Band Power Spectra in the COBE^* DMR Four-Year Anisotropy Maps

We employ a pixel-based likelihood technique to estimate the angular power spectrum of the COBE Differential Microwave Radiometer (DMR) 4 yr sky maps. The spectrum is consistent with a scale-invariant power-law form with a normalization, expressed in terms of the expected quadrupole anisotropy, of Q_rms-PS|n=1 = 18 ± 1.4 μK, and a best-fit spectral index of 1.2 ± 0.3. The normalization is somewhat smaller than we concluded from the 2 yr data, mainly due to additional Galactic modeling. We extend the analysis to investigate the extent to which the "small" quadrupole observed in our sky is statistically consistent with a power-law spectrum. The most likely quadrupole amplitude ranges between 7 and 10 μK, depending on the details of Galactic modeling and data selection, but in no case is there compelling evidence that the quadrupole is inconsistent with a power-law spectrum. We conclude with a likelihood analysis of the band power amplitude in each of four spectral bands between ℓ = 2 and 40, and find no evidence for deviations from a simple power-law spectrum.