A roadmap to cosmological parameter analysis with third-order shear statistics II. Analytic covariance estimate☆

Context. Third-order weak lensing statistics are a promising tool for cosmological analyses since they extract cosmological information in the non-Gaussianity of the cosmic large-scale structure. However, such analyses require precise and accurate models for the covariance of the statistics. Aims. In this second paper of a series on third-order weak lensing statistics, we derive and validate an analytic model for the covariance of the third-order aperture statistics < M-ap(3)>. Methods. We derive the covariance model from a real-space estimator for < M-ap(3)>, including the Gaussian and non-Gaussian parts. We validate the model by comparing it to estimates from simulated Gaussian random fields (GRFs) and two sets of N-body simulations. Finally, we perform mock cosmological analyses with the model covariance and the simulation estimate to compare the resulting parameter constraints. Results. We find good agreement between the analytic model and the simulations, both for the GRFs and the N-body simulations. The figure of merit in the S-8 Omega(m) plane from our covariance model is within 3% of the one obtained from the simulated covariances. We also show that our model, which is based on an estimator using convergence maps, can be used to obtain upper and lower bounds for the covariance of an estimator based on three-point shear correlation functions. This second estimator is required to measure < M-ap(3)> in realistic survey data. In our derivation, we find that the covariance of < M-ap(3)> cannot be obtained from the bispectrum covariance and that it includes several `finite-field terms' that do not scale with the inverse survey area. Conclusions. Our covariance model is su fficiently accurate for analysing stage III surveys. Covariances for statistics in Fourier space cannot always be straightforwardly converted into covariance for real-space statistics.