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

.

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