How to estimate the 3D power spectrum of the Lymanα forest
Here, we derive and numerically implement an algorithm for estimating the 3D power spectrum of the Lymanα (Lyα) forest flux fluctuations. The algorithm exploits the unique geometry of Lyα forest data to efficiently measure the crossspectrum between lines of sight as a function of parallel wavenumber, transverse separation and redshift. We start by approximating the global covariance matrix as blockdiagonal, where only pixels from the same spectrum are correlated. We then compute the eigenvectors of the derivative of the signal covariance with respect to crossspectrum parameters, and project the inversecovarianceweighted spectra onto them. This acts much like a radial Fourier transform over redshift windows. The resulting crossspectrum 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]}
 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:
 Report Number(s):
 BNL2000522018JAAM
Journal ID: ISSN 14757516; TRN: US1801980
 Grant/Contract Number:
 SC0012704; ST/N003853/1; AC0205CH11231
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Cosmology and Astroparticle Physics
 Additional Journal Information:
 Journal Volume: 2018; Journal Issue: 01; Journal ID: ISSN 14757516
 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) (SC25); Univ. College London, Bloomsbury (United Kingdom)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTRONOMY AND ASTROPHYSICS
 OSTI Identifier:
 1424960
FontRibera, Andreu, McDonald, Patrick, and Slosar, Anže. How to estimate the 3D power spectrum of the Lymanα forest. United States: N. p.,
Web. doi:10.1088/14757516/2018/01/003.
FontRibera, Andreu, McDonald, Patrick, & Slosar, Anže. How to estimate the 3D power spectrum of the Lymanα forest. United States. doi:10.1088/14757516/2018/01/003.
FontRibera, Andreu, McDonald, Patrick, and Slosar, Anže. 2018.
"How to estimate the 3D power spectrum of the Lymanα forest". United States.
doi:10.1088/14757516/2018/01/003.
@article{osti_1424960,
title = {How to estimate the 3D power spectrum of the Lymanα forest},
author = {FontRibera, Andreu and McDonald, Patrick and Slosar, Anže},
abstractNote = {Here, we derive and numerically implement an algorithm for estimating the 3D power spectrum of the Lymanα (Lyα) forest flux fluctuations. The algorithm exploits the unique geometry of Lyα forest data to efficiently measure the crossspectrum between lines of sight as a function of parallel wavenumber, transverse separation and redshift. We start by approximating the global covariance matrix as blockdiagonal, where only pixels from the same spectrum are correlated. We then compute the eigenvectors of the derivative of the signal covariance with respect to crossspectrum parameters, and project the inversecovarianceweighted spectra onto them. This acts much like a radial Fourier transform over redshift windows. The resulting crossspectrum 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 = {10.1088/14757516/2018/01/003},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 01,
volume = 2018,
place = {United States},
year = {2018},
month = {1}
}