We show how to estimate the covariance of the power spectrum of astatistically homogeneous and isotropic density field from a single periodicsimulation, by applying a set of weightings to the density field, and bymeasuring the scatter in power spectra between different weightings. Werecommend a specific set of 52 weightings containing only combinations offundamental modes, constructed to yield a minimum variance estimate of thecovariance of power. Numerical tests reveal that at nonlinear scales thevariance of power estimated by the weightings method substantially exceeds thatestimated from a simple ensemble method. We argue that the discrepancy iscaused by beat-coupling, in which products of closely spaced Fourier modescouple by nonlinear gravitational growth to the beat mode between them.Beat-coupling appears whenever nonlinear power is measured from Fourier modeswith a finite spread of wavevector, and is therefore present in the weightingsmethod but not the ensemble method. Beat-coupling inevitably affects realgalaxy surveys, whose Fourier modes have finite width. Surprisingly, thebeat-coupling contribution dominates the covariance of power at nonlinearscales, so that, counter-intuitively, it is expected that the covariance ofnonlinear 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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