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[82.06] Covariance of the One-dimensional Mass Power Spectrum

H. Zhan (Dept of Physics, University of Arizona), D. Eisenstein (Steward Observatory, University of Arizona)

We provide an analysis of the covariance of the one-dimensional mass power spectrum. The covariance reveals the correlation between different wavenumbers in the cosmic density field, and gives the sample variance error for measurements of the power spectrum from limited observations such as the Ly\alpha forest. For Gaussian random fields, the covariance matrix is diagonal. As expected, the variance of the measured one-dimensional power spectrum is inversely proportional to the number of lines of sight that are sampled from each random field -- assuming they are well separated. Using N-body simulations, we find that the covariance matrix of the one-dimensional power spectrum is generally not diagonal for the cosmic density field due to non-Gaussianity and that the variance is higher than that of a Gaussian random field. We quantify the effects of non-Gaussianity as a function of the separation between the lines of sight. Once the covariance is known, one can not only determine the cosmic variance in the measured one-dimensional power spectrum but also estimate how many lines of sight are needed to achieve a given accuracy.

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Bulletin of the American Astronomical Society, 35#5
© 2003. The American Astronomical Soceity.