Statistics and Topology of the COBE Differential Microwave Radiometer FirstYear Sky Maps
Abstract
We use statistical and topological quantities to test the COBEDMR first year sky maps against the hypothesis that the observed temperature fluctuations reflect Gaussian initial density perturbations with random phases. Recent papers discuss specific quantities as discriminators between Gaussian and nonGaussian behavior, but the treatment of instrumental noise on the data is largely ignored. The presence of noise in the data biases many statistical quantities in a manner dependent on both the noise properties and the unknown CMB temperature field. Appropriate weighting schemes can minimize this effect, but it cannot be completely eliminated. Analytic expressions are presented for these biases, and Monte Carlo simulations used to assess the best strategy for determining cosmologically interesting information from noisy data. The genus is a robust discriminator that can be used to estimate the power law quadrupolenormalized amplitude independently of the 2point correlation function. The genus of the DMR data are consistent with Gaussian initial fluctuations with Q_rms = 15.7 +/ 2.2  (6.6 +/ 0.3)(n  1) uK where n is the power law index. Fitting the rms temperature variations at various smoothing angles gives Q_rms = 13.2 +/ 2.5 uK and n = 1.7 +0.3 0.6. While consistent with Gaussian fluctuations, the first year data are only sufficient to rule out strongly nonGaussian distributions of fluctuations.
 Publication:

The Astrophysical Journal
 Pub Date:
 December 1994
 DOI:
 10.1086/174970
 arXiv:
 arXiv:astroph/9312031
 Bibcode:
 1994ApJ...437....1S
 Keywords:

 Astronomical Maps;
 Background Radiation;
 Cosmic Rays;
 Cosmology;
 Microwaves;
 Radio Astronomy;
 Statistical Analysis;
 Topology;
 Universe;
 Cosmic Background Explorer Satellite;
 Density Distribution;
 Microwave Radiometers;
 Normal Density Functions;
 Statistical Distributions;
 Temperature Distribution;
 Astronomy;
 COSMOLOGY: COSMIC MICROWAVE BACKGROUND;
 COSMOLOGY: OBSERVATIONS;
 COSMOLOGY: LARGESCALE STRUCTURE OF UNIVERSE;
 METHODS: STATISTICAL;
 Astrophysics
 EPrint:
 17 pages post script