Sample Variance of non-Gaussian Sky Distributions

• Published in: arXiv.org
• Main Author: Luo, Xiaochun
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 03.05.1994
• Subjects: Cosmic microwave background; Normal distribution; Sample variance
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.9404069

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.