Spherical Mexican hat wavelet: an application to detect non-Gaussianity in the COBE-DMR maps

• Published in: Monthly notices of the Royal Astronomical Society Vol. 326; no. 4; pp. 1243 - 1248
• Main Authors: Cayón, L., Sanz, J.L., Martínez-González, E., Banday, A.J., Argüeso, F., Gallegos, J.E., Górski, K.M., Hinshaw, G.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Science Ltd 01.10.2001
• Subjects: cosmic microwave background; methods: data analysis; cosmic microwave background; methods: data analysis
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1111/j.1365-2966.2001.04641.x

The spherical Mexican hat wavelet is introduced in this paper, with the aim of testing the Gaussianity of the cosmic microwave background temperature fluctuations. Using the information given by the wavelet coefficients at several scales, we have performed several statistical tests on the COBE-DMR maps to search for evidence of non-Gaussianity. Skewness, kurtosis, scale–scale correlations (for two and three scales) and Kolmogorov–Smirnov tests indicate that the COBE-DMR data are consistent with a Gaussian distribution. We have extended the analysis to compare temperature values provided by COBE-DMR data with distributions (obtained from Gaussian simulations) at each pixel and at each scale. The number of pixels with temperature values outside the 95 and 99 per cent limits is consistent with that obtained from Gaussian simulations, at all scales. Moreover, the extrema values for COBE-DMR data (maximum and minimum temperatures in the map) are also consistent with those obtained from Gaussian simulations.