Sample Variance of non-Gaussian Sky Distributions

Abstract

Non-Gaussian distributions of cosmic microwave background (CMB) anisotropies have been proposed to reconcile the discrepancies between different experiments at half-degree scales (Coulson et al. 1994). Each experiment probes a different part of the sky, furthermore, sky coverage is very small, hence the sample variance of each experiment can be large, especially when the sky signal is non-Gaussian. We model the degree-scale CMB sky as a $\chi_{n}^{2}$ field with $n$-degrees of freedom and show that the sample variance is enhanced over that of a Gaussian distribution by a factor of $ {(n +6)/ n}$. The sample variance for different experiments are calculated, both for Gaussian and non-Gaussian distributions. We also show that if the distribution is highly non-Gaussian $(n \ltwid 4)$ at half-degree scales, then the non-Gaussian signature of the CMB could be detected in the FIRS map, though probably not in the COBE map.