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To investigate and specify the statistical properties of cosmological fieldswith particular attention to possible non-Gaussian features, accurate formulaefor the bispectrum and the bispectrum covariance are required. The bispectrumis the lowest-order statistic providing an estimate for non-Gaussianities of adistribution, and the bispectrum covariance depicts the errors of thebispectrum measurement and their correlation on different scales. Currently,there do exist fitting formulae for the bispectrum and an analytical expressionfor the bispectrum covariance, but the former is not very accurate and thelatter contains several intricate terms and only one of them can be readilyevaluated from the power spectrum of the studied field. Neglecting allhigher-order terms results in the Gaussian approximation of the bispectrumcovariance. We study the range of validity of this Gaussian approximation fortwo-dimensional non-Gaussian random fields. For this purpose, we simulateGaussian and non-Gaussian random fields, the latter represented by log-normalfields and obtained directly from the former by a simple transformation. Fromthe simulated fields, we calculate the power spectra, the bispectra, and thecovariance from the sample variance of the bispectra, for different degrees ofnon-Gaussianity \alpha, which is equivalent to the skewness on a given angularscale \theta g. We find that the Gaussian approximation provides a goodapproximation for \alpha<0.6 and a reasonably accurate approximation for\alpha< 1, both on scales >8\theta g. Using results from cosmic shearsimulations, we estimate that the cosmic shear convergence fields are describedby \alpha<0.7 at \theta g~4". We therefore conclude that the Gaussianapproximation for the bispectrum covariance is likely to be applicable inongoing and future cosmic shear studies.

The bispectrum covariance beyond Gaussianity: A log-normal approach