CMB Broad-Band Power Spectrum Estimation

The natural outcome of theoretical calculations of microwave background anisotropy is the angular power spectrum Cl as a function of multipole number l. Experimental Cl’s are needed for direct comparison. Estimation procedures using statistics linear in the pixel amplitudes as well as the conventional but less useful quadratic combinations are described. For most current experiments, a single broad-band power amplitude is all that one can get with accuracy. Results are given for the Capri-meeting detections. Mapping experiments, sensitive to many base-lines, can also give spectral “colour” information, either with a series of contiguous narrow-band powers or as parameterized by a local “colour” index n∆T (scale invariant is -2, white noise is 0). Bayesian analyses of the full first year DMR and FIRS maps give very similar band-powers (e.g., Qrms,PS = 17.9± 2.9μK c.f. 18.6± 4.7μK for n∆T = −2) and colour indices (with 1 and 2 sigma error bars) n∆T +3 = 2.0 +0.4;+0.7 −0.4;−1.0 and 1.8 −0.8;−1.3 (c.f. the value 1.15 for a “standard” scale invariant CDM model). The 53 and 90 GHz DMR maps, as well as the FIRS map, have residual shortdistance noise which steepens n∆T . This residual has so far been modelled by allowing the pixel error bars to increase, absorbing much of the effect, but further exploration is needed to see if a second residual evident in the data — which is, in part, responsible for the high n∆T — is from systematic errors or is physical.