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 2 year maps produced by the COBE DMR. The power spectrum of the real 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 $P(k) \propto k^n$. Within the limited range of spatial scales covered by the COBE DMR, corresponding to spherical harmonic indices $3 \leq \ell \lsim 30$, the best fitting value of the spectral index is $n = 1.25^{+0.4}_{-0.45}$ with the Harrison-Zeldovich value $n = 1$ approximately 0.5$\sigma$ below the best fit. For $3 \leq \ell \lsim 19$, the best fit is $n = 1.46^{+0.39}_{-0.44}$. Comparing the COBE DMR $\Delta T/T$ at small $\ell$ to the $\Delta T/T$ at $\ell \approx 50$ from degree scale anisotropy experiments gives a smaller range of acceptable spectral indices which includes $n = 1$.