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

We calculate the mean power spectrum of galaxies using published powerspectra of galaxies and clusters of galaxies. On small scales we use the powerspectrum derived from the 2-dimensional distribution of APM galaxies, on largescales we use power spectra derived from 3-dimensional data for galaxy andcluster samples. Spectra are reduced to real space and to the amplitude of thepower spectrum of APM galaxies. Available data indicate the presence of twodifferent populations in the nearby Universe. Clusters of galaxies sample arelatively large region in the Universe where rich, medium and poorsuperclusters are well represented. Their mean power spectrum has a spike onscale 120 h^{-1}Mpc, followed by an approximate power-law spectrum of index n =-1.9 towards small scales. The power spectrum found from LCRS and IRAS 1.2 Jysurveys is flatter around the maximum, which may represent regions of theUniverse with medium-rich and poor superclusters.Comment: LaTex (sty files added), 35 pages, 5 PostScript figures and Table with mean power spectrum embedded, Astrophysical Journal (accepted