EDP Sciences
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Volume 395, Number 2, November IV 2002
Page(s) 409 - 415
Section Cosmology
DOI http://dx.doi.org/10.1051/0004-6361:20021264

A&A 395, 409-415 (2002)
DOI: 10.1051/0004-6361:20021264

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

H. K. Eriksen1, A. J. Banday2 and K. M. Górski3, 4

1  Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315, Norway
2  Max-Planck-Institut für Astrophysik, Garching bei München, Germany
3  European Southern Observatory, Garching bei München, Germany
4  Warsaw University Observatory, Aleje Ujazdowskie 4, 00-478 Warszawa, Poland

(Recieved 19 June 2002 / Accepted 28 August 2002)

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 realizations 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.

Key words: cosmic microwave background -- cosmology: observations -- methods: statistical

© ESO 2002