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

Abstract

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 $n=1.25_{-0.45}^{+0.4}$ 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 $n=1.46_{-0.44}^{+0.39}$. 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 $n=1$.

22 pages of LaTex using aaspp.sty and epsf.sty with appended Postscript figures, COBE Preprint 94-02

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