Angular Power Spectrum of the Microwave Background Anisotropy seen by the COBE Differential Microwave Radiometer

The angular power spectrum estimator developed by Peebles (1973) and Hauser & Peebles (1973) has been modified and applied to the 4 year maps produced by the COBE DMR. The power spectrum of the observed sky has been compared to the power spectra of a large number of simulated random skies produced with noise equal to the observed noise and primordial density fluctuation power spectra of power law form, with $P(k) \propto k^n$. The best fitting value of the spectral index in the range of spatial scales corresponding to spherical harmonic indices $3 \leq \ell \lesssim 30$ is an apparent spectral index $n_{app}$ = 1.13 (+0.3) (-0.4) which is consistent with the Harrison-Zel'dovich primordial spectral index $n_{pri} = 1$ The best fitting amplitude for $n_{app} = 1$ is $\langle Q_{RMS}^2\rangle^{0.5}$ = 18 uK.