GENUS AND SPOT DENSITY IN THE COBE-DMR FIRST-YEAR ANISOTROPY MAPS

A statistical analysis of texture on the COBE-DMR first-year sky maps based on the genus and spot number is presented. A generalized chi(2) statistic is defined in terms of 'observable' quantities: the genus an d spot density that would be measured by different cosmic observers. T his strategy, together with the use of Monte Carlo simulations of the temperature fluctuations, including all the relevant experimental para meters, represents the main difference from previous analyses. Based o n the genus analysis we find a strong anticorrelation between the quad rupole amplitude Q(rms-PS) and the spectral index n of the density flu ctuation power spectrum at recombination of the form Q(rms-PS) = 22.2 +/- 1.7 - (4.7 +/- 1.3)x n mu K for fixed n, consistent with previous works. The result obtained based on the spot density is consistent wit h this Q(rms-PS)(n) relation. In addition to the previous results, we have determined, using Monte Carlo simulations, the minimum uncertaint y due to cosmic variance for the determination of the spectral index w ith the genus analysis. This uncertainty is delta n approximate to 0.2 .