Comments on the statistical analysis of excess variance in the COBE differential microwave radiometer maps

Cosmic anisotropy produces an excess variance σ²_sky in the ΔT maps produced by the Differential Microwave Radiometer (DMR) on COBE that is over and above the instrument noise. After smoothing to an effective resolution of 10°, this excess, σ_sky(10°), provides an estimate for the amplitude of the primordial density perturbation power spectrum with a cosmic uncertainty of only 12%. We employ detailed Monte Carlo techniques to express the amplitude derived from this statistic in terms of the universal rms quadrupole amplitude, 〈Q²_RMS〉^0.5. The effects of monopole and dipole subtraction and the non-Gaussian shape of the DMR beam cause the derived 〈Q²_RMS〉_0.5 to be 5%-10% larger than would be derived using simplified analytic approximations. We also investigate the properties of two other map statistics: the actual quadrupole and the Boughn-Cottingham statistic. Both the σ_sky(10°) statistic and the Boughn-Cottingham statistic are consistent with the 〈Q²_RMS〉^0.5 = 17 ± 5 μK reported by Smoot et al. (1992) and Wright et al. (1992).