The effects of incomplete sky coverage on the analysis of large angular scale microwave background anisotropy

We discuss three possible methods of analyzing large angular scale microwave background anisotropy, paying particular attention to the effects of incomplete sky coverage on these methods. We have performed Monte Carlo simulations in which we created sky maps containing fluctuations with a Harrison-Zel'dovich spectrum, and then masked out a region of half-width 20 deg about the equator. We then attempted to recover the quadrupole moment Q as well as the power-spectrum normalization Qrms-PS and power-law index n from the incomplete data set. We find that it is in general impossible to extract reliable information about particular multipoles from an incomplete data set; for example, attempts to determine the local quadrupole moment of the Cosmic Microwave Background (CMB) anisotropy from the masked Cosmic Background Explorer (COBE) data set will inevitably have large uncertainties. Attempts to determine n and Qrms-PS suffer less from the effects of masking; however, cosmic variance sets stringent limits on the accuracy of determinations of these quantities. We conclude that the COBE Differential Microwave Radiometer (DMR) will be unable to determine the power-law index n of the power spectrum to an accuracy better than about +/- 0.2, even if noise levels are reduced to negligible levels. Similarly, the accuracy with which COBE will be able to determine Qrms-PS will be limited to approximately +/- 20%, even in the absence of noise.