On the RMS Anisotropy at 7 degrees and 10 degrees Observed in the COBE-DMR Two Year Sky Maps

The frequency-independent RMS temperature fluctuations determined from the COBE-DMR two year sky maps are used to infer the parameter Q_{rms-PS}, which characterizes the normalization of power law models of primordial cosmological temperature anisotropy. In particular, a ‘cross’-RMS statistic is used to determine Q_{rms-PS} for a forced fit to a scale-invariant Harrison-Zel’dovich (n = 1) spectral model. Using a joint analysis of the 7 degree and 10 degree RMS temperature derived from both the 53 and 90 GHz sky maps, we find Q_{rms-PS} = 17.0^{+2.5}{-2.1} uK when the low quadrupole is included, and Q{rms-PS} = 19.4^{+2.3}{-2.1} uK excluding the quadrupole. These results are consistent with the n = 1 fits from more sensitive methods (e.g. power spectrum, correlation function). The effect of the low quadrupole derived from the COBE-DMR data on the inferred Q{rms-PS} normalization is investigated. A bias to lower Q_{rms-PS} is found when the quadrupole is included. The higher normalization for a forced n = 1 fit is then favored by the cross-RMS technique. As initially pointed out in Wright et al. (1994a) and further discussed here, analytic formulae for the RMS sky temperature fluctuations will NOT provide the correct normalization amplitude.