Structure in Galaxy Distribution. III. Fourier Transforming the Universe

摘要

We demonstrate the effectiveness of a relatively straightforward analysis ofthe complex 3D Fourier transform of galaxy coordinates derived from redshiftsurveys. Numerical demonstrations of this approach are carried out on avolume-limited sample of the Sloan Digital Sky Survey redshift survey. Thedirect unbinned transform yields a complex 3D data cube quite similar to thatfrom the Fast Fourier Transform (FFT) of finely binned galaxy positions. Inboth cases deconvolution of the sampling window function yields estimates ofthe true transform. Simple power spectrum estimates from these transforms areroughly consistent with those using more elaborate methods. However weconcentrate on the less often studied Fourier phase spectrum, a simple andgeneral framework for characterizing non-Gaussianity, more easily interpretablethan the tangled, incomplete multi-point methods conventionally used. Nosignificant signature of non-Gaussianity has been found in the relatively smalldata set analyzed, but we identify some threads of modern large scale inferencemethodology that will presumably yield detections in new wider and deepersurveys.