Information content of weak lensing power spectrum and bispectrum: including the non-Gaussian error covariance matrix

We address the amount of information in the non-Gaussian regime of weak lensing surveys by modelling all relevant covariances of the power spectra and bispectra, using 1000 ray-tracing simulation realizations for a Lambda-CDM model and an analytical halo model. We develop a formalism to describe the covariance matrices of power spectra and bispectra of all triangle configurations. In addition to the known contributions which extend up to six-point correlation functions, we propose a new contribution `the halo sample variance (HSV)' arising from the coupling of the lensing Fourier modes with large-scale mass fluctuations on scales comparable with the survey region via halo bias theory. We show that the model predictions are in good agreement with the simulation once we take the HSV into account. The HSV gives a dominant contribution to the covariance matrices at multipoles l > 10^3, which arises from massive haloes with a mass of > 10^14 solar mass and at relatively low redshifts z < 0.4. Since such haloes are easily identified from a multi-colour imaging survey, the effect can be estimated from the data. By adding the bispectrum to the power spectrum, the total information content or the cumulative signal-to-noise ratio up to a certain maximum multipole of a few 10^3 is improved by 20--50 per cent, which is equivalent to a factor of 1.4--2.3 larger survey area for the power spectrum measurement alone. However, it is still smaller than the case of a Gaussian field by a factor of 3 mostly due to the HSV. Thus bispectrum measurements are useful for cosmology, but using information from upcoming surveys requires that non-Gaussian covariances are carefully estimated.
28 pages, 15 figures, MNRAS accepted. Errors in Figs. 4, 5 and 7 are corrected