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 $3 \leq \ell \lsim 30$,thebestfittingvalueofthespectralindexis$n = 1.25^{+0.4}{-0.45}$withtheHarrison-Zeldovichvalue$n = 1$ approximately 0.5$\sigma$ below the best fit. For $3\le \mathrm{\ell }\text{lsim}19$, the best fit is $n = 1.46^{+0.39}{-0.44}$\mathrm{.}ComparingtheCOBEDMR$\Delta T/T$atsmall$\ell$ to the $\mathrm{\Delta }T\mathrm{/}T$ at $\mathrm{\ell }\approx 50$ from degree scale anisotropy experiments gives a smaller range of acceptable spectral indices which includes $n=1$.