The Estimation of the Noise in Cosmic Microwave Background Anisotropy Experiments

Even the most sensitive cosmic microwave background anisotropy experimentshave signal to noise ratios <=5, so that an accurate determination of theproperties of the cosmological signal requires a careful assessment of theexperimental noise. Most of the experiments combine simultaneous multi-channelobservations in which the presence of correlated noise is likely. This case iscommon for ground-based experiments in which an important fraction of the noisecould be atmospheric in origin. Here, the way to compute and determine theeffects produced by this correlated noise is discussed; in particular, thepaper considers the Tenerife experiments (three radiometers at 10, 15 and 33GHz with two independent receivers each) showing how this effect has beentaking into account properly in the more recent analysis of these data. It willbe demonstrated that for each of the three radiometers of these experiments,the atmospheric noise is equivalent to a Gaussian noise common to both channelswith a coherence time smaller than the binning time, the net effect being anenhancement of the error-bars in the stacked scan as compared with theestimation for the case of pure uncorrelated noise. As expected from thespectral index of the atmosphere, the effect is more important at higherfrequencies. The formalism is generalized and applied to the general case ofsimultaneous multi-channel observations.Comment: ApJ accepted for publication. 12 pages Latex (uses AASTEX) and 2 encapsulated postscript figure