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Steps toward the Power Spectrum of Matter. I. The Mean Spectrum of Galaxies

We calculate the mean power spectrum of all galaxies using published power spectra of galaxies and clusters of galaxies. On small scales we use the power spectrum derived from the two-dimensional distribution of Automatic Plate Measuring Facility (APM) galaxies, since this sample is not influenced by redshift distortions and is the largest and deepest sample of galaxies available. On large scales we use power spectra derived from three-dimensional data for various galaxy and cluster samples which are reduced to real space and in amplitude to the power spectrum of APM galaxies. We find that available data indicate the presence of two different populations in the nearby universe. Clusters of galaxies sample a relatively large region in the universe where rich, medium, and poor superclusters are well represented. Their mean power spectrum has a spike at wavenumber k = 0.05 ± 0.01 h Mpc-1, followed by an approximate power-law spectrum of index n ≈ -1.9 toward small scales. Some galaxy surveys (APM three-dimensional, IRAS QDOT, and SSRS+CfA2 130 Mpc) have similar spectra. The power spectrum found from the Las Campanas Redshift Survey and IRAS 1.2 Jy surveys is flatter around the maximum, which may represent regions of the universe with medium-rich and poor superclusters. Differences in power spectra for these populations may partly be due to the survey geometries of the data sets in question and/or to features of the original data analysis.