Mathematics – Functional Analysis
Scientific paper
Aug 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994phdt.........2l&link_type=abstract
Ph.D. Thesis California Univ., Berkeley. Lawrence Berkeley Lab, CA.
Mathematics
Functional Analysis
4
Anisotropy, Correlation, Cosmic Background Explorer Satellite, Functional Analysis, Functions (Mathematics), Microwave Radiometers, Microwaves, Background Radiation, Latitude, Matrices (Mathematics), Pixels, Stability, Statistical Analysis, Variance (Statistics)
Scientific paper
The Differential Microwave Radiometer (DMR) aboard the COBE satellite has detected anisotropies in the cosmic microwave background (CMB) radiation. A two-point correlation function analysis which helped lead to this discovery is presented in detail. The results of a correlation function analysis of the two year DMR data set is presented. The first and second year data sets are compared and found to be reasonably consistent. The positive correlation for separation angles less than approximately 20 deg is robust to Galactic latitude cuts and is very stable from year to year. The Galactic latitude cut independence of the correlation function is strong evidence that the signal is not Galactic in origin. The statistical significance of the structure seen in the correlation function of the first, second and two year maps is respectively greater than 9(sigma), greater than 10(sigma) and greater than 18(sigma) above the noise. The noise in the DMR sky maps is correlated at a low level. The structure of the pixel temperature covariance matrix is given. The noise covariance matrix of a DMR sky map is diagonal to an accuracy of better than 1%. For a given sky pixel, the dominant noise covariance occurs with the ring of pixels at an angular separation of 60 deg due to the 60 deg separation of the DMR horns. The mean covariance of 60 deg is 0.45%-0.14+0.18 of the mean variance. The noise properties of the DMR maps are thus well approximated by the noise properties of maps made by a single-beam experiment. Previously published DMR results are not significantly affected by correlated noise.
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