CFHTLenS: The Canada-France-Hawaii Telescope Lensing Survey

TL;DR

CFHTLenS tackles the challenge of precise weak lensing measurements by re-engineering the entire data-analysis pipeline from raw exposures to shear and photometric redshifts. It introduces a cosmology-agnostic systematic-error framework using CFHTLenS clone simulations and a star–galaxy cross-correlation diagnostic to identify and remove PSF-related contaminants on a field-by-field basis. The study demonstrates calibrated, field-selected cosmic shear statistics that are robust to redshift-dependent biases, producing science-ready catalogues suitable for cosmological analyses. This holistic, exposure-level approach, combined with detailed simulations, sets a high standard for end-to-end weak lensing pipelines and informs future large surveys.

Abstract

We present the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS) that accurately determines a weak gravitational lensing signal from the full 154 square degrees of deep multi-colour data obtained by the CFHT Legacy Survey. Weak gravitational lensing by large-scale structure is widely recognised as one of the most powerful but technically challenging probes of cosmology. We outline the CFHTLenS analysis pipeline, describing how and why every step of the chain from the raw pixel data to the lensing shear and photometric redshift measurement has been revised and improved compared to previous analyses of a subset of the same data. We present a novel method to identify data which contributes a non-negligible contamination to our sample and quantify the required level of calibration for the survey. Through a series of cosmology-insensitive tests we demonstrate the robustness of the resulting cosmic shear signal, presenting a science-ready shear and photometric redshift catalogue for future exploitation.

Figures (12)

• Figure 1: The star-galaxy cross correlation function $\xi_{\rm sg}(\theta)$ for the eight individual exposures in example field W1m0m0 as a function of angular separation (triangles, where each panel is a different exposure). The measured angular correlation function in each exposure can be compared to the predicted angular star-galaxy correlation (equation \ref{['eqn:sgtheta']}, shown as a curve) calculated using only the zero separation measure $\xi_{\rm sg}(0)$ (shown offset, circle). The correlation between the exposures and angular scales is shown in the covariance matrix of the data points in the upper right panel. Each block shows one of the eight exposures and contains a $6 \times 6$ matrix showing the correlation between the angular scales. The greyscale bar shows the amplitude of the values in the matrix.
• Figure 2: The distribution of the components of $A_{\rm obs}$ for individual exposures in CFHTLenS. The open symbols show the distribution for the full data set. As the number of exposures is discrete we change from a log to linear scale below $n(A) = 1$. The data can be compared with the different components of the star-galaxy cross correlation function $\bm{\xi}_{\rm sg}$ as measured from the simulated CFHTLenS 'clone' data. The dashed curve shows the contribution to the star-galaxy cross correlation function from the intrinsic ellipticity distribution $A_{\rm noise}$ and the dotted curve shows the contribution from chance alignments with the galaxy shear field $A_\gamma$, demonstrating that significant star-galaxy correlations can be measured from chance alignments of the PSF with the galaxy shear and intrinsic ellipticity field in one-square degree regions.
• Figure 3: Additive Calibration Correction. The upper panel shows the weighted average $\langle \epsilon_2^{\rm obs} \rangle$ as a function of galaxy size, $r$, for four galaxy samples split by signal-to-noise ratio (circles, $\nu_{\rm SN} \sim 10$, crosses, $\nu_{SN} \sim 15$, open triangles, $\nu_{\rm SN} \sim 20$, and filled triangles $\nu_{SN} \sim 50$ ). It is therefore the small bright galaxies that contribute the most to the average raw measure of $\langle \epsilon_2^{\rm obs} \rangle$ shown in the lower panel (circles). The $r$ and $\nu_{\rm SN}$ dependent model in equation \ref{['eqn:cmodel']} is fit to the data in fine bins of size and signal-to-noise ratio. The best-fit calibration correction for each $\nu_{\rm SN}$ in the upper panel is shown by the dashed curves. The average $\langle \epsilon_2^{\rm obs} \rangle$ when measured from the calibrated galaxy catalogues is shown to be consistent with zero (triangles, lower panel). All errors come from a bootstrap analysis of the catalogue.
• Figure 4: Comparison of the measured $\Sigma(\Delta \xi_{\rm obs})$ (hatched) where the sum is taken over all fields (upper panel) or over the fields with a measured probability of zero systematics $p(\bm{U}=0)>0.11$ (lower panel). These measures can be compared with the probability distribution of measuring $\Sigma(\Delta \xi_{\rm obs})$ from the same number of fields realized in the systematics free CFHTLenS 'clone' (solid). For the full data set (upper panel), we find that the measured $\Sigma(\Delta \xi_{\rm obs})$ far exceeds what is expected from the simulations. Once a conservative cut is applied to the data (lower panel) removing 25% of the data, we find the measured $\Sigma(\Delta \xi_{\rm obs})$ is fully consistent with the expected distribution for the same number of simulated fields. For comparison we also show the probability distribution of $\Sigma (\Delta \xi_{\rm obs})$ as measured from a random correlation between the pure cosmic shear $\gamma$ and the range of CFHTLenS PSFs (dashed).
• Figure 5: Comparison of fields which pass and fail the PSF systematics test to different observables. The open symbols indicate fields that pass. The crosses and filled circles indicate fields that fail. These two sets are split into data observed before the CFHT 'lens flip' (open and filled circles) and the majority of the data observed after the CFHT 'lens flip' (open triangles and crosses). Each panel shows a different combination of observables; upper left the average PSF ellipticity in both components; upper right, the average variation of the PSF ellipticity across the field of view; lower left a comparison of the average variation across the field of view to the PSF variation between the dithered image exposures of the field; lower right a comparison of seeing and airmass. See text for the other combinations of parameters linked to the observations that were also found to show no clear trend between the accepted and rejected fields.