Weak lensing by large-scale mass inhomogeneities in the Universe induces correlations in the observed ellipticities of distant sources. We first review the harmonic analysis and statistics required ...of these correlations and discuss calculations for the predicted signal. We consider the ellipticity correlation function, the mean-square ellipticity, the ellipticity power spectrum and a global maximum-likelihood analysis to isolate a weak-lensing signal from the data. Estimates for the sensitivity of a survey of a given area, surface density, and mean intrinsic source ellipticity are presented. We then apply our results to the FIRST radio-source survey. We predict an rms ellipticity of roughly 0.011 in 1 × 1 deg2 pixels and 0.018 in 20 × 20 arcmin2 pixels if the power spectrum is normalized to σ8Ω0.53 = 0.6, as indicated by the cluster abundance. The signal is significantly larger in some models if the power spectrum is normalized instead to the COBE anisotropy. The uncertainty in the predictions from imprecise knowledge of the FIRST redshift distribution is about 25 per cent in the rms ellipticity. We show that FIRST should be able to make a statistically significant detection of a weak-lensing signal for cluster-abundance-normalized power spectra.
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ABSTRACT
The next generation of weak lensing surveys will measure the matter distribution of the local universe with unprecedented precision, allowing the resolution of non-Gaussian features of the ...convergence field. This encourages the use of higher-order mass-map statistics for cosmological parameter inference. We extend the forward-modelling based methodology introduced in a previous forecast paper to match these new requirements. We provide multiple forecasts for the $w$CDM parameter constraints that can be expected from stage 3 and 4 weak lensing surveys. We consider different survey setups, summary statistics and mass map filters including wavelets. We take into account the shear bias, photometric redshift uncertainties, and intrinsic alignment. The impact of baryons is investigated and the necessary scale cuts are applied. We compare the angular power spectrum analysis to peak and minima counts as well as Minkowski functionals of the mass maps. We find a preference for Starlet over Gaussian filters. Our results suggest that using a survey setup with 10 instead of 5 tomographic redshift bins is beneficial. Adding cross-tomographic information improves the constraints on cosmology and especially on galaxy intrinsic alignment for all statistics. In terms of constraining power, we find the angular power spectrum and the peak counts to be equally matched for stage 4 surveys, followed by minima counts and the Minkowski functionals. Combining different summary statistics significantly improves the constraints and compensates the stringent scale cuts. We identify the most ‘cost-effective’ combination to be the angular power spectrum, peak counts and Minkowski functionals following Starlet filtering.
Information gains from cosmological probes Grandis, S.; Seehars, S.; Refregier, A. ...
Journal of Cosmology and Astroparticle Physics,
05/2016, Volume:
2016, Issue:
5
Journal Article
Peer reviewed
Open access
In light of the growing number of cosmological observations, it is important to develop versatile tools to quantify the constraining power and consistency of cosmological probes. Originally motivated ...from information theory, we use the relative entropy to compute the information gained by Bayesian updates in units of bits. This measure quantifies both the improvement in precision and the 'surprise', i.e. the tension arising from shifts in central values. Our starting point is a WMAP9 prior which we update with observations of the distance ladder, supernovae (SNe), baryon acoustic oscillations (BAO), and weak lensing as well as the 2015 Planck release. We consider the parameters of the flat ΛCDM concordance model and some of its extensions which include curvature and Dark Energy equation of state parameter w . We find that, relative to WMAP9 and within these model spaces, the probes that have provided the greatest gains are Planck (10 bits), followed by BAO surveys (5.1 bits) and SNe experiments (3.1 bits). The other cosmological probes, including weak lensing (1.7 bits) and (H{sub 0}) measures (1.7 bits), have contributed information but at a lower level. Furthermore, we do not find any significant surprise when updating the constraints of WMAP9 with any of the other experiments, meaning that they are consistent with WMAP9. However, when we choose Planck15 as the prior, we find that, accounting for the full multi-dimensionality of the parameter space, the weak lensing measurements of CFHTLenS produce a large surprise of 4.4 bits which is statistically significant at the 8 σ level. We discuss how the relative entropy provides a versatile and robust framework to compare cosmological probes in the context of current and future surveys.
The cosmological potential of large-scale structure observations for cosmology have been extensively discussed in the litterature. In particular, it has recently been shown how Sunyaev-Zel'dovich ...(SZ) cluster surveys can be used to constrain dark energy parameters. In this paper, we study whether selection and systematics effects will limit future wide-field SZ surveys from achieving their cosmological potential. For this purpose, we use a sky simulation and an SZ-cluster detection software presented in Pires et al. (2006, A&A, 455, 741), using the future Olimpo survey as a concrete example. We show that the SZ-cluster selection function and contamination of SZ-cluster catalogues are more complex than is usually assumed. In particular, the simulated field-to-field detected cluster counts variance can be a factor 3 larger than the expected Poisson fluctuations. We also study the impact of missing redshift information and of the uncertainty of the scaling relations for low mass clusters. We quantify, through hypothesis tests, how near-future SZ experiments can be used to discriminate between different structure formation models. Using a maximum likelihood approach, we then study the impact of these systematics on the joint measurement of cosmological models and of cluster scaling relations.
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Polar shapelets Massey, Richard; Refregier, Alexandre
Monthly Notices of the Royal Astronomical Society,
10/2005, Volume:
363, Issue:
1
Journal Article
Peer reviewed
Open access
The shapelets method for image analysis is based upon the decomposition of localized objects into a series of orthogonal components with convenient mathematical properties. We extend the ‘Cartesian ...shapelet’ formalism from earlier work, and construct ‘polar shapelet’ basis functions that separate an image into components with explicit rotational symmetries. These frequently provide a more compact parametrization, and can be interpreted in an intuitive way. Image manipulation in shapelet space is simplified by the concise expressions for linear coordinate transformations, and shape measures (including object photometry, astrometry and galaxy morphology estimators) take a naturally elegant form. Particular attention is paid to the analysis of astronomical survey images, and we test shapelet techniques upon real data from the Hubble Space Telescope. We present a practical method to automatically optimize the quality of an arbitrary shapelet decomposition in the presence of observational noise, pixelization and a point spread function. A central component of this procedure is the adaptive choice of the scale size and the truncation order of the shapelet expansion. A complete software package to perform shapelet image analysis is made available on the World Wide Web.
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Numerical simulations of weak lensing measurements Bacon, David J.; Refregier, Alexandre; Clowe, Douglas ...
Monthly notices of the Royal Astronomical Society,
08/2001, Volume:
325, Issue:
3
Journal Article
Peer reviewed
Open access
Weak gravitational lensing induces distortions on the images of background galaxies, and thus provides a direct measure of mass fluctuations in the Universe. The distortion signature from large-scale ...structure has recently been detected by several groups for the first time, opening promising prospects for the near future. Since the distortions induced by lensing on the images of background galaxies are only of the order of a few per cent, a reliable measurement demands very accurate galaxy shape estimation and a careful treatment of systematic effects. Here, we present a study of a shear measurement method using detailed simulations of artificial images. The images are produced using realizations of a galaxy ensemble drawn from the Hubble Space Telescope Groth strip. We consider realistic observational effects including atmospheric seeing, point spread function (PSF) anisotropy and pixelization, incorporated in such a manner as to reproduce actual observations with the William Herschel Telescope. By applying an artificial shear to the simulated images, we test the shear measurement method proposed by Kaiser, Squires & Broadhurst (KSB). Overall, we find the KSB method to be reliable with the following provisos. First, although the recovered shear is linearly related to the input shear, we find a coefficient of proportionality of about 0.8. In addition, we find a residual anti-correlation between the PSF ellipticity and the corrected ellipticities of faint galaxies. To guide future weak lensing surveys, we study the ways in which seeing size, exposure time and pixelization affect the sensitivity to shear. We find that worsened seeing linearly increases the noise in the shear estimate, while the sensitivity depends only weakly on exposure time. The noise is dramatically increased if the pixel scale is larger than that of the seeing. In addition, we study the impact both of overlapping isophotes between neighbouring galaxies, and of PSF correction residuals: together these are found to produce spurious lensing signals on small scales. We discuss the prospects of using the KSB method for future, more sensitive, surveys. Numerical simulations of this kind are a required component of present and future analyses of weak lensing surveys.
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Context. High-precision cosmology requires the analysis of large-scale surveys in 3D spherical coordinates, i.e. spherical Fourier-Bessel decomposition. Current methods are insufficient for future ...data-sets from wide-field cosmology surveys. Aims. The aim of this paper is to present a public code for fast spherical Fourier-Bessel decomposition that can be applied to cosmological data or 3D data in spherical coordinates in other scientific fields. Methods. We present an equivalent formulation of the spherical Fourier-Bessel decomposition that separates radial and tangential calculations. We propose to use the existing pixelisation scheme HEALPix for a rapid calculation of the tangential modes. Results. 3DEX (3D EXpansions) is a public code for fast spherical Fourier-Bessel decomposition of 3D all-sky surveys that takes advantage of HEALPix for the calculation of tangential modes. We perform tests on very large simulations and we compare the precision and computation time of our method with an optimised implementation of the spherical Fourier-Bessel original formulation. For surveys with millions of galaxies, computation time is reduced by a factor 4–12 depending on the desired scales and accuracy. The formulation is also suitable for pre-calculations and external storage of the spherical harmonics, which allows for additional speed improvements. The 3DEX code can accommodate data with masked regions of missing data. 3DEX can also be used in other disciplines, where 3D data are to be analysed in spherical coordinates.
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The nature of dark matter, dark energy and large-scale gravity pose some of the most pressing questions in cosmology today. These fundamental questions require highly precise measurements, and a ...number of wide-field spectroscopic survey instruments are being designed to meet this requirement. A key component in these experiments is the development of a simulation tool to forecast science performance, define requirement flow-downs, optimize implementation, demonstrate feasibility, and prepare for exploitation. We present SPOKES (SPectrOscopic KEn Simulation), an end-to-end simulation facility for spectroscopic cosmological surveys designed to address this challenge. SPOKES is based on an integrated infrastructure, modular function organization, coherent data handling and fast data access. These key features allow reproducibility of pipeline runs, enable ease of use and provide flexibility to update functions within the pipeline. The cyclic nature of the pipeline offers the possibility to make the science output an efficient measure for design optimization and feasibility testing. We present the architecture, first science, and computational performance results of the simulation pipeline. The framework is general, but for the benchmark tests, we use the Dark Energy Spectrometer (DESpec), one of the early concepts for the upcoming project, the Dark Energy Spectroscopic Instrument (DESI). We discuss how the SPOKES framework enables a rigorous process to optimize and exploit spectroscopic survey experiments in order to derive high-precision cosmological measurements optimally.
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The upcoming XMM Large Scale Structure Survey (XMM-LSS) will ultimately provide a unique mapping of the distribution of X-ray sources in a contiguous 64 deg2 region. In particular, it will provide ...the location of about 900 galaxy clusters out to a redshift of about 1. We study the prospects that this cluster catalogue offers for measuring cosmological parameters. We use the Press-Schechter formalism to predict the counts of clusters and their X-ray properties in several CDM models. We compute the detection efficiency of clusters, using realistic simulations of XMM X-ray images, and study how it differs from a conventional flux limit. We compute the expected correlation function of clusters using the extended halo model, and show that it is expected to evolve very little out to $z\simeq 2$, once the selection function of the survey is taken into account. The shape and the amplitude of the correlation function can be used to brake degeneracies present when cluster counts alone are considered. Ignoring systematic uncertainties, the combination of cluster counts evolution and of the correlation function yields measurements of $\Omega_{{\rm m}}$, $\sigma_{8}$ and Γ with a precision of about 15%, 10% and 35%, respectively, in a ΛCDM model. This combination will also provide a consistency check for the ΛCDM model, and a discrimination between this model and the OCDM model. The XMM-LSS will therefore provide important constraints on cosmological parameters, complementing that from other methods such as the Cosmic Microwave Background. We discuss how these constraints are affected by instrumental systematics and by the uncertainties in the scaling relations of clusters.
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Baryon acoustic oscillations (BAO) are oscillatory features in the galaxy power spectrum which are used as a standard rod to measure the cosmological expansion. These have been studied in Cartesian ...space or in spherical harmonic space in thin shells. In this paper, the authors present a new way to analyse BAOs by studying the BAO wiggles from the spherical Fourier-Bessel (SFB) power spectrum. In the deep survey limit and ignoring evolution, the SFB power spectrum is purely radial and reduces to the Cartesian Fourier power spectrum. In the opposite limit of a thin shell, all the information is contained in the tangential modes described by the 2D spherical harmonic power spectrum. The authors find that the radialisation of the SFB power spectrum is still a good approximation even when considering an evolving and biased galaxy field with a finite selection function. This effect can be observed by all-sky surveys with depths comparable to current surveys.
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