skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Abstract

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:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); Univ. College London, Bloomsbury (United Kingdom)
OSTI Identifier:
1424960
Alternate Identifier(s):
OSTI ID: 1530316
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:
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:https://doi.org/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:https://doi.org/10.1088/1475-7516/2018/01/003. https://www.osti.gov/servlets/purl/1424960.
@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 = {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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Figures / Tables:

FIG. 1. FIG. 1.: S̃,α matrices for two different parameters. Left: eighth k-bin (k = 0.0015s km −1) of the second z-bin (z = 2.15); Right: first non-zero k-bin (k = 0.0002s km −1) of the fifth z-bin (z = 2.88). The redshift bin (z-bin) of the parameter sets the diagonal bandmore » that is non-zero, and the wavenumber bin (k-bin) sets the oscillation frequency.« less

Save / Share:

Works referenced in this record:

Power-spectrum analysis of three-dimensional redshift surveys
journal, May 1994

  • Feldman, Hume A.; Kaiser, Nick; Peacock, John A.
  • The Astrophysical Journal, Vol. 426
  • DOI: 10.1086/174036

Cosmological constraints from the SDSS luminous red galaxies
journal, December 2006


The one-dimensional Ly α forest power spectrum from BOSS
journal, November 2013

  • Palanque-Delabrouille, Nathalie; Yèche, Christophe; Borde, Arnaud
  • Astronomy & Astrophysics, Vol. 559
  • DOI: 10.1051/0004-6361/201322130

Baryon acoustic oscillations in the Ly α forest of BOSS quasars
journal, April 2013


Baryon acoustic oscillations in the Ly α forest of BOSS DR11 quasars
journal, January 2015


Measurement of baryon acoustic oscillation correlations at z  = 2.3 with SDSS DR12 Ly α -Forests
journal, June 2017


A maximum likelihood analysis of the low cosmic microwave background multipoles from the Wilkinson Microwave Anisotropy Probe
journal, March 2004


An evolution free test for non-zero cosmological constant
journal, October 1979

  • Alcock, Charles; Paczyński, Bohdan
  • Nature, Vol. 281, Issue 5730
  • DOI: 10.1038/281358a0

Cosmic microwave background anisotropy window functions revisited
journal, October 1999


High-performance P3M N-body code: CUBEP3M
journal, September 2013

  • Harnois-Deraps, J.; Pen, U. -L.; Iliev, I. T.
  • Monthly Notices of the Royal Astronomical Society, Vol. 436, Issue 1
  • DOI: 10.1093/mnras/stt1591

Mining weak lensing surveys
journal, August 2003


    Works referencing / citing this record:

    Improved renormalization group computation of likelihood functions for cosmological data sets
    journal, August 2019


    Impact of inhomogeneous reionization on the Lyman-α forest
    journal, May 2019

    • Montero-Camacho, Paulo; Hirata, Christopher M.; Martini, Paul
    • Monthly Notices of the Royal Astronomical Society, Vol. 487, Issue 1
    • DOI: 10.1093/mnras/stz1388