A fitting formula for the non-Gaussian contribution to the lensing power spectrum covariance

Abstract

Context. Weak gravitational lensing is one of the most promising tools to investigate the equation-of-state of dark energy. In order to obtain reliable parameter estimations for current and future experiments, a good theoretical understanding of dark matter clustering is essential. Of particular interest is the statistical precision to which weak lensing observables, such as cosmic shear correlation functions, can be determined. Aims. We construct a fitting formula for the non-Gaussian part of the covariance of the lensing power spectrum. The Gaussian contribution to the covariance, which is proportional to the lensing power spectrum squared, and optionally shape noise can be included easily by adding their contributions. Methods. Starting from a canonical estimator for the dimensionless lensing power spectrum, we model first the covariance in the halo model approach including all four halo terms for one fiducial cosmology and then fit two polynomials to the expression found. On large scales, we use a first-order polynomial in the wave-numbers and dimensionless power spectra that goes asymptotically towards 1.1 C pt for → 0, i.e., the result for the non-Gaussian part of the covariance using tree-level perturbation theory. On the other hand, for small scales we employ a second-order polynomial in the dimensionless power spectra for the fit. Results. We obtain a fitting formula for the non-Gaussian contribution of the convergence power spectrum covariance that is accurate to 10% for the off-diagonal elements, and to 5% for the diagonal elements, in the range 50 < ∼ < ∼ 5000 and can be used for single source redshifts z s ∈ [0.5, 2.0] in WMAP5-like cosmologies.

Cosmic shear covariance: the log-normal approximation

“…In contrast, the simplified log-normal approximation is as simple as the normal approximation, yet appears as accurate as the log-normal approximation. Moreover, the simplified log-normal approximation is simpler than several proposed approximations based on halo models (e.g., Takada & Jain 2009;Pielorz et al 2010). The simplified log-normal approximation is also more general than approximations based on empirical fits to numerical simulations Sato et al 2011b).…”

“…The resulting expressions for the covariance of lensing two-point statistics require considerable more effort to compute than the corresponding expressions in the normal approximation, even if simplified by fitting formulas (Pielorz et al 2010). A thorough assessment of the accuracy of the halo model approach to cosmic shear covariances (e.g.…”

Galaxy-galaxy lensing constraints on the relation between baryons and dark matter in galaxies in the Red Sequence Cluster Survey 2

“…which we calculate using the analytical formula given in Pielorz et al (2010). The dark matter profiles of adjacent haloes cannot overlap, which is prevented by implementing halo exclusion.…”

Breaking the degeneracy: Optimal use of three-point weak lensing statistics

“…Semi analytical methods are available in the literature ( [31] and [32]), but rely on the assumption of Gaussian statistics. An extension to the nonlinear angular scales has been recently developed ( [33], [34] and [35]), however the three-point statistics and source redshift distribution and shape noise of realistic surveys were not considered. In this work the full covariance matrix C was estimated directly from the ray-tracing simulation as in [33] and [34], by taking into account the realistic characteristics of lensing surveys described in the previous sections.…”