Bayesian Galaxy Shape Measurement for Weak Lensing Surveys - III. Application to the Canada-France-Hawaii Telescope Lensing Survey

TL;DR

The paper introduces a likelihood-based Bayesian pipeline (lensfit) for weak lensing shape measurement that handles PSF variations, multi-epoch data, and blending in CFHTLenS. It uses pixel-based PSF models and two-component bulge+disk galaxy models with full marginalisation over nuisance parameters, jointly fitting seven exposures per field without co-addition to obtain unbiased ellipticity estimates and a robust shear estimator. Extensive image simulations (GREAT CFHTLenS and SkyMaker) calibrate noise bias and quantify systematics, enabling calibrated two-point shear statistics across tomographic bins, with multiplicative biases addressed as a function of signal-to-noise, size, and redshift. The method demonstrates controlled systematics and provides insights and calibrations for future wide-field surveys, while acknowledging limitations in model bias and the ongoing goal of developing a fully Bayesian, noise-bias-free estimator for next-generation cosmological analyses.

Abstract

A likelihood-based method for measuring weak gravitational lensing shear in deep galaxy surveys is described and applied to the Canada-France-Hawaii Telescope (CFHT) Lensing Survey (CFHTLenS). CFHTLenS comprises 154 sq deg of multicolour optical data from the CFHT Legacy Survey, with lensing measurements being made in the i' band to a depth i'(AB)<24.7, for galaxies with signal-to-noise ratio greater than about 10. The method is based on the lensfit algorithm described in earlier papers, but here we describe a full analysis pipeline that takes into account the properties of real surveys. The method creates pixel-based models of the varying point spread function (PSF) in individual image exposures. It fits PSF-convolved two-component (disk plus bulge) models, to measure the ellipticity of each galaxy, with bayesian marginalisation over model nuisance parameters of galaxy position, size, brightness and bulge fraction. The method allows optimal joint measurement of multiple, dithered image exposures, taking into account imaging distortion and the alignment of the multiple measurements. We discuss the effects of noise bias on the likelihood distribution of galaxy ellipticity. Two sets of image simulations that mirror the observed properties of CFHTLenS have been created, to establish the method's accuracy and to derive an empirical correction for the effects of noise bias.

Figures (17)

• Figure 1: Fitted disk semi-major axis scalelength, plotted as a function of $i'$-band magnitude, for galaxies identified as being disk-dominated, from the fits of simard02a to HST WFPC2 data. The large filled circles indicate the median size measured in bins of apparent magnitude. The horizontal lines indicate the CFHT MegaCam pixel size of $0.187"$ (lower line) and a typical CFHTLenS PSF half-width half maximum of $0.35"$ (upper line).
• Figure 2: An example of the distribution of lensing weights for 10,000 measured galaxies in one typical CFHTLenS field, W1m2m3. Galaxies were measured on seven exposures to a limiting magnitude $i'<24.7$. Weights are shown as a function of ( left) apparent magnitude $i$, ( centre) fitted semi-major axis disk scalelength $r$ and ( right) signal-to-noise ratio $\nu_{\rm SN}$.
• Figure 3: Examples of four galaxies excluded from measurement by the criteria described in Section \ref{['sec:blends']}, in field W1m0m1. Each panel shows a coadded image 48 pixels (approximately $9"$) square, centred on each target galaxy, and the inverted grey scale is linear up to some maximum value which varies between images.
• Figure 4: Example PSF models derived in a typical CFHTLenS exposure: ID 720093 in field W1p3m0. The upper panels show the model PSF sampled at three locations across the MegaCam field, with a linear greyscale varying from 0 to 0.05, where the values are relative to the total flux in the PSF. Each panel is 32 pixels (approximately $6"$) square. The centre panels show the mean residuals, averaged over all the stars selected on that CCD, between the PSF model and the star images, with a linear greyscale varying over the range $\pm 5\times 10^{-4}$. No residuals are larger than $7\times 10^{-4}$ anywhere in these panels. The lower panels show the rms variation in the model, measured as described in the text, with a linear greyscale over the range 0 (black) to $5\times 10^{-4}$ (white), with maximum rms $5.6 \times 10^{-4}$. The PSFs and the residuals are shown: (left) at the centre of the CCD in the highest right ascension, lowest declination part of the MegaCam field; (centre) at the centre of the CCD immediately below the centre of the MegaCam field; (right) at the centre of the CCD in the lowest right ascension, highest declination part of the MegaCam field;
• Figure 5: The variation of measured PSF over one of the CFHTLenS fields with a highly variable PSF, W1m1p2. The plot has been made by combining information from seven exposures, which are somewhat offset with respect to each other. PSF ellipticities have been simply averaged. (left) stick plot showing the variation of measured PSF ellipticity across the field. The maximum stick length on the plot corresponds to ellipticity of 0.13. (centre) greyscale showing the ellipticity amplitude, with black having an ellipticity of 0.16. (right) greyscale showing the fraction of the light in the central pixel of the PSF, with black indicating a fraction 0.1.