## Abstract

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 non-linear 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 non-linear gravitational growth to the beat mode between them. Beat-coupling appears whenever non-linear power is measured from Fourier modes with a finite spread of wavevector, and is therefore present in the weightings method but not in 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 non-linear scales, so that, counter-intuitively, it is expected that the covariance of non-linear power in galaxy surveys is dominated not by small-scale structure, but rather by beat-coupling to the largest scales of the survey.

Original language | English (US) |
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Pages (from-to) | 1188-1204 |

Number of pages | 17 |

Journal | Monthly Notices of the Royal Astronomical Society |

Volume | 371 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2006 |

## Keywords

- Large-scale structure of Universe
- Methods: data analysis

## ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science