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Register a new userProblems using ratios of galaxy shape moments on requirements for weak lensing surveys
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Holger Israel
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The shapes of galaxies can be quantified by ratios of their quadrupole moments. For faint galaxies, observational noise can make the denominator close to zero, so the ratios become ill-defined. Knowledge of these ratios (i.e. their measured standard deviation) is commonly used to assess the efficiency of weak gravitational lensing surveys. Since the requirements cannot be formally tested for faint galaxies, we explore two complementary mitigation strategies. In many weak lensing contexts, the most problematic sources can be removed by a cut in measured size. We investigate how a size cuts affects the required precision of the charge transfer inefficiency model and find slightly wider tolerance margins compared to the full size distribution. However, subtle biases in the data analysis chain may be introduced. Instead, as our second strategy, we propose requirements directly on the quadrupole moments themselves. To optimally exploit a Stage-IV dark energy survey, we find that the mean and standard deviation of a population of galaxies quadrupole moments must to be known to better than $1.4times10^{-3}$ arcsec$^{2}$, or the Stokes parameters to $1.9times10^{-3}$ arcsec$^2$. This testable requirement can now form the basis for future performance validation, or for proportioning the requirements between subsystems to ensure unbiased cosmological parameter inference.
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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 methods accuracy and to derive an empirical correction for the effects of noise bias.
One of the most powerful techniques to study the dark sector of the Universe is weak gravitational lensing. In practice, to infer the reduced shear, weak lensing measures galaxy shapes, which are the consequence of both the intrinsic ellipticity of the sources and of the integrated gravitational lensing effect along the line of sight. Hence, a very large number of galaxies is required in order to average over their individual properties and to isolate the weak lensing cosmic shear signal. If this `shape noise can be reduced, significant advances in the power of a weak lensing surveys can be expected. This paper describes a general method for extracting the probability distributions of parameters from catalogues of data using Voronoi cells, which has several applications, and has synergies with Bayesian hierarchical modelling approaches. This allows us to construct a probability distribution for the variance of the intrinsic ellipticity as a function of galaxy property using only photometric data, allowing a reduction of shape noise. As a proof of concept the method is applied to the CFHTLenS survey data. We use this approach to investigate trends of galaxy properties in the data and apply this to the case of weak lensing power spectra.
We use dense redshift surveys of nine galaxy clusters at $zsim0.2$ to compare the galaxy distribution in each system with the projected matter distribution from weak lensing. By combining 2087 new MMT/Hectospec redshifts and the data in the literature, we construct spectroscopic samples within the region of weak-lensing maps of high (70--89%) and uniform completeness. With these dense redshift surveys, we construct galaxy number density maps using several galaxy subsamples. The shape of the main cluster concentration in the weak-lensing maps is similar to the global morphology of the number density maps based on cluster members alone, mainly dominated by red members. We cross correlate the galaxy number density maps with the weak-lensing maps. The cross correlation signal when we include foreground and background galaxies at 0.5$z_{rm cl}<z<2z_{rm cl}$ is $10-23$% larger than for cluster members alone at the cluster virial radius. The excess can be as high as 30% depending on the cluster. Cross correlating the galaxy number density and weak-lensing maps suggests that superimposed structures close to the cluster in redshift space contribute more significantly to the excess cross correlation signal than unrelated large-scale structure along the line of sight. Interestingly, the weak-lensing mass profiles are not well constrained for the clusters with the largest cross correlation signal excesses ($>$20% for A383, A689 and A750). The fractional excess in the cross correlation signal including foreground and background structures could be a useful proxy for assessing the reliability of weak-lensing cluster mass estimates.
Weak gravitational lensing is becoming a mature technique for constraining cosmological parameters, and future surveys will be able to constrain the dark energy equation of state $w$. When analyzing galaxy surveys, redshift information has proven to be a valuable addition to angular shear correlations. We forecast parameter constraints on the triplet $(Omega_m,w,sigma_8)$ for an LSST-like photometric galaxy survey, using tomography of the shear-shear power spectrum, convergence peak counts and higher convergence moments. We find that redshift tomography with the power spectrum reduces the area of the $1sigma$ confidence interval in $(Omega_m,w)$ space by a factor of 8 with respect to the case of the single highest redshift bin. We also find that adding non-Gaussian information from the peak counts and higher-order moments of the convergence field and its spatial derivatives further reduces the constrained area in $(Omega_m,w)$ by a factor of 3 and 4, respectively. When we add cosmic microwave background parameter priors from Planck to our analysis, tomography improves power spectrum constraints by a factor of 3. Adding moments yields an improvement by an additional factor of 2, and adding both moments and peaks improves by almost a factor of 3, over power spectrum tomography alone. We evaluate the effect of uncorrected systematic photometric redshift errors on the parameter constraints. We find that different statistics lead to different bias directions in parameter space, suggesting the possibility of eliminating this bias via self-calibration.
Correlations between the intrinsic shapes of galaxies and the large-scale galaxy density field provide an important tool to investigate galaxy intrinsic alignments, which constitute a major astrophysical systematic in cosmological weak lensing (cosmic shear) surveys, but also yield insight into the formation and evolution of galaxies. We measure galaxy position-shape correlations in the MegaZ-LRG sample for more than 800,000 luminous red galaxies, making the first such measurement with a photometric redshift sample. In combination with a re-analysis of several spectroscopic SDSS samples, we constrain an intrinsic alignment model for early-type galaxies over long baselines in redshift (z ~ 0.7) and luminosity (4mag). We develop and test the formalism to incorporate photometric redshift scatter in the modelling. For r_p > 6 Mpc/h, the fits to galaxy position-shape correlation functions are consistent with the scaling with r_p and redshift of a revised, nonlinear version of the linear alignment model for all samples. An extra redshift dependence proportional to (1+z)^n is constrained to n=-0.3+/-0.8 (1sigma). To obtain consistent amplitudes for all data, an additional dependence on galaxy luminosity proportional to L^b with b=1.1+0.3-0.2 is required. The normalisation of the intrinsic alignment power spectrum is found to be (0.077 +/- 0.008)/rho_{cr} for galaxies at redshift 0.3 and r band magnitude of -22 (k- and evolution-corrected to z=0). Assuming zero intrinsic alignments for blue galaxies, we assess the bias on cosmological parameters for a tomographic CFHTLS-like lensing survey. Both the resulting mean bias and its uncertainty are smaller than the 1sigma statistical errors when using the constraints from all samples combined. The addition of MegaZ-LRG data reduces the uncertainty in intrinsic alignment bias on cosmological parameters by factors of three to seven. (abridged)
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