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Register a new user3D Reconstruction of the Density Field: An SVD Approach to Weak Lensing Tomography
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We present a new method for constructing three-dimensional mass maps from gravitational lensing shear data. We solve the lensing inversion problem using truncation of singular values (within the context of generalized least squares estimation) without a priori assumptions about the statistical nature of the signal. This singular value framework allows a quantitative comparison between different filtering methods: we evaluate our method beside the previously explored Wiener filter approaches. Our method yields near-optimal angular resolution of the lensing reconstruction and allows cluster sized halos to be de-blended robustly. It allows for mass reconstructions which are 2-3 orders-of-magnitude faster than the Wiener filter approach; in particular, we estimate that an all-sky reconstruction with arcminute resolution could be performed on a time-scale of hours. We find however that linear, non-parametric reconstructions have a fundamental limitation in the resolution achieved in the redshift direction.
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In this paper, we compare three methods to reconstruct galaxy cluster density fields with weak lensing data. The first method called FLens integrates an inpainting concept to invert the shear field with possible gaps, and a multi-scale entropy denoising procedure to remove the noise contained in the final reconstruction, that arises mostly from the random intrinsic shape of the galaxies. The second and third methods are based on a model of the density field made of a multi-scale grid of radial basis functions. In one case, the model parameters are computed with a linear inversion involving a singular value decomposition. In the other case, the model parameters are estimated using a Bayesian MCMC optimization implemented in the lensing software Lenstool. Methods are compared on simulated data with varying galaxy density fields. We pay particular attention to the errors estimated with resampling. We find the multi-scale grid model optimized with MCMC to provide the best results, but at high computational cost, especially when considering resampling. The SVD method is much faster but yields noisy maps, although this can be mitigated with resampling. The FLens method is a good compromise with fast computation, high signal to noise reconstruction, but lower resolution maps. All three methods are applied to the MACS J0717+3745 galaxy cluster field, and reveal the filamentary structure discovered in Jauzac et al. 2012. We conclude that sensitive priors can help to get high signal to noise, and unbiased reconstructions.
We develop and apply an analytic method to predict peak counts in weak-lensing surveys. It is based on the theory of Gaussian random fields and suitable to quantify the level of spurious detections caused by chance projections of large-scale structures as well as the shape and shot noise contributed by the background galaxies. We compare our method to peak counts obtained from numerical ray-tracing simulations and find good agreement at the expected level. The number of peak detections depends substantially on the shape and size of the filter applied to the gravitational shear field. Our main results are that weak-lensing peak counts are dominated by spurious detections up to signal-to-noise ratios of 3--5 and that most filters yield only a few detections per square degree above this level, while a filter optimised for suppressing large-scale structure noise returns up to an order of magnitude more.
We introduce a novel approach to reconstruct dark matter mass maps from weak gravitational lensing measurements. The cornerstone of the proposed method lies in a new modelling of the matter density field in the Universe as a mixture of two components:(1) a sparsity-based component that captures the non-Gaussian structure of the field, such as peaks or halos at different spatial scales; and (2) a Gaussian random field, which is known to well represent the linear characteristics of the field.Methods. We propose an algorithm called MCALens which jointly estimates these two components. MCAlens is based on an alternating minimization incorporating both sparse recovery and a proximal iterative Wiener filtering. Experimental results on simulated data show that the proposed method exhibits improved estimation accuracy compared to state-of-the-art mass map reconstruction methods.
We use matter power spectra from cosmological hydrodynamic simulations to quantify the effect of baryon physics on the weak gravitational lensing shear signal. The simulations consider a number of processes, such as radiative cooling, star formation, supernovae and feedback from active galactic nuclei (AGN). Van Daalen et al. (2011) used the same simulations to show that baryon physics, in particular the strong feedback that is required to solve the overcooling problem, modifies the matter power spectrum on scales relevant for cosmological weak lensing studies. As a result, the use of power spectra from dark matter simulations can lead to significant biases in the inferred cosmological parameters. We show that the typical biases are much larger than the precision with which future missions aim to constrain the dark energy equation of state, w_0. For instance, the simulation with AGN feedback, which reproduces X-ray and optical properties of groups of galaxies, gives rise to a ~40% bias in w_0. We demonstrate that the modification of the power spectrum is dominated by groups and clusters of galaxies, the effect of which can be modelled. We consider an approach based on the popular halo model and show that simple modifications can capture the main features of baryonic feedback. Despite its simplicity, we find that our model, when calibrated on the simulations, is able to reduce the bias in w_0 to a level comparable to the size of the statistical uncertainties for a Euclid-like mission. While observations of the gas and stellar fractions as a function of halo mass can be used to calibrate the model, hydrodynamic simulations will likely still be needed to extend the observed scaling relations down to halo masses of 10 ^12 M_sun/h.
We construct the spin flaglet transform, a wavelet transform to analyze spin signals in three dimensions. Spin flaglets can probe signal content localized simultaneously in space and frequency and, moreover, are separable so that their angular and radial properties can be controlled independently. They are particularly suited to analyzing of cosmological observations such as the weak gravitational lensing of galaxies. Such observations have a unique 3D geometrical setting since they are natively made on the sky, have spin angular symmetries, and are extended in the radial direction by additional distance or redshift information. Flaglets are constructed in the harmonic space defined by the Fourier-Laguerre transform, previously defined for scalar functions and extended here to signals with spin symmetries. Thanks to various sampling theorems, both the Fourier-Laguerre and flaglet transforms are theoretically exact when applied to bandlimited signals. In other words, in numerical computations the only loss of information is due to the finite representation of floating point numbers. We develop a 3D framework relating the weak lensing power spectrum to covariances of flaglet coefficients. We suggest that the resulting novel flaglet weak lensing estimator offers a powerful alternative to common 2D and 3D approaches to accurately capture cosmological information. While standard weak lensing analyses focus on either real or harmonic space representations (i.e., correlation functions or Fourier-Bessel power spectra, respectively), a wavelet approach inherits the advantages of both techniques, where both complicated sky coverage and uncertainties associated with the physical modeling of small scales can be handled effectively. Our codes to compute the Fourier-Laguerre and flaglet transforms are made publicly available.
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