On measuring the covariance matrix of the nonlinear power spectrum from simulations

Details On measuring the covariance matrix of the nonlinear power spectrum from simulations On measuring the covariance matrix of the nonlinear power spectrum from simulations

2005-11-14

arxiv.org/abs/astro-ph/0511416v2

Mon.Not.Roy.Astron.Soc.371:1188-1204,2006

Astronomy and Astrophysics

Astrophysics

19 pages, 4 figures. To appear in Monthly Notices of the Royal Astronomical Society. Revised to match accepted version

Scientific paper

10.1111/j.1365-2966.2006.10709.x

We show how to estimate the covariance of the power spectrum of a statistically homogeneous and isotropic density field from a single periodic simulation, by applying a set of weightings to the density field, and by measuring the scatter in power spectra between different weightings. We recommend a specific set of 52 weightings containing only combinations of fundamental modes, constructed to yield a minimum variance estimate of the covariance of power. Numerical tests reveal that at nonlinear scales the variance of power estimated by the weightings method substantially exceeds that estimated from a simple ensemble method. We argue that the discrepancy is caused by beat-coupling, in which products of closely spaced Fourier modes couple by nonlinear gravitational growth to the beat mode between them. Beat-coupling appears whenever nonlinear power is measured from Fourier modes with a finite spread of wavevector, and is therefore present in the weightings method but not the ensemble method. Beat-coupling inevitably affects real galaxy surveys, whose Fourier modes have finite width. Surprisingly, the beat-coupling contribution dominates the covariance of power at nonlinear scales, so that, counter-intuitively, it is expected that the covariance of nonlinear power in galaxy surveys is dominated not by small scale structure, but rather by beat-coupling to the largest scales of the survey.

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