The N-point correlation functions of the COBE-DMR maps revisited

Abstract

We calculate the two-, three- and (for the first time) four-point correlation functions of the COBE-DMR 4-year sky maps, and search for evidence of non-Gaussianity by comparing the data to Monte Carlo-simulations of the functions. The analysis is performed for the 53 and 90 GHz channels, and five linear combinations thereof. For each map, we simulate an ensemble of 10,000 Gaussian realisations based on an a priori best-fit scale-invariant cosmological power spectrum, the DMR beam pattern and instrument-specific noise properties. Each observed COBE-DMR map is compared to the ensemble using a simple chi^2 statistic, itself calibrated by simulations. In addition, under the assumption of Gaussian fluctuations, we find explicit expressions for the expected values of the four-point functions in terms of combinations of products of the two-point functions, then compare the observed four-point statistics to those predicted by the observed two-point function, using a redefined chi^2 statistic. Both tests accept the hypothesis that the DMR maps are consistent with Gaussian initial perturbations.