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Title: Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra

Abstract

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Authors:
; ;  [1]
  1. NASA Ames Research Center, Astrobiology and Space Science Division, Moffett Field, CA 94035 (United States)
Publication Date:
OSTI Identifier:
22661145
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 839; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; DATA ANALYSIS; DETECTION; DISTRIBUTION; FOURIER TRANSFORMATION; GALAXIES; GALAXY CLUSTERS; RED SHIFT; SAMPLING; SPECTRA; UNIVERSE

Citation Formats

Scargle, Jeffrey D., Way, M. J., and Gazis, P. R., E-mail: Jeffrey.D.Scargle@nasa.gov, E-mail: Michael.J.Way@nasa.gov, E-mail: PGazis@sbcglobal.net. Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra. United States: N. p., 2017. Web. doi:10.3847/1538-4357/AA692D.
Scargle, Jeffrey D., Way, M. J., & Gazis, P. R., E-mail: Jeffrey.D.Scargle@nasa.gov, E-mail: Michael.J.Way@nasa.gov, E-mail: PGazis@sbcglobal.net. Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra. United States. doi:10.3847/1538-4357/AA692D.
Scargle, Jeffrey D., Way, M. J., and Gazis, P. R., E-mail: Jeffrey.D.Scargle@nasa.gov, E-mail: Michael.J.Way@nasa.gov, E-mail: PGazis@sbcglobal.net. Mon . "Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra". United States. doi:10.3847/1538-4357/AA692D.
@article{osti_22661145,
title = {Structure in the 3D Galaxy Distribution. III. Fourier Transforming the Universe: Phase and Power Spectra},
author = {Scargle, Jeffrey D. and Way, M. J. and Gazis, P. R., E-mail: Jeffrey.D.Scargle@nasa.gov, E-mail: Michael.J.Way@nasa.gov, E-mail: PGazis@sbcglobal.net},
abstractNote = {We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform of finely binned galaxy positions. In both cases, deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multipoint hierarchy. We identify some threads of modern large-scale inference methodology that will presumably yield detections in new wider and deeper surveys.},
doi = {10.3847/1538-4357/AA692D},
journal = {Astrophysical Journal},
number = 1,
volume = 839,
place = {United States},
year = {Mon Apr 10 00:00:00 EDT 2017},
month = {Mon Apr 10 00:00:00 EDT 2017}
}
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