The bispectrum covariance beyond Gaussianity: A log-normal approach
  To investigate and specify the statistical properties of cosmological fields
with particular attention to possible non-Gaussian features, accurate formulae
for the bispectrum and the bispectrum covariance are required. The bispectrum
is the lowest-order statistic providing an estimate for non-Gaussianities of a
distribution, and the bispectrum covariance depicts the errors of the
bispectrum measurement and their correlation on different scales. Currently,
there do exist fitting formulae for the bispectrum and an analytical expression
for the bispectrum covariance, but the former is not very accurate and the
latter contains several intricate terms and only one of them can be readily
evaluated from the power spectrum of the studied field. Neglecting all
higher-order terms results in the Gaussian approximation of the bispectrum
covariance. We study the range of validity of this Gaussian approximation for
two-dimensional non-Gaussian random fields. For this purpose, we simulate
Gaussian and non-Gaussian random fields, the latter represented by log-normal
fields and obtained directly from the former by a simple transformation. From
the simulated fields, we calculate the power spectra, the bispectra, and the
covariance from the sample variance of the bispectra, for different degrees of
non-Gaussianity \alpha, which is equivalent to the skewness on a given angular
scale \theta g. We find that the Gaussian approximation provides a good
approximation for \alpha<0.6 and a reasonably accurate approximation for
\alpha< 1, both on scales >8\theta g. Using results from cosmic shear
simulations, we estimate that the cosmic shear convergence fields are described
by \alpha<0.7 at \theta g~4". We therefore conclude that the Gaussian
approximation for the bispectrum covariance is likely to be applicable in
ongoing and future cosmic shear studies.
