},
month = {1}
}