Source Distributions of Cosmic Shear Surveys in Efficiency Space

TL;DR

The paper demonstrates that the cosmic shear lensing efficiency $q(x)$ is a smooth function largely determined by a few descriptors, allowing source distributions to be modeled in efficiency space rather than redshift space. By parameterizing the source density with a gamma distribution $n(x;\alpha,\beta)$ and expressing $q(x;\alpha,\beta)$ in terms of the regularised gamma functions, the authors show that two parameters per tomographic bin, namely the mean $\mu$ and inverse mean $\eta$, suffice to describe the efficiency to about 1% accuracy in DES Y1-like simulations. They validate this approach with Buzzard DES Y1 data and demonstrate that cosmological inferences on $\Omega_m$ and $\sigma_8$ remain robust when marginalising over efficiency parameters with realistic priors (up to ~10% width), though degeneracies shift compared to traditional redshift-space analyses. The results suggest efficiency-space modelling reduces dependence on detailed redshift distributions while maintaining cosmological constraints, and point to future extensions involving outlier mixtures and hierarchical priors that can further enhance robustness in real data analyses.

Abstract

We show that the lensing efficiency of cosmic shear generically has a simple shape, even in the case of a tomographic survey with badly behaved photometric redshifts. We argue that source distributions for cosmic shear can therefore be more effectively parametrised in ``efficiency space''. Using realistic simulations, we find that the true lensing efficiency of a current cosmic shear survey without disconnected outliers in the redshift distributions can be described to per cent accuracy with only two parameters, and the approach straightforwardly generalises to other parametric forms and surveys. The cosmic shear signal is thus largely insensitive to the details of the source distributions, and the features that matter can be summarised by a small number of suitable efficiency parameters. For the simulated survey, we show that prior knowledge at the 10% level, which is attainable e.g. from photometric redshifts, is enough to marginalise over the efficiency parameters without severely affecting the constraints on the cosmology parameters $Ω_m$ and $σ_8$.

Figures (9)

• Figure 1: Distinct source distance distributions (top) with visually (and cosmologically, see Section \ref{['sec:cosmology']}) similar lensing efficiencies (bottom). The total area under the curve $q(x)$ is $\mu/2$, whereas it would be the shaded area $\eta^{-1}/2$ for a curve with fixed slope.
• Figure 2: Two-dimensional distribution of intrinsic redshifts $z_{\rm intr}$ and the photometric redshifts $z_{\rm tomo}$ used for tomographic binning. Source selection into tomographic bins corresponds to horizontal cuts in the plane. Since the distribution is not purely diagonal, this creates complicated intrinsic redshift distributions when using photometric tomography.
• Figure 3: Number count histograms for intrinsic redshifts $z_{\rm intr}$ (top) and photometric redshifts $z_{\rm phot}$ (bottom) after selection of the photometric redshifts $z_{\rm tomo}$ into nominal tomographic redshift bins (dashed lines).
• Figure 4: Top: Tomographic lensing efficiency $q(x)$ from photometric redshifts (solid) and intrinsic redshifts (dotted). Bottom: Absolute difference $\Delta q(x)$ between photometric and intrinsic lensing efficiencies.
• Figure 5: Top: Parametric (solid) and intrinsic (dotted) lensing efficiencies $q(x)$. Bottom: Absolute difference $\Delta q(x)$ between parametric and intrinsic efficiencies. All curves lie inside the 1% band (dashed).