arXiv subjects

Adam Amara

Publications and source records attributed to Adam Amara.

106 records · Page 6Linked to original sources

arXiv2011

Probe combination in large galaxy surveys : Application of Fisher information and Shannon entropy to weak lensing

This paper is aimed at developing a better understanding of the structure of the information that in contained in galaxy surveys, so as to find optimal ways to combine observables from such surveys. We first show how Jaynes' Maximal Entropy Principle allows us, in the general case, to express the Fisher information content of data sets in terms of the curvature of the Shannon entropy surface with respect to the relevant observables. This allows us to understand the Fisher information content of a data set, once a physical model is specified, independently of the specific way that the data will be processed, and without any assumptions of Gaussianity. This includes as a special case the standard Fisher matrix prescriptions for Gaussian variables widely used in the cosmological community, for instance for power spectra extraction. As an application of this approach, we evaluate the prospects of a joint analysis of weak lensing tracers up to second order in the shapes distortions, in the case that the noise in each probe can be effectively treated as model independent. These include the magnification, the two ellipticity and the four flexion fields. At the two point level, we show that the only effect of treating these observables in combination is a simple scale dependent decrease of the noise contaminating the accessible spectrum of the lensing E-mode. We provide simple bounds to its extraction by a combination of such probes, as well as its quantitative evaluation when the correlations between the noise variables for any two such probes can be neglected.

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arXiv2011

iCosmo: an Interactive Cosmology Package

Aims: The interactive software package iCosmo, designed to perform cosmological calculations is described. Methods: iCosmo is a software package to perform interactive cosmological calculations for the low redshift universe. Computing distance measures, the matter power spectrum, and the growth factor is supported for any values of the cosmological parameters. It also computes derived observed quantities for several cosmological probes such as cosmic shear, baryon acoustic oscillations and type Ia supernovae. The associated errors for these observables can be derived for customised surveys, or for pre-set values corresponding to current or planned instruments. The code also allows for the calculation of cosmological forecasts with Fisher matrices which can be manipulated to combine different surveys and cosmological probes. The code is written in the IDL language and thus benefits from the convenient interactive features and scientific library available in this language. iCosmo can also be used as an engine to perform cosmological calculations in batch mode, and forms a convenient adaptive platform for the development of further cosmological modules. With its extensive documentation, it may also serve as a useful resource for teaching and for newcomers in the field of cosmology. Results: The iCosmo package is described with various examples and command sequences. The code is freely available with documentation at http://www.icosmo.org, along with an interactive web interface and is part of the Initiative for Cosmology, a common archive for cosmological resources.

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arXiv2010

Figures of Merit for Testing Standard Models: Application to Dark Energy Experiments in Cosmology

Given a standard model to test, an experiment can be designed to: (i) measure the standard model parameters; (ii) extend the standard model; or (iii) look for evidence of deviations from the standard model. To measure (or extend) the standard model, the Fisher matrix is widely used in cosmology to predict expected parameter errors for future surveys under Gaussian assumptions. In this article, we present a frame- work that can be used to design experiments such that it maximises the chance of finding a deviation from the standard model. Using a simple illustrative example, discussed in the appendix, we show that the optimal experimental configuration can depend dramatically on the optimisation approach chosen. We also show some simple cosmology calculations, where we study Baryonic Acoustic Oscillation and Supernove surveys. In doing so, we also show how external data, such as the positions of the CMB peaks measured by WMAP, and theory priors can be included in the analysis. In the cosmological cases that we have studied (DETF Stage III), we find that the three optimisation approaches yield similar results, which is reassuring and indicates that the choice of optimal experiment is fairly robust at this level. However, this may not be the case as we move to more ambitious future surveys.

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arXiv2010

Optimal capture of non-Gaussianity in weak lensing surveys: power spectrum, bispectrum and halo counts

We compare the efficiency of weak lensing-selected galaxy clusters counts and of the weak lensing bispectrum at capturing non-Gaussian features in the dark matter distribution. We use the halo model to compute the weak lensing power spectrum, the bispectrum and the expected number of detected clusters, and derive constraints on cosmological parameters for a large, low systematic weak lensing survey, by focusing on the $Ω_m$-$σ_8$ plane and on the dark energy equation of state. We separate the power spectrum into the resolved and the unresolved parts of the data, the resolved part being defined as detected clusters, and the unresolved part as the rest of the field. We consider four kinds of clusters counts, taking into account different amount of information : signal-to-noise ratio peak counts; counts as a function of clusters' mass; counts as a function of clusters' redshift; and counts as a function of clusters' mass and redshift. We show that when combined with the power spectrum, those four kinds of counts provide similar constraints, thus allowing one to perform the most direct counts, signal-to-noise peaks counts, and get percent level constraints on cosmological parameters. We show that the weak lensing bispectrum gives constraints comparable to those given by the power spectrum and captures non-Gaussian features as well as clusters counts, its combination with the power spectrum giving errors on cosmological parameters that are similar to, if not marginally smaller than, those obtained when combining the power spectrum with cluster counts. We finally note that in order to reach its potential, the weak lensing bispectrum must be computed using all triangle configurations, as equilateral triangles alone do not provide useful information.

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arXiv2010

Weak lensing forecasts for dark energy, neutrinos and initial conditions

Weak gravitational lensing provides a sensitive probe of cosmology by measuring the mass distribution and the geometry of the low redshift universe. We show how an all-sky weak lensing tomographic survey can jointly constrain different sets of cosmological parameters describing dark energy, massive neutrinos (hot dark matter), and the primordial power spectrum. In order to put all sectors on an equal footing, we introduce a new parameter $β$, the second order running spectral index. Using the Fisher matrix formalism with and without CMB priors, we examine how the constraints vary as the parameter set is enlarged. We find that weak lensing with CMB priors provides robust constraints on dark energy parameters and can simultaneously provide strong constraints on all three sectors. We find that the dark energy sector is largely insensitive to the inclusion of the other cosmological sectors. Implications for the planning of future surveys are discussed.

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arXiv2009

Photo-z Performance for Precision Cosmology

Current and future weak lensing surveys will rely on photometrically estimated redshifts of very large numbers of galaxies. In this paper, we address several different aspects of the demanding photo-z performance that will be required for future experiments, such as the proposed ESA Euclid mission. It is first shown that the proposed all-sky near-infrared photometry from Euclid, in combination with anticipated ground-based photometry (e.g. PanStarrs-2 or DES) should yield the required precision in individual photo-z of sigma(z) < 0.05(1+z) at I_AB < 24.5. Simple a priori rejection schemes based on the photometry alone can be tuned to recognise objects with wildly discrepant photo-z and to reduce the outlier fraction to < 0.25% with only modest loss of otherwise usable objects. Turning to the more challenging problem of determining the mean redshift of a set of galaxies to a precision of 0.002(1+z) we argue that, for many different reasons, this is best accomplished by relying on the photo-z themselves rather than on the direct measurement of from spectroscopic redshifts of a representative subset of the galaxies. A simple adaptive scheme based on the statistical properties of the photo-z likelihood functions is shown to meet this stringent systematic requirement. We also examine the effect of an imprecise correction for Galactic extinction and the effects of contamination by fainter over-lapping objects in photo-z determination. The overall conclusion of this work is that the acquisition of photometrically estimated redshifts with the precision required for Euclid, or other similar experiments, will be challenging but possible. (abridged)

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arXiv2009

Results of the GREAT08 Challenge: An image analysis competition for cosmological lensing

We present the results of the GREAT08 Challenge, a blind analysis challenge to infer weak gravitational lensing shear distortions from images. The primary goal was to stimulate new ideas by presenting the problem to researchers outside the shear measurement community. Six GREAT08 Team methods were presented at the launch of the Challenge and five additional groups submitted results during the 6 month competition. Participants analyzed 30 million simulated galaxies with a range in signal to noise ratio, point-spread function ellipticity, galaxy size, and galaxy type. The large quantity of simulations allowed shear measurement methods to be assessed at a level of accuracy suitable for currently planned future cosmic shear observations for the first time. Different methods perform well in different parts of simulation parameter space and come close to the target level of accuracy in several of these. A number of fresh ideas have emerged as a result of the Challenge including a re-examination of the process of combining information from different galaxies, which reduces the dependence on realistic galaxy modelling. The image simulations will become increasingly sophisticated in future GREAT challenges, meanwhile the GREAT08 simulations remain as a benchmark for additional developments in shear measurement algorithms.

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arXiv2009

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 http://www.great08challenge.info for the latest information.

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arXiv2009

Full-Sky Weak Lensing Simulation with 70 Billion Particles

We have performed a 70 billion dark-matter particles N-body simulation in a 2 $h^{-1}$ Gpc periodic box, using the concordance, cosmological model as favored by the latest WMAP3 results. We have computed a full-sky convergence map with a resolution of $Δθ\simeq 0.74$ arcmin$^{2}$, spanning 4 orders of magnitude in angular dynamical range. Using various high-order statistics on a realistic cut sky, we have characterized the transition from the linear to the nonlinear regime at $\ell \simeq 1000$ and shown that realistic galactic masking affects high-order moments only below $\ell < 200$. Each domain (Gaussian and non-Gaussian) spans 2 decades in angular scale. This map is therefore an ideal tool for testing map-making algorithms on the sphere. As a first step in addressing the full map reconstruction problem, we have benchmarked in this paper two denoising methods: 1) Wiener filtering applied to the Spherical Harmonics decomposition of the map and 2) a new method, called MRLens, based on the modification of the Maximum Entropy Method on a Wavelet decomposition. While the latter is optimal on large spatial scales, where the signal is Gaussian, MRLens outperforms the Wiener method on small spatial scales, where the signal is highly non-Gaussian. The simulated full-sky convergence map is freely available to the community to help the development of new map-making algorithms dedicated to the next generation of weak-lensing surveys.

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arXiv2009

Cloud Cosmology : Building the Web Interface for iCosmo

Astronomy and cosmology have embraced the internet. We routinely and successfully use the internet as a repository for sharing code, publications and information, and as a computational resource. However the interactive nature of the web, for use as an alternative to downloading code has been largely overlooked. In this article we will outline a simple framework in which a cosmological code can be turned into an interactive web interface. This is presented as a result of creating http://www.icosmo.org which is a front-end for the open-source software iCosmo. We explain how an HTML page can be created and how a cosmological code can be incorporated into a web environment using CGI scripts. We outline how plots and downloadable text can be made, and describe how help and documentation can be created. By using simple HTML and CGI scripts a basic web interface for any cosmological code can be created easily. We provide a worked example of the methods outlined, which can be used as a simple template by any researcher who wants to share their work online.

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arXiv2008

Deconstructing Baryon Acoustic Oscillations: A Comparison of Methods

The Baryon Acoustic Oscillations (BAOs) or baryon wiggles which are present in the galaxy power spectrum at scales 100-150Mpc/h are powerful features with which to constrain cosmology. The potential of these probes is such that these are now included as primary science goals in the planning of several future galaxy surveys. However, there is not a uniquely defined BAO Method in the literature but a range of implementations. We study the assumptions and cosmological performances of three different BAO methods: the full Fourier space power spectrum [P(k)], the `wiggles only' in Fourier space and the spherical harmonics power spectrum [C(l)]. We contrast the power of each method to constrain cosmology for two fiducial surveys taken from the Dark Energy Task Force (DETF) report and equivalent to future ground and space based spectroscopic surveys. We find that, depending on the assumptions used, the dark energy Figure of Merit (FoM) can change by up to a factor of 35 for a given fiducial model and survey. We compare our results with the DETF implementation and, discuss the robustness of each probe, by quantifying the dependence of the FoM with the wavenumber range. The more information used by a method, the higher its statistical performance, but the higher its sensitivity to systematics and implementations details.

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arXiv2008

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 XMM-LSS 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 6 weak-lensing-detected clusters of galaxies. We show that their counts can be used to constrain the power spectrum normalisation $σ_8 =0.92_{-0.30}^{+0.26}$ for $Ω_m=0.24$. We show that despite the large scatter generally observed in the M-T relation derived from lensing masses, tight constraints on both its slope and normalisation $M_*$ can be obtained with a moderate number of sources provided that the covered mass range is large enough. Adding clusters from Bardeau et al. (2007) to our sample, we measure $M_* = 2.71_{-0.61}^{+0.79} 10^{14} h^{-1} M_\odot$. 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 $σ_8$ 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% accuracy in the estimation of the power spectrum and the M-T relation normalisations.

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arXiv2007

Systematic Bias in Cosmic Shear: Beyond the Fisher Matrix

We describe a method for computing the biases that systematic signals introduce in parameter estimation using a simple extension of the Fisher matrix formalism. This allows us to calculate the offset of the best fit parameters relative to the fiducial model, in addition to the usual statistical error ellipse. As an application, we study the impact that residual systematics in tomographic weak lensing measurements. In particular we explore three different types of shape measurement systematics: (i) additive systematic with no redshift evolution; (ii) additive systematic with redshift evolution; and (iii) multiplicative systematic. In each case, we consider a wide range of scale dependence and redshift evolution of the systematics signal. For a future DUNE-like full sky survey, we find that, for cases with mild redshift evolution, the variance of the additive systematic signal should be kept below 10^-7 to ensure biases on cosmological parameters that are sub-dominant to the statistical errors. For the multiplicative systematics, which depends on the lensing signal, we find the multiplicative calibration m0 needs to be controlled to an accuracy better than 10^-3. We find that the impact of systematics can be underestimated if their assumes redshift dependence is too simplistic. We provide simple scaling relations to extend these requirements to any survey geometry and discuss the impact of our results for current and future weak lensing surveys.

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arXiv2007

Optimal Surveys for Weak Lensing Tomography

Weak lensing surveys provide a powerful probe of dark energy through the measurement of the mass distribution of the local Universe. A number of ground-based and space-based surveys are being planned for this purpose. Here, we study the optimal strategy for these future surveys using the joint constraints on the equation of state parameter wn and its evolution wa as a figure of merit by considering power spectrum tomography. For this purpose, we first consider an `ideal' survey which is both wide and deep and exempt from systematics. We find that such a survey has great potential for dark energy studies, reaching one sigma precisions of 1% and 10% on the two parameters respectively. We then study the relative impact of various limitations by degrading this ideal survey. In particular, we consider the effect of sky coverage, survey depth, shape measurements systematics, photometric redshifts systematics and uncertainties in the non-linear power spectrum predictions. We find that, for a given observing time, it is always advantageous to choose a wide rather than a deep survey geometry. We also find that the dark energy constraints from power spectrum tomography are robust to photometric redshift errors and catastrophic failures, if a spectroscopic calibration sample of 10^4-10^5 galaxies is available. The impact of these systematics is small compared to the limitations that come from potential uncertainties in the power spectrum, due to shear measurement and theoretical errors. To help the planning of future surveys, we summarize our results with comprehensive scaling relations which avoid the need for full Fisher matrix calculations.

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arXiv2006

Smooth Particle Lensing

We present a numerical technique to compute the gravitational lensing induced by simulated haloes. It relies on a 2D-Tree domain decomposition in the lens plane combined with a description of N-Body particles as extended clouds with a non-singular density. This technique is made fully adaptive by the use of a density-dependent smoothing which allows one to probe the lensing properties of haloes from the densest regions in the center or in substructures to the low-density regions in the outskirts. 'Smooth Particle Lensing' has some promising features. First, the deflection potential, the deflection angles, the convergence and the shear are direct and separate end-products of the SPL calculation and can be computed at an arbitrary distribution of points on the lens plane. Second, this flexibility avoids the use of interpolation or a finite differentiation procedure on a grid, does not require padding the region with zeros and focuses the computing power on relevant regions. The SPL algorithm is tested by populating isothermal spheres and ellipsoids with particles and then comparing the lensing calculations to the classical FFT-based technique and analytic solutions. We assess issues related to the resolution of the lensing code and the limitations set by the simulations themselves. We conclude by discussing how SPL can be used to predict the impact of substructures on strong lensing and how it can be generalized to weak lensing and cosmic shear simulations.

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arXiv2006

Simulations of Strong Gravitational Lensing with Substructure

Galactic sized gravitational lenses are simulated by combining a cosmological N-body simulation and models for the baryonic component of the galaxy. The lens caustics, critical curves, image locations and magnification ratios are calculated by ray-shooting on an adaptive grid. When the source is near a cusp in a smooth lens' caustic the sum of the magnifications of the three closest images should be close to zero. It is found that in the observed cases this sum is generally too large to be consistent with the simulations implying that there is not enough substructure in the simulations. This suggests that other factors play an important role. These may include limited numerical resolution, lensing by structure outside the halo, selection bias and the possibility that a randomly selected galaxy halo may be more irregular, for example due to recent mergers, than the isolated halo used in this study. It is also shown that, with the level of substructure computed from the N-body simulations, the image magnifications of the Einstein cross type lenses are very weak functions of source size up to $\sim 1\kpc$. This is also true for the magnification ratios of widely separated images in the fold and cusp caustic lenses. This means that selected magnification ratios for different the emission regions of a lensed quasar should agree with each other, barring microlensing by stars. The source size dependence of the magnification ratio between the closest pair of images is more sensitive to substructure.

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