We present a new method for the analysis of images, a fundamental task in observational astronomy. It is based on the linear decomposition of each object in the image into a series of localized basis ...functions of different shapes, which we call ‘shapelets’. A particularly useful set of complete and orthonormal shapelets is that consisting of weighted Hermite polynomials, which correspond to perturbations around a circular Gaussian. They are also the eigenstates of the two dimensional quantum harmonic oscillator, and thus allow us to use the powerful formalism developed for this problem. One of their special properties is their invariance under Fourier transforms (up to a rescaling), leading to an analytic form for convolutions. The generator of linear transformations such as translations, rotations, shears and dilatations can be written as simple combinations of raising and lowering operators. We derive analytic expressions for practical quantities, such as the centroid (astrometry), flux (photometry) and radius of the object, in terms of its shapelet coefficients. We also construct polar basis functions which are eigenstates of the angular momentum operator, and thus have simple properties under rotations. As an example, we apply the method to Hubble Space Telescope images, and show that the small number of shapelet coefficients required to represent galaxy images lead to compression factors of about 40 to 90. We discuss applications of shapelets for the archival of large photometric surveys, for weak and strong gravitational lensing and for image deprojection.
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.
Context. Baryon acoustic oscillations (BAOs) 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 (Fourier or real space) or in spherical harmonic space in thin shells. Aims. Future wide-field surveys will cover both wide and deep regions of the sky and thus require a simultaneous treatment of the spherical sky and of an extended radial coverage. The spherical Fourier-Bessel (SFB) decomposition is a natural basis for the analysis of fields in this geometry and facilitates the combination of BAO surveys with other cosmological probes readily described in this basis. In this paper, we present a new way to analyse BAOs by studying the BAO wiggles from the SFB power spectrum. Methods. In SFB space, the power spectrum generally has both a radial (k) and tangential (ℓ) dependence and so do the BAOs. 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. Results. We 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. We also find that the BAOs radialise more rapidly than the full SFB power spectrum. Conclusions. Our results suggest the first peak of the BAOs in SFB space becomes radial out to ℓ ~ 10 for all-sky surveys with the same depth as SDSS or 2dF, and out to ℓ ~ 70 for an all-sky stage IV survey. Subsequent BAO peaks will also become radial, but for shallow surveys these may be in the non-linear regime. For modes that have become radial, measurements at different ℓ’s are useful in practice to reduce measurement errors.
Abstract
The Physics of the Accelerating Universe Survey (PAUS) is an innovative photometric survey with 40 narrow-bands at the William Herschel Telescope (WHT). The narrow-bands are spaced at 100 Å ...intervals covering the range 4500–8500 Å and, in combination with standard broad-bands, enable excellent redshift precision. This paper describes the technique, galaxy templates, and additional photometric calibration used to determine early photometric redshifts from PAUS. Using bcnz2, a new photometric redshift code developed for this purpose, we characterize the photometric redshift performance using PAUS data on the COSMOS field. Comparison to secure spectra from zCOSMOS DR3 shows that PAUS achieves σ68/(1 + $z$) = 0.0037 to iAB < 22.5 for the redshift range 0 < $z$ < 1.2, when selecting the best 50 per cent of the sources based on a photometric redshift quality cut. Furthermore, a higher photo-z precision σ68/(1 + $z$) ∼ 0.001 is obtained for a bright and high-quality selection, which is driven by the identification of emission lines. We conclude that PAUS meets its design goals, opening up a hitherto uncharted regime of deep, wide, and dense galaxy survey with precise redshifts that will provide unique insights into the formation, evolution, and clustering of galaxies, as well as their intrinsic alignments.
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 $\Delta \theta \simeq 0.74$ arcmin2, 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.
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.
We present measurements of weak gravitational lensing cosmic shear two-point statistics using Dark Energy Survey Science Verification data. We demonstrate that our results are robust to the choice of ...shear measurement pipeline, either ngmix or im3shape, and robust to the choice of two-point statistic, including both real and Fourier-space statistics. Our results pass a suite of null tests including tests for B-mode contamination and direct tests for any dependence of the two-point functions on a set of 16 observing conditions and galaxy properties, such as seeing, airmass, galaxy color, galaxy magnitude, etc. We furthermore use a large suite of simulations to compute the covariance matrix of the cosmic shear measurements and assign statistical significance to our null tests. We find that our covariance matrix is consistent with the halo model prediction, indicating that it has the appropriate level of halo sample variance. We compare the same jackknife procedure applied to the data and the simulations in order to search for additional sources of noise not captured by the simulations. We find no statistically significant extra sources of noise in the data. The overall detection significance with tomography for our highest source density catalog is 9.7sigma. Cosmological constraints from the measurements in this work are presented in a companion paper DES et al., Phys. Rev. D 94, 022001 (2016)..
The Dark UNiverse Explorer (DUNE) is a wide-field space imager whose primary goal is the study of dark energy and dark matter with unprecedented precision. For this purpose, DUNE is optimised for the ...measurement of weak gravitational lensing but will also provide complementary measurements of baryonic accoustic oscillations, cluster counts and the Integrated Sachs Wolfe effect. Immediate auxiliary goals concern the evolution of galaxies, to be studied with unequalled statistical power, the detailed structure of the Milky Way and nearby galaxies, and the demographics of Earth-mass planets. DUNE is an Medium-class mission which makes use of readily available components, heritage from other missions, and synergy with ground based facilities to minimise cost and risks. The payload consists of a 1.2 m telescope with a combined visible/NIR field-of-view of 1 deg
2
. DUNE will carry out an all-sky survey, ranging from 550 to 1600 nm, in one visible and three NIR bands which will form a unique legacy for astronomy. DUNE will yield major advances in a broad range of fields in astrophysics including fundamental cosmology, galaxy evolution, and extrasolar planet search. DUNE was recently selected by ESA as one of the mission concepts to be studied in its Cosmic Vision programme.
With increasingly large data sets, weak lensing measurements are able to measure cosmological parameters with ever-greater precision. However, this increased accuracy also places greater demands on ...the statistical tools used to extract the available information. To date, the majority of lensing analyses use the two-point statistics of the cosmic shear field. These can be either studied directly using the two-point correlation function or in Fourier space, using the power spectrum. But analysing weak lensing data inevitably involves the masking out of regions, for example to remove bright stars from the field. Masking out the stars is common practice but the gaps in the data need proper handling. In this paper, we show how an inpainting technique allows us to properly fill in these gaps with only Nlog N operations, leading to a new image from which we can compute straightforwardly and with a very good accuracy both the power spectrum and the bispectrum. We then propose a new method to compute the bispectrum with a polar fft algorithm, which has the main advantage of avoiding any interpolation in the Fourier domain. Finally, we propose a new method for dark matter mass map reconstruction from shear observations, which integrates this new inpainting concept. A range of examples based on 3D N-body simulations illustrates the results.
With a primary goal of conducting precision weak-lensing measurements from space, the COSMOS survey has imaged the largest contiguous area observed by Hubble Space Telescope to date, using the ...Advanced Camera for Surveys (ACS). This is the first paper in a series in which we describe our strategy for addressing the various technical challenges in the production of weak-lensing measurements from COSMOS data. We first construct a source catalog from 575 ACS/WFC tiles (1.64 deg super(2)) subsampled at a pixel scale of 0.03". Defects and diffraction spikes are carefully removed, leaving a total of 1.2 x 10 super(6) objects to a limiting magnitude of F814W = 26.5. This catalog is made publicly available. Multiwavelength follow-up observations of the COSMOS field provide photometric redshifts for 73% of the source galaxies in the lensing catalog. We analyze and discuss the COSMOS redshift distribution and show broad agreement with other surveys to z similar to 1. Our next step is to measure the shapes of galaxies and correct them for the distortion induced by the time-varying ACS point-spread function and for charge transfer efficiency (CTE) effects. Simulated images are used to derive the shear susceptibility factors that are necessary in transforming shape measurements into unbiased shear estimators. For every galaxy we derive a shape measurement error and utilize this quantity to extract the intrinsic shape noise of the galaxy sample. Interestingly, our results indicate that intrinsic shape noise varies little with size, magnitude, or redshift. Representing a number density of 66 galaxies per arcmin super(2), the final COSMOS weak-lensing catalog contains 3.9 x 10 super(5) galaxies with accurate shape measurements. The properties of the COSMOS weak-lensing catalog described throughout this paper will provide key input numbers for the preparation and design of next-generation wide field space missions.
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