ANALYSIS OF SMALL-SCALE MICROWAVE BACKGROUND-RADIATION ANISOTROPY IN THE PRESENCE OF FOREGROUND CONTAMINATION

Many of the current round of experiments searching for anisotroPies in the microwave background radiation (MBR) are confronting the problem of how to disentangle the cosmic signal from contamination due to Gala ctic and intergalactic foreground sources. Here we show how commonly u sed likelihood function techniques can be generalized to account for f oreground. Specifically we set some restrictions on the spectrum of fo reground contamination but allow the amplitude to vary arbitrarily. Th e likelihood function thus generalized gives reasonable limits on the MBR anisotropy which, in some cases, are not much less restrictive tha n what one would get from more detailed modeling of the foreground. Fu rthermore, the likelihood function is exactly the same as one would ob tain by simply projecting out foreground contamination and looking at the reduced data set. We apply this generalized analysis to the recent medium-angle data sets of ACME-HEMT (Gaier et al. 1992; Schuster et a l. 1993) and MAX (Meinhold et al. 1993; Gunderson et al. 1993). The re sulting analysis constrains the one free parameter in the standard col d dark matter theory to be Q(rms-ps) = 18(-5)+8 muK. This best fit val ue, although in striking agreement with the normalization from COBE, i s not a very good fit, with an overall chi2/degrees of freedom = 208/1 68. We also argue against three commonly used methods of dealing with foreground: (1) ignoring it completely; (2) subtracting off a best-fit foreground and treating the residuals as if uncontaminated; and (3) c ulling data which appears to be contaminated by foreground.