Joel Bergé

The Shear Testing Programme ¿ I. Weak lensing analysis of simulated ground-based observations

The Shear Testing Programme (STEP) is a collaborative project to improve the accuracy and reliability of all weak lensing measurements in preparation for the next generation of wide-field surveys. In this first STEP paper, we present the results of a blind analysis of simulated ground-based observations of relatively simple galaxy morphologies. The most successful methods are shown to achieve percent level accuracy. From the cosmic shear pipelines that have been used to constrain cosmology, we find weak lensing shear measured to an accuracy that is within the statistical errors of current weak lensing analyses, with shear measurements accurate to better than 7 per cent. The dominant source of measurement error is shown to arise from calibration uncertainties where the measured shear is over or underestimated by a constant multiplicative factor. This is of concern as calibration errors cannot be detected through standard diagnostic tests. The measured calibration errors appear to result from stellar contamination, false object detection, the shear measurement method itself, selection bias and/or the use of biased weights. Additive systematics (false detections of shear) resulting from residual point-spread function anisotropy are, in most cases, reduced to below an equivalent shear of 0.001, an order of magnitude below cosmic shear distortions on the scales probed by current surveys. Our results provide a snapshot view of the accuracy of current ground-based weak lensing methods and a benchmark upon which we can improve. To this end we provide descriptions of each method tested and include details of the eight different implementations of the commonly used Kaiser, Squires & Broadhurst method (KSB+) to aid the improvement of future KSB+ analyses.

The shear testing programme 2 : factors affecting high-precision weak-lensing analyses.

The Shear Testing Programme (STEP) is a collaborative project to improve the accuracy and reliability of weak-lensing measurement, in preparation for the next generation of wide-field surveys. We review 16 current and emerging shear-measurement methods in a common language, and assess their performance by running them (blindly) on simulated images that contain a known shear signal. We determine the common features of algorithms that most successfully recover the input parameters. A desirable goal would be the combination of their best elements into one ultimate shear-measurement method. In this analysis, we achieve previously unattained discriminatory precision via a combination of more extensive simulations and pairs of galaxy images that have been rotated with respect to each other. That removes the otherwise overwhelming noise from their intrinsic ellipticities. Finally, the robustness of our simulation approach is confirmed by testing the relative calibration of methods on real data. Weak-lensing measurements have improved since the first STEP paper. Several methods now consistently achieve better than 2 per cent precision, and are still being developed. However, we can now distinguish all methods from perfect performance. Our main concern continues to be the potential for a multiplicative shear calibration bias: not least because this cannot be internally calibrated with real data. We determine which galaxy populations are responsible for bias and, by adjusting the simulated observing conditions, we also investigate the effects of instrumental and atmospheric parameters. The simulated point spread functions are not allowed to vary spatially, to avoid additional confusion from interpolation errors. We have isolated several previously unrecognized aspects of galaxy shape measurement, in which focused development could provide further progress towards the sub-per cent level of precision desired for future surveys. These areas include the suitable treatment of image pixellization and galaxy morphology evolution. Ignoring the former effect affects the measurement of shear in different directions, leading to an overall underestimation of shear and hence the amplitude of the matter power spectrum. Ignoring the second effect could affect the calibration of shear estimators as a function of galaxy redshift, and the evolution of the lensing signal, which will be vital to measure parameters including the dark energy equation of state.

Handbook for the GREAT08 Challenge: An image analysis competition for cosmological lensing

The GRavitational lEnsing Accuracy Testing 2008 (GREAT08) Challenge focuses on a problem that is of crucial importance for future observations in cosmology. The shapes of distant galaxies can be used to determine the properties of dark energy and the nature of gravity, because light from those galaxies is bent by gravity from the intervening dark matter. The observed galaxy images appear distorted, although only slightly, and their shapes must be precisely disentangled from the effects of pixelisation, convolution and noise. The worldwide gravitational lensing community has made significant progress in techniques to measure these distortions via the Shear TEsting Program (STEP). Via STEP, we have run challenges within our own community, and come to recognise that this particular image analysis problem is ideally matched to experts in statistical inference, inverse problems and computational learning. Thus, in order to continue the progress seen in recent years, we are seeking an infusion of new ideas from these communities. This document details the GREAT08 Challenge for potential participants. Please visit www.great08challenge.info for the latest information.

Dark energy and the evolution of spherical overdensities

We use the non-linear spherical model in cold dark matter (CDM) cosmologies with dark energy to investigate the effects of dark energy on the growth of structure and the formation of virialized structures. We consider dark energy models with a constant equation-of-state parameter w. For −1 <w< −1/3, clusters form earlier and are more concentrated in quintessence than inCDM models, but they form later and are less concentrated than in the corresponding open model with the same matter density and no dark energy. We point out some confusion in the literature around the expression of the collapse factor (ratio of the radius of the sphere at virialization to that at turnaround) derived from the virial theorem. We use the Sheth & Tormen extension of the Press-Schechter framework to calculate the evolution of the cluster abundance in different models and show the sensitivity of the cluster abundance to both the amplitude of the mass fluctuations, σ 8, and the σ 8-w normalization, selected to match either the cosmic microwave background observations or the abundance of X-ray clusters. Ke yw ords: galaxies: clusters: general - galaxies: formation - cosmology: theory - large-scale structure of Universe.

COSMOS: Stochastic Bias from Measurements of Weak Lensing and Galaxy Clustering

In the theory of structure formation, galaxies are biased tracers of the underlying matter density field. The statistical relation between galaxy and matter density field is commonly referred to as galaxy bias. In this paper, we test the linear bias model with weak-lensing and galaxy clustering measurements in the 2 deg^2 COSMOS field. We estimate the bias of galaxies between redshifts z = 0.2 and z = 1 and over correlation scales between R = 0.2 h^(–1) Mpc and R = 15 h^(–1) Mpc. We focus on three galaxy samples, selected in flux (simultaneous cuts I_(814W) 2 h^(–1) Mpc, our measurements support a model of bias increasing with redshift. The Tinker et al. fitting function provides a good fit to the data. We find the best-fit mass of the galaxy halos to be log (M_(200)/h^(–1) M_☉) = 11.7^(+0.6)_(–1.3) and log (M_(200)/h^(–1) M_☉) = 12.4^(+0.2)_(–2.9), respectively, for the low and high stellar-mass samples. In the halo model framework, bias is scale dependent with a change of slope at the transition scale between the one and the two halo terms. We detect a scale dependence of bias with a turndown at scale R = 2.3 ± 1.5 h^(–1) Mpc, in agreement with previous galaxy clustering studies. We find no significant amount of stochasticity, suggesting that a linear bias model is sufficient to describe our data. We use N-body simulations to quantify both the amount of cosmic variance and systematic errors in the measurement.

Weak gravitational shear and flexion with polar shapelets

We derive expressions, in terms of ‘polar shapelets’, for the image distortion operations associated with weak gravitational lensing. Shear causes galaxy shapes to become elongated, and is sensitive to the second derivative of the projected gravitational potential along their line of sight; flexion bends galaxy shapes into arcs, and is sensitive to the third derivative. Polar shapelets provide a natural representation, in which both shear and flexion transformations are compact. Through this tool, we understand progress in several weak lensing methods. We then exploit various symmetries of shapelets to construct a range of shear estimators with useful properties. Through an analogous investigation, we also explore several flexion estimators. In particular, some of the estimators can be measured simultaneously and independently for every galaxy, and will provide unique checks for systematics in future weak lensing analyses. Using simulated images from the Shear TEsting Programme, we show that we can recover input shears with no significant bias. A complete software package to parametrize astronomical images in terms of polar shapelets, and to perform a full weak lensing analysis, is available on the Internet.

Combined analysis of weak lensing and X-ray blind surveys★

We present a joint weak lensing and X-ray analysis of 4 deg^2 from the CFHTLS and XMMLSS surveys. Our weak lensing analysis is the first analysis of a real survey using shapelets, a new generation weak lensing analysis method. We create projected mass maps of the images, and extract six weak-lensing-detected clusters of galaxies. We show that their counts can be used to constrain the power-spectrum normalization σ8 = 0.92^(+0.26)_(−0.30) for Ωm = 0.24. We show that despite the large scatter generally observed in the mass–temperature (M–T) relation derived from lensing masses, tight constraints on both its slope and normalization M∗ can be obtained with a moderate number of sources provided that the covered mass range is large enough. Adding clusters given by Bardeau et al. to our sample, we measure M∗ =2.71^(+0.79)_(−0.61) × 10^(14) h^(−1) Mסּ. Although they are dominated by shot noise and sample variance, our measurements are consistent with currently favoured values, and set the stage for future surveys. We thus investigate the dependence of those estimates on survey size, depth and integration time, for joint weak lensing and X-ray surveys. We show that deep surveys should be dedicated to the study of the physics of clusters and groups of galaxies. For a given exposure time, wide surveys provide a larger number of detected clusters and are therefore preferred for the measurement of cosmological parameters, such as σ8 and M∗.We show that a wide survey of a few hundred square degrees is needed to improve upon current measurements of these parameters. More ambitious surveys covering 7000 deg^2 will provide the 1 per cent accuracy in the estimation of the power-spectrum and the M–T relation normalizations.

MICROSCOPE Mission: First Results of a Space Test of the Equivalence Principle

According to the weak equivalence principle, all bodies should fall at the same rate in a gravitational field. The MICROSCOPE satellite, launched in April 2016, aims to test its validity at the 10^{-15} precision level, by measuring the force required to maintain two test masses (of titanium and platinum alloys) exactly in the same orbit. A nonvanishing result would correspond to a violation of the equivalence principle, or to the discovery of a new long-range force. Analysis of the first data gives δ(Ti,Pt)=[-1±9(stat)±9(syst)]×10^{-15} (1σ statistical uncertainty) for the titanium-platinum Eötvös parameter characterizing the relative difference in their free-fall accelerations.

CALIBRATED ULTRA FAST IMAGE SIMULATIONS FOR THE DARK ENERGY SURVEY

Weak lensing by large-scale structure is a powerful technique to probe the dark components of the universe. To understand the measurement process of weak lensing and the associated systematic effects, image simulations are becoming increasingly important. For this purpose we present a first implementation of the

Status of MICROSCOPE, a mission to test the Equivalence Principle in space

\textit{Monte Carlo Control Loops}