Structure in Galaxy Distribution. III. Fourier Transforming the Universe

TL;DR

This paper demonstrates a straightforward Fourier transform analysis of galaxy distributions from redshift surveys, focusing on the phase spectrum to characterize non-Gaussianity, with initial results showing no significant non-Gaussian features.

Contribution

It introduces a simple Fourier transform method for galaxy data analysis emphasizing the phase spectrum, providing a new framework for non-Gaussianity detection in large-scale structure.

Findings

Power spectrum estimates are consistent with traditional methods.

No significant non-Gaussianity detected in the data set.

Method shows promise for future larger surveys.

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 (FFT) 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. However we concentrate on the less often studied Fourier phase spectrum, a simple and general framework for characterizing non-Gaussianity, more easily interpretable than the tangled, incomplete multi-point methods conventionally used. No significant signature of non-Gaussianity has been found in the relatively small data set analyzed, but we identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.