UNCERTAINTY OF THE COSMIC BACKGROUND EXPLORER QUADRUPOLE DETECTION

The uncertainty of the quadrupole component of cosmic microwave backgr ound (CMB) heterogeneity estimated from Cosmic Background Explorer (CO BE) data is sensitive to assumptions about other multipoles. Smoot et al. (1992) and Bennett et al. (1992) implicitly assume that multipoles of degree l > 2 vanish. Higher order multipoles can ''alias'' into le ast-squares estimates of the quadrupole. If CMB heterogeneity is Gauss ian with a power-law spectrum of index n, normalized to a quadrupole v alue Q(rms-PS), aliasing effectively contributes to each quadrupole co mponent a zero-mean Gaussian noise whose variance depends on n, Q(rms- PS), and the spatial distribution of data. Gould's (1993) approach to adjusting COBE quadrupole estimates for the expected contribution of i nstrument noise can be used to adjust for such ''aliasing noise'' as w ell. If n = 1 and Q(rms-PS) = 16, the adjusted estimate using 53 GHz d ata from Galactic latitudes Absolute value of b > 20-degrees is 2.4 +/ - 5.5 muK, and the adjusted estimate using ''combination'' data from G alactic latitudes Absolute value of b > 10-degrees is 9.3 +/- 3.8 muK. If n = 1.5 and Q(rms-PS) = 20, the adjusted ''combination'' estimate becomes 8.3 +/- 4.2 muK. These uncertainties neglect systematic errors , errors in the estimated kinematic quadrupole, covariance among the q uadrupole components, and covariance of the aliasing effect. In 530 of 1000 simulations with Q(rms) = 0, n = 1.5, Q(rms-PS) = 20, and Absolu te value of b > 10-degrees, the inferred rms quadrupole exceeds Gould' s (1993) corresponding adjusted ''combination'' estimate less twice it s standard deviation. In 910 of 1000 simulations with n = 1.5, Q(rms-P S) = 20 muK, and Absolute value of b > 20-degrees, the inferred rms qu adrupole exceeds Gould's adjusted 53 GHz estimate less twice its stand ard deviation. Most of the strength of the 10-degrees ''combination ma p'' detection is due to components Q2 and Q3: they are large, have rel atively low noise, and suffer least from aliasing. The reliability of the COBE detection depends on the true spectrum of CMB heterogeneity, and on how well the combination map suppresses Galactic structure in t he range 10-degrees less-than-or-equal-to Absolute value of b less-tha n-or-equal-to 20-degrees.