Aims. Cosmic shear is a powerful method to constrain cosmology, provided that any systematic effects are under control. The intrinsic alignment of galaxies is expected to severely bias parameter ...estimates if not taken into account. We explore the potential of a joint analysis of tomographic galaxy ellipticity, galaxy number density, and ellipticity-number density cross-correlations to simultaneously constrain cosmology and self-calibrate unknown intrinsic alignment and galaxy bias contributions. Methods. We treat intrinsic alignments and galaxy biasing as free functions of scale and redshift and marginalise over the resulting parameter sets. Constraints on cosmology are calculated by combining the likelihoods from all two-point correlations between galaxy ellipticity and galaxy number density. The information required for these calculations is already available in a standard cosmic shear data set. We include contributions to these functions from cosmic shear, intrinsic alignments, galaxy clustering and magnification effects. Results. In a Fisher matrix analysis we compare our constraints with those from cosmic shear alone in the absence of intrinsic alignments. For a potential future large area survey, such as Euclid, the extra information from the additional correlation functions can make up for the additional free parameters in the intrinsic alignment and galaxy bias terms, depending on the flexibility in the models. For example, the dark energy task force figure of merit is recovered even when more than 100 free parameters are marginalised over. We find that the redshift quality requirements are similar to those calculated in the absence of intrinsic alignments.
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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 the major ...potential 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 for comoving transverse separations of 0.3 < rp < 60 h-1 Mpc, 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 (4 mag) with high statistical precision. We develop and test the formalism to incorporate photometric redshift scatter in the modelling of these observations. For rp > 6 h-1 Mpc, the fits to galaxy position-shape correlation functions are consistent with the scaling with rp and redshift of a revised, nonlinear version of the linear alignment model (Hirata & Seljak 2004) for all samples. An extra redshift dependence ∝ (1 + z)ηother is constrained to ηother = −0.3 ± 0.8 (1σ). To obtain consistent amplitudes for all data, an additional dependence on galaxy luminosity ∝ Lβ with $\beta=1.1^{+0.3}_{-0.2}$β=1.1-0.2+0.3 is required. The normalisation of the intrinsic alignment power spectrum is found to be $(0.077 \pm 0.008)\, \rho_{\rm cr}^{-1}$(0.077±0.008) ρcr-1 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 given our new constraints on the intrinsic alignment model parameter space. Both the resulting mean bias and its uncertainty are smaller than the 1σ statistical errors when using the constraints from all samples combined. The addition of MegaZ-LRG data is critical to achieving constraints this strong, reducing the uncertainty in intrinsic alignment bias on cosmological parameters by factors of three to seven.
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Gravitational lensing shear has the potential to be the most powerful tool for constraining the nature of dark energy. However, accurate measurement of galaxy shear is crucial and has been shown to ...be non-trivial by the Shear TEsting Programme. Here, we demonstrate a fundamental limit to the accuracy achievable by model-fitting techniques, if oversimplistic models are used. We show that even if galaxies have elliptical isophotes, model-fitting methods which assume elliptical isophotes can have significant biases if they use the wrong profile. We use noise-free simulations to show that on allowing sufficient flexibility in the profile the biases can be made negligible. This is no longer the case if elliptical isophote models are used to fit galaxies made up of a bulge plus a disc, if these two components have different ellipticities. The limiting accuracy is dependent on the galaxy shape, but we find the most significant biases (∼1 per cent of the shear) for simple spiral-like galaxies. The implications for a given cosmic shear survey will depend on the actual distribution of galaxy morphologies in the Universe, taking into account the survey selection function and the point spread function. However, our results suggest that the impact on cosmic shear results from current and near future surveys may be negligible. Meanwhile, these results should encourage the development of existing approaches which are less sensitive to morphology, as well as methods which use priors on galaxy shapes learnt from deep surveys.
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We present constraints on extensions of the minimal cosmological models dominated by dark matter and dark energy, ΛCDM and wCDM, by using a combined analysis of galaxy clustering and weak ...gravitational lensing from the first-year data of the Dark Energy Survey (DES Y1) in combination with external data. We consider four extensions of the minimal dark energy-dominated scenarios: (1) nonzero curvature Ωk, (2) number of relativistic species Neff different from the standard value of 3.046, (3) time-varying equation-of-state of dark energy described by the parameters w0 and wa (alternatively quoted by the values at the pivot redshift, wp, and wa), and (4) modified gravity described by the parameters μ0 and Σ0 that modify the metric potentials. We also consider external information from Planck cosmic microwave background measurements; baryon acoustic oscillation measurements from SDSS, 6dF, and BOSS; redshift-space distortion measurements from BOSS; and type Ia supernova information from the Pantheon compilation of datasets. Constraints on curvature and the number of relativistic species are dominated by the external data; when these are combined with DES Y1, we find Ωk=0.0020−0.0032+0.0037 at the 68% confidence level, and the upper limit Neff<3.28(3.55) at 68% (95%) confidence, assuming a hard prior Neff>3.0. For the time-varying equation-of-state, we find the pivot value (wp,wa)=(−0.91−0.23+0.19,−0.57−1.11+0.93) at pivot redshift zp=0.27 from DES alone, and (wp,wa)=(−1.01−0.04+0.04,−0.28−0.48+0.37) at zp=0.20 from DES Y1 combined with external data; in either case we find no evidence for the temporal variation of the equation of state. For modified gravity, we find the present-day value of the relevant parameters to be Σ0=0.43−0.29+0.28 from DES Y1 alone, and (Σ0,μ0)=(0.06−0.07+0.08,−0.11−0.46+0.42) from DES Y1 combined with external data. These modified-gravity constraints are consistent with predictions from general relativity.
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Context. The control of systematic effects when measuring background galaxy shapes is one of the main challenges for cosmic shear analyses. Aims. Study the fundamental limitations on shear accuracy ...due to the measurement of the point spread function (PSF) from the finite number of stars that are available. We translate the accuracy required for cosmological parameter estimation to the minimum number of stars over which the PSF must be calibrated. Methods. We characterise the error made in the shear arising from errors on the PSF. We consider different PSF models, from a simple elliptical Gaussian to various shapelet parametrisations. First we derive our results analytically in the case of infinitely small pixels (i.e. infinitely high resolution), then image simulations are used to validate these results and investigate the effect of finite pixel size in the case of the elliptical Gaussian PSF. Results. Our results are expressed in terms of the minimum number of stars required to calibrate the PSF in order to ensure that systematic errors are smaller than statistical errors when estimating the cosmological parameters. On scales smaller than the area containing this minimum number of stars, there is not enough information to model the PSF. This means that these small scales should not be used to constrain cosmology unless the instrument and the observing strategy are optimised to make this variability extremely small. The minimum number of stars varies with the square of the star Signal-to-Noise Ratio, with the complexity of the PSF and with the pixel size. In the case of an elliptical Gaussian PSF and in the absence of dithering, 2 pixels per PSF full width at half maximum (FWHM) implies a 20% increase of the minimum number of stars compared to the ideal case of infinitely small pixels; 0.9 pixels per PSF FWHM implies a factor 100 increase. Conclusions. In the case of a good resolution and a typical Signal-to-Noise Ratio distribution of stars, we find that current surveys need the PSF to be calibrated over a few stars, which may explain residual systematics on scales smaller than a few arcmins. Future all-sky cosmic shear surveys require the PSF to be calibrated over a region containing about 50 stars. Due to the simplicity of our models these results should be interpreted as optimistic and therefore provide a measure of a systematic “floor' intrinsic to shape measurements.
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We investigate potential gains in cosmological constraints from the combination of galaxy clustering and galaxy-galaxy lensing by optimizing the lens galaxy sample selection using information from ...Dark Energy Survey (DES) Year 3 data and assuming the DES Year 1 metacalibration sample for the sources. We explore easily reproducible selections based on magnitude cuts in i-band as a function of (photometric) redshift, zphot, and benchmark the potential gains against those using the well-established redMaGiC E. Rozo et al., Mon. Not. R. Astron. Soc. 461, 1431 (2016) sample. We focus on the balance between density and photometric redshift accuracy, while marginalizing over a realistic set of cosmological and systematic parameters. Our optimal selection, the MagLim sample, satisfies i < 4zphot + 18 and has ∼ 30% wider redshift distributions but ∼ 3.5 times more galaxies than redMaGiC. Assuming a w CDM model (i.e. with a free parameter for the dark energy equation of state) and equivalent scale cuts to mitigate nonlinear effects, this leads to 40% increase in the figure of merit for the pair combinations of Ωm, w, and σ8, and gains of 16% in σ8, 10% in Ωm, and 12% in w. Similarly, in Λ CDM, we find an improvement of 19% and 27% on σ8 and Ωm, respectively. We also explore flux-limited samples with a flat magnitude cut finding that the optimal selection, i < 22.2, has ∼ 7 times more galaxies and ∼ 20% wider redshift distributions compared to MagLim, but slightly worse constraints. We show that our results are robust with respect to the assumed galaxy bias and photometric redshift uncertainties with only moderate further gains from increased number of tomographic bins or the inclusion of bin cross-correlations, except in the case of the flux-limited sample, for which these gains are more significant.
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In this paper, we present results from the weak-lensing shape measurement GRavitational lEnsing Accuracy Testing 2010 (GREAT10) Galaxy Challenge. This marks an order of magnitude step change in the ...level of scrutiny employed in weak-lensing shape measurement analysis. We provide descriptions of each method tested and include 10 evaluation metrics over 24 simulation branches.
GREAT10 was the first shape measurement challenge to include variable fields; both the shear field and the point spread function (PSF) vary across the images in a realistic manner. The variable fields enable a variety of metrics that are inaccessible to constant shear simulations, including a direct measure of the impact of shape measurement inaccuracies, and the impact of PSF size and ellipticity, on the shear power spectrum. To assess the impact of shape measurement bias for cosmic shear, we present a general pseudo-C
ℓ formalism that propagates spatially varying systematics in cosmic shear through to power spectrum estimates. We also show how one-point estimators of bias can be extracted from variable shear simulations.
The GREAT10 Galaxy Challenge received 95 submissions and saw a factor of 3 improvement in the accuracy achieved by other shape measurement methods. The best methods achieve sub-per cent average biases. We find a strong dependence on accuracy as a function of signal-to-noise ratio, and indications of a weak dependence on galaxy type and size. Some requirements for the most ambitious cosmic shear experiments are met above a signal-to-noise ratio of 20. These results have the caveat that the simulated PSF was a ground-based PSF. Our results are a snapshot of the accuracy of current shape measurement methods and are a benchmark upon which improvement can be brought. This provides a foundation for a better understanding of the strengths and limitations of shape measurement methods.
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We present the first constraints on cosmology from the Dark Energy Survey (DES), using weak lensing measurements from the preliminary Science Verification (SV) data. We use 139 square degrees of SV ...data, which is less than 3% of the full DES survey area. Using cosmic shear 2-point measurements over three redshift bins we find sigma sub(8)(Omega sub(m)/0.3 ) super(0.5) = 0.81+ or -0.06 (68% confidence), after marginalizing over 7 systematics parameters and 3 other cosmological parameters. We examine the robustness of our results to the choice of data vector and systematics assumed, and find them to be stable. About 20% of our error bar comes from marginalizing over shear and photometric redshift calibration uncertainties. The current state-of-the-art cosmic shear measurements from CFHTLenS are mildly discrepant with the cosmological constraints from Planck CMB data; our results are consistent with both data sets. Our uncertainties are ~ 30% larger than those from CFHTLenS when we carry out a comparable analysis of the two data sets, which we attribute largely to the lower number density of our shear catalogue. We investigate constraints on dark energy and find that, with this small fraction of the full survey, the DES SV constraints make negligible impact on the Planck constraints. The moderate disagreement between the CFHTLenS and Planck values of sigma sub(8)(Omega sub(m)/0.3 ) super(0.5) is present regardless of the value of w.
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We present photometric redshift estimates for galaxies used in the weak lensing analysis of the Dark Energy Survey Science Verification (DES SV) data. Four model- or machine learning-based ...photometric redshift methods-annz2, bpz calibrated against BCC-Ufig simulations, skynet, and tpz-are analyzed. For training, calibration, and testing of these methods, we construct a catalogue of spectroscopically confirmed galaxies matched against DES SV data. The performance of the methods is evaluated against the matched spectroscopic catalogue, focusing on metrics relevant for weak lensing analyses, with additional validation against COSMOS photo-z's. From the galaxies in the DES SV shear catalogue, which have mean redshift 0.72 + or - 0.01 over the range 0.3 < z< 1.3, we construct three tomographic bins with means of z= {0.45,0.67,1.00}. These bins each have systematic uncertainties delta sub(z)<, ~ 0.05 in the mean of the fiducial skynet photo-z n(z). We propagate the errors in the redshift distributions through to their impact on cosmological parameters estimated with cosmic shear, and find that they cause shifts in the value of sigma sub(8) of approximately 3%. This shift is within the one sigma statistical errors on sigma sub(8) for the DES SV shear catalogue. We further study the potential impact of systematic differences on the critical surface density, capital sigma sub(crit), finding levels of bias safely less than the statistical power of DES SV data. We recommend a final Gaussian prior for the photo-z bias in the mean of n(z) of width 0.05 for each of the three tomographic bins, and show that this is a sufficient bias model for the corresponding cosmology analysis.
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Abstract
Weak gravitational lensing has the potential to constrain cosmological parameters to high precision. However, as shown by the Shear Testing Programmes and Gravitational lensing Accuracy ...Testing challenges, measuring galaxy shears is a non-trivial task: various methods introduce different systematic biases which have to be accounted for. We investigate how pixel noise on the image affects the bias on shear estimates from a maximum likelihood forward model-fitting approach using a sum of co-elliptical Sérsic profiles, in complement to the theoretical approach of an associated paper. We evaluate the bias using a simple but realistic galaxy model and find that the effects of noise alone can cause biases of the order of 1-10 per cent on measured shears, which is significant for current and future lensing surveys. We evaluate a simulation-based calibration method to create a bias model as a function of galaxy properties and observing conditions. This model is then used to correct the simulated measurements. We demonstrate that, for the simple case in which the correct range of galaxy models is used in the fit, the calibration method can reduce noise bias to the level required for estimating cosmic shear in upcoming lensing surveys.
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