Fourier spectra of three-dimensional data

We evaluate the power spectrum, bispectrum, and tentatively the trispectrum, i.e., the two-, three-, and four-point galaxy correlation functions in Fourier transform space, for data from the CfA catalog and from the Perseus-Pisces redshift compilation of Giovanelli & Haynes. We work in the transform domain to avoid many systematic problems that afflict direct evaluations of correlation functions; this enables us to extend our knowledge of galaxy clustering to scales of order 100h^-1^ Mpc. At these large scales, the observed power spectrum ought to reflect directly the initial conditions. Our observed power spectrum agrees well with cold dark matter. The best fit gives {OMEGA}h = 0.34 +/- 0.10, while the inferred amplitude of scale-invariant horizon fluctuations is ɛ~(2-4) x 10^-5^. The observed bispectrum obeys the so-called hierarchical pattern, with a reduced threepoint amplitude that is consistent with gravitational instability in perturbation theory starting from Gaussian initial conditions. The trispectrum is only marginally detected, but is again consistent with the hierarchical pattern; the reduced four-point amplitude is determined only to be of order unity. These results constitute perhaps the first direct observational suggestion that gravitational instability in the perturbative regime indeed operates on large scales.