Multi-CCD Point Spread Function Modelling

Context. Galaxy imaging surveys observe a vast number of objects that are affected by the instrument’s Point Spread Function (PSF). Weak lensing missions, in particular, aim at measuring the shape of galaxies, and PSF effects represent an important source of systematic errors which must be handled appropriately. This demands a high accuracy in the modelling as well as the estimation of the PSF at galaxy positions.

Aims. Sometimes referred to as non-parametric PSF estimation, the goal of this paper is to estimate a PSF at galaxy positions, starting from a set of noisy star image observations distributed over the focal plane. To accomplish this, we need our model to first of all, precisely capture the PSF field variations over the Field of View (FoV), and then to recover the PSF at the selected positions. Methods. This paper proposes a new method, coined MCCD (Multi-CCD PSF modelling), that creates, simultaneously, a PSF field model over all of the instrument’s focal plane. This allows to capture global as well as local PSF features through the use of two complementary models which enforce different spatial constraints. Most existing non-parametric models build one model per Charge-Coupled Device (CCD), which can lead to difficulties in capturing global ellipticity patterns.

Results. We first test our method on a realistic simulated dataset comparing it with two state-of-the-art PSF modelling methods (PSFEx and RCA). We outperform both of them with our proposed method. Then we contrast our approach with PSFEx on real data from CFIS (Canada-France Imaging Survey) that uses the CFHT (Canada-France-Hawaii Telescope). We show that our PSF model is less noisy and achieves a ~ 22% gain on pixel Root Mean Squared Error (RMSE) with respect to PSFEx.

Conclusions. We present, and share the code of, a new PSF modelling algorithm that models the PSF field on all the focal plane that is mature enough to handle real data.

Reference: Tobias Liaudat, Jérôme Bonnin,  Jean-Luc Starck, Morgan A. Schmitz, Axel Guinot, Martin Kilbinger and Stephen D. J. Gwyn. “Multi-CCD Point Spread Function Modelling, submitted 2020.

arXiv, code.

Euclid: The reduced shear approximation and magnification bias for Stage IV cosmic shear experiments

Euclid: The reduced shear approximation and magnification bias for Stage IV cosmic shear experiments

Authors: A.C. Deshpande, ..., S. Casas, M. Kilbinger, V. Pettorino, S. Pires, J.-L. Starck, F. Sureau, et al.
Journal: Astronomy and Astrophysics
Year: 2020
DOI:  10.1051/0004-6361/201937323
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ADS | arXiv

 


Abstract

Stage IV weak lensing experiments will offer more than an order of magnitude leap in precision. We must therefore ensure that our analyses remain accurate in this new era. Accordingly, previously ignored systematic effects must be addressed. In this work, we evaluate the impact of the reduced shear approximation and magnification bias, on the information obtained from the angular power spectrum. To first-order, the statistics of reduced shear, a combination of shear and convergence, are taken to be equal to those of shear. However, this approximation can induce a bias in the cosmological parameters that can no longer be neglected. A separate bias arises from the statistics of shear being altered by the preferential selection of galaxies and the dilution of their surface densities, in high-magnification regions. The corrections for these systematic effects take similar forms, allowing them to be treated together. We calculated the impact of neglecting these effects on the cosmological parameters that would be determined from Euclid, using cosmic shear tomography. To do so, we employed the Fisher matrix formalism, and included the impact of the super-sample covariance. We also demonstrate how the reduced shear correction can be calculated using a lognormal field forward modelling approach. These effects cause significant biases in Omega_m, sigma_8, n_s, Omega_DE, w_0, and w_a of -0.53 sigma, 0.43 sigma, -0.34 sigma, 1.36 sigma, -0.68 sigma, and 1.21 sigma, respectively. We then show that these lensing biases interact with another systematic: the intrinsic alignment of galaxies. Accordingly, we develop the formalism for an intrinsic alignment-enhanced lensing bias correction. Applying this to Euclid, we find that the additional terms introduced by this correction are sub-dominant.

Euclid preparation: VI. Verifying the Performance of Cosmic Shear Experiments

Euclid preparation: VI. Verifying the Performance of Cosmic Shear Experiments

Authors: Euclid Collaboration, P. Paykari, ..., S. Farrens, M. Kilbinger, V. Pettorino, S. Pires, J.-L. Starck, F. Sureau, et al.
Journal: Astronomy and Astrophysics
Year: 2020
DOI:  10.1051/0004-6361/201936980
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Abstract

Our aim is to quantify the impact of systematic effects on the inference of cosmological parameters from cosmic shear. We present an end-to-end approach that introduces sources of bias in a modelled weak lensing survey on a galaxy-by-galaxy level. Residual biases are propagated through a pipeline from galaxy properties (one end) through to cosmic shear power spectra and cosmological parameter estimates (the other end), to quantify how imperfect knowledge of the pipeline changes the maximum likelihood values of dark energy parameters. We quantify the impact of an imperfect correction for charge transfer inefficiency (CTI) and modelling uncertainties of the point spread function (PSF) for Euclid, and find that the biases introduced can be corrected to acceptable levels.

Euclid preparation. V. Predicted yield of redshift 7 < z < 9 quasars from the wide survey

Euclid preparation: V. Predicted yield of redshift 7

Authors: Euclid Collaboration, R. Barnett, ..., S. Farrens, M. Kilbinger, V. Pettorino, F. Sureau, et al.
Journal: Astronomy and Astrophysics
Year: 2019
DOI:  10.1051/0004-6361/201936427
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Abstract

We provide predictions of the yield of 7<z<9 quasars from the Euclid wide survey, updating the calculation presented in the Euclid Red Book in several ways. We account for revisions to the Euclid near-infrared filter wavelengths; we adopt steeper rates of decline of the quasar luminosity function (QLF; Φ) with redshift, Φ∝10k(z−6), k=−0.72, and a further steeper rate of decline, k=−0.92; we use better models of the contaminating populations (MLT dwarfs and compact early-type galaxies); and we use an improved Bayesian selection method, compared to the colour cuts used for the Red Book calculation, allowing the identification of fainter quasars, down to JAB∼23. Quasars at z>8 may be selected from Euclid OYJH photometry alone, but selection over the redshift interval 7<z<8 is greatly improved by the addition of z-band data from, e.g., Pan-STARRS and LSST. We calculate predicted quasar yields for the assumed values of the rate of decline of the QLF beyond z=6. For the case that the decline of the QLF accelerates beyond z=6, with k=−0.92, Euclid should nevertheless find over 100 quasars with 7.0<z<7.5, and ∼25 quasars beyond the current record of z=7.5, including ∼8 beyond z=8.0. The first Euclid quasars at z>7.5 should be found in the DR1 data release, expected in 2024. It will be possible to determine the bright-end slope of the QLF, 7<z<8, M1450<−25, using 8m class telescopes to confirm candidates, but follow-up with JWST or E-ELT will be required to measure the faint-end slope. Contamination of the candidate lists is predicted to be modest even at JAB∼23. The precision with which k can be determined over 7<z<8 depends on the value of k, but assuming k=−0.72 it can be measured to a 1 sigma uncertainty of 0.07.

Cosmological parameters from weak cosmological lensing

 

Authors: M. Kilbinger
Journal:  
Year: 07/2018
Download: ADS| Arxiv


Abstract

In this manuscript of the habilitation à diriger des recherches (HDR), the author presents some of his work over the last ten years. The main topic of this thesis is cosmic shear, the distortion of images of distant galaxies due to weak gravitational lensing by the large-scale structure in the Universe. Cosmic shear has become a powerful probe into the nature of dark matter and the origin of the current accelerated expansion of the Universe. Over the last years, cosmic shear has evolved into a reliable and robust cosmological probe, providing measurements of the expansion history of the Universe and the growth of its structure.
I review the principles of weak gravitational lensing and show how cosmic shear is interpreted in a cosmological context. Then I give an overview of weak-lensing measurements, and present observational results from the Canada-France Hawai'i Lensing Survey (CFHTLenS), as well as the implications for cosmology. I conclude with an outlook on the various future surveys and missions, for which cosmic shear is one of the main science drivers, and discuss promising new weak cosmological lensing techniques for future observations.

 

A highly precise shape-noise-free shear bias estimator

 

Authors: A. Pujol, M. Kilbinger, F. Sureau & J. Bobin
Journal:  
Year: 06/2018
Download: ADS| Arxiv


Abstract

We present a new method to estimate shear measurement bias in image simulations that significantly improves its precision with respect to the state-of-the-art methods. This method is based on measuring the shear response for individual images. We generate sheared versions of the same image to measure how the shape measurement changes with the changes in the shear, so that we obtain a shear response for each original image, as well as its additive bias. Using the exact same noise realizations for each sheared version allows us to obtain an exact estimation of its shear response. The estimated shear bias of a sample of galaxies comes from the measured averages of the shear response and individual additive bias. The precision of this method supposes an improvement with respect to previous methods since our method is not affected by shape noise. As a consequence, the method does not require shape noise cancellation for a precise estimation of shear bias. The method can be easily applied to many applications such as shear measurement validation and calibration, reducing the number of necessary simulated images by a few orders of magnitude to achieve the same precision requirements.

Shear measurement bias: dependencies on methods, simulation parameters and measured parameters

 

Authors: A. Pujol, F. Sureau, J. Bobin et al.
Journal: A&A
Year: 06/2017
Download: ADS| Arxiv


Abstract

We present a study of the dependencies of shear and ellipticity bias on simulation (input) and measured (output) parameters, noise, PSF anisotropy, pixel size and the model bias coming from two different and independent shape estimators. We use simulated images from Galsim based on the GREAT3 control-space-constant branch and we measure ellipticity and shear bias from a model-fitting method (gFIT) and a moment-based method (KSB). We show the bias dependencies found on input and output parameters for both methods and we identify the main dependencies and causes. We find consistent results between the two methods (given the precision of the analysis) and important dependencies on orientation and morphology properties such as flux, size and ellipticity. We show cases where shear bias and ellipticity bias behave very different for the two methods due to the different nature of these measurements. We also show that noise and pixelization play an important role on the bias dependences on the output properties. We find a large model bias for galaxies consisting of a bulge and a disk with different ellipticities or orientations. We also see an important coupling between several properties on the bias dependences. Because of this we need to study several properties simultaneously in order to properly understand the nature of shear bias.

Quantifying systematics from the shear inversion on weak-lensing peak counts

Authors: C. Lin, M. Kilbinger
Journal: Submitted to A&A letters
Year: 2017
Download: ADS | arXiv

 


Abstract

Weak-lensing (WL) peak counts provide a straightforward way to constrain cosmology, and results have been shown promising. However, the importance of understanding and dealing with systematics increases as data quality reaches an unprecedented level. One of the sources of systematics is the convergence-shear inversion. This effect, inevitable from observations, is usually neglected by theoretical peak models. Thus, it could have an impact on cosmological results. In this letter, we study the bias from neglecting the inversion and find it small but not negligible. The cosmological dependence of this bias is difficult to model and depends on the filter size. We also show the evolution of parameter constraints. Although weak biases arise in individual peak bins, the bias can reach 2-sigma for the dark energy equation of state w0. Therefore, we suggest that the inversion cannot be ignored and that inversion-free approaches, such as aperture mass, would be a more suitable tool to study weak-lensing peak counts.

Precision calculations of the cosmic shear power spectrum projection

Authors: M. Kilbinger, C. Heymans, M. Asgari et al.
Journal: MNRAS
Year: 2017
Download: ADS | arXiv


Abstract

We compute the spherical-sky weak-lensing power spectrum of the shear and convergence. We discuss various approximations, such as flat-sky, and first- and second- order Limber equations for the projection. We find that the impact of adopting these approximations are negligible when constraining cosmological parameters from current weak lensing surveys. This is demonstrated using data from the Canada-France-Hawaii Lensing Survey (CFHTLenS). We find that the reported tension with Planck Cosmic Microwave Background (CMB) temperature anisotropy results cannot be alleviated, in contrast to the recent claim made by Kitching et al. (2016, version 1). For future large-scale surveys with unprecedented precision, we show that the spherical second-order Limber approximation will provide sufficient accuracy. In this case, the cosmic-shear power spectrum is shown to be in agreement with the full projection at the sub-percent level for l > 3, with the corresponding errors an order of magnitude below cosmic variance for all l. When computing the two-point shear correlation function, we show that the flat-sky fast Hankel transformation results in errors below two percent compared to the full spherical transformation. In the spirit of reproducible research, our numerical implementation of all approximations and the full projection are publicly available within the package nicaea at http://www.cosmostat.org/software/nicaea.


Summary

We discuss various methods to calculate projections for weak gravitational lensing: Since lenses galaxies pick up matter inhomogeneities of the cosmic web along the line of sight while photons from the galaxies propagate through the Universe to the observer, these inhomogeneities have to be projected to a 2D observable, the cumulative shear or convergence. The full projection involves three-dimensional integrals over highly oscillating Bessel functions, and can be time-consuming to compute numerically to high accuracy. Most previous work have therefore used approximations such as the Limber approximation, that reduce the integrals to 1D, and thereby neglecting modes along the line of sight.

The authors show that these projections are more than adequate for present surveys. Sub-percent accuracy is reached for l>20, for example as shown by the pink curve, which is the ratio of the case 'ExtL1Hyb' to the full projection. The abbreviation means 'extended', corresponding to the improved approximation introduced by LoVerde & Afshordi (2008), first-order Limber, and hybrid, since this is a hybrid between flat-sky and spherical coordinates. This case has been used in most of the recent publications (e.g. for KiDS), whereas the cast 'L1Fl' (first-order Limber flat-sky) was popular for most publications since 2014.

These approximations are sufficient for the small areas of current observations coming from CFHTLenS, KiDS, and DES, and well below cosmic variance of even future surveys (the figure shows Euclid - 15,000 deg2 and Kids -1,500 deg2).

K17_Fig1b

The paper then discusses the second-order Limber approximation, introduced in a general framework by LoVerde & Afshordi (2008), and applied to weak lensing in the current paper. The best 2nd-order case 'ExtL2Sph' reaches sub-percent accuracy down to l=3, sufficient for all future surveys.

The paper also computes the shear correlation function in real space, and shows that those approximations have a very minor influence.

We then go on to re-compute the cosmological constraints obtained in Kilbinger et al. (2013), and find virtually no change when choosing different approximations. Only the depreciated case 'ExtL1Fl' makes a noticeable difference, which is however still well within the statistical error bars. This case shows a particular slow convergence to the full projection.

Similar results have been derived in two other recent publications, Kitching et al. (2017), and Lemos, Challinor & Efstathiou (2017).
Note however that Kitching et al. (2017) conclude that errors from projection approximations of the types we discussed here (Limber, flat sky) could make up to 11% of the error budget of future surveys. This is however assuming the worst-case scenario including the deprecated cast 'ExtL1Fl', and we do not share their conclusion, but think that for example the projection 'ExtL2Sph' is sufficient for future surveys such as LSST and Euclid.

Cosmological constraints with weak-lensing peak counts and second-order statistics in a large-field survey

Cosmological constraints with weak-lensing peak counts and second-order statistics in a large-field survey

 

Authors: A. Peel, C.-A. Lin, F. Lanusse, A. Leonard, J.-L. Starck, M. Kilbinger
Journal: A&A
Year: 2017
Download: ADS | arXiv

 


Abstract

Peak statistics in weak-lensing maps access the non-Gaussian information contained in the large-scale distribution of matter in the Universe. They are therefore a promising complementary probe to two-point and higher-order statistics to constrain our cosmological models. Next-generation galaxy surveys, with their advanced optics and large areas, will measure the cosmic weak-lensing signal with unprecedented precision. To prepare for these anticipated data sets, we assess the constraining power of peak counts in a simulated Euclid-like survey on the cosmological parameters Ωm, σ8, and w0. In particular, we study how the Camelus model--a fast stochastic algorithm for predicting peaks--can be applied to such large surveys. We measure the peak count abundance in a mock shear catalogue of ~5,000 sq. deg. using a multiscale mass map filtering technique. We then constrain the parameters of the mock survey using Camelus combined with approximate Bayesian computation (ABC). We find that peak statistics yield a tight but significantly biased constraint in the σ8-Ωm plane, indicating the need to better understand and control the model's systematics. We calibrate the model to remove the bias and compare results to those from the two-point correlation functions (2PCF) measured on the same field. In this case, we find the derived parameter Σ8=σ8(Ωm/0.27)^α=0.76−0.03+0.02 with α=0.65 for peaks, while for 2PCF the value is Σ8=0.76−0.01+0.02 with α=0.70. We therefore see comparable constraining power between the two probes, and the offset of their σ8-Ωm degeneracy directions suggests that a combined analysis would yield tighter constraints than either measure alone. As expected, w0 cannot be well constrained without a tomographic analysis, but its degeneracy directions with the other two varied parameters are still clear for both peaks and 2PCF.