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Register a new userProbing Cosmology with Weak Lensing Minkowski Functionals
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Jan M. Kratochvil
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In this paper, we show that Minkowski Functionals (MFs) of weak gravitational lensing (WL) convergence maps contain significant non-Gaussian, cosmology-dependent information. To do this, we use a large suite of cosmological ray-tracing N-body simulations to create mock WL convergence maps, and study the cosmological information content of MFs derived from these maps. Our suite consists of 80 independent 512^3 N-body runs, covering seven different cosmologies, varying three cosmological parameters Omega_m, w, and sigma_8 one at a time, around a fiducial LambdaCDM model. In each cosmology, we use ray-tracing to create a thousand pseudo-independent 12 deg^2 convergence maps, and use these in a Monte Carlo procedure to estimate the joint confidence contours on the above three parameters. We include redshift tomography at three different source redshifts z_s=1, 1.5, 2, explore five different smoothing scales theta_G=1, 2, 3, 5, 10 arcmin, and explicitly compare and combine the MFs with the WL power spectrum. We find that the MFs capture a substantial amount of information from non-Gaussian features of convergence maps, i.e. beyond the power spectrum. The MFs are particularly well suited to break degeneracies and to constrain the dark energy equation of state parameter w (by a factor of ~ three better than from the power spectrum alone). The non-Gaussian information derives partly from the one-point function of the convergence (through V_0, the area MF), and partly through non-linear spatial information (through combining different smoothing scales for V_0, and through V_1 and V_2, the boundary length and genus MFs, respectively). In contrast to the power spectrum, the best constraints from the MFs are obtained only when multiple smoothing scales are combined.
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We compare the efficiency of moments and Minkowski functionals (MFs) in constraining the subset of cosmological parameters (Omega_m,w,sigma_8) using simulated weak lensing convergence maps. We study an analytic perturbative expansion of the MFs in terms of the moments of the convergence field and of its spatial derivatives. We show that this perturbation series breaks down on smoothing scales below 5, while it shows a good degree of convergence on larger scales (15). Most of the cosmological distinguishing power is lost when the maps are smoothed on these larger scales. We also show that, on scales comparable to 1, where the perturbation series does not converge, cosmological constraints obtained from the MFs are approximately 1.5-2 times better than the ones obtained from the first few moments of the convergence distribution --- provided that the latter include spatial information, either from moments of gradients, or by combining multiple smoothing scales. Including either a set of these moments or the MFs can significantly tighten constraints on cosmological parameters, compared to the conventional method of using the power spectrum alone.
We propose counting peaks in weak lensing (WL) maps, as a function of their height, to probe models of dark energy and to constrain cosmological parameters. Because peaks can be identified in two-dimensional WL maps directly, they can provide constraints that are free from potential selection effects and biases involved in identifying and determining the masses of galaxy clusters. We have run cosmological N-body simulations to produce WL convergence maps in three models with different constant values of the dark energy equation of state parameter, w=-0.8, -1, and -1.2, with a fixed normalization of the primordial power spectrum (corresponding to present-day normalizations of sigma8=0.742, 0.798, and 0.839, respectively). By comparing the number of WL peaks in 8 convergence bins in the range of -0.1 < kappa < 0.2, in multiple realizations of a single simulated 3x3 degree field, we show that the first (last) pair of models can be distinguished at the 95% (85%) confidence level. A survey with depth and area (20,000 sq. degrees), comparable to those expected from LSST, should have a factor of approx. 50 better parameter sensitivity. We find that relatively low-amplitude peaks (kappa = 0.03), which typically do not correspond to a single collapsed halo along the line of sight, account for most of this sensitivity. We study a range of smoothing scales and source galaxy redshifts (z_s). With a fixed source galaxy density of 15/arcmin^2, the best results are provided by the smallest scale we can reliably simulate, 1 arcminute, and z_s=2 provides substantially better sensitivity than z_s< 1.5.
We present a new harmonic-domain approach for extracting morphological information, in the form of Minkowski Functionals (MFs), from weak lensing (WL) convergence maps. Using a perturbative expansion of the MFs, which is expected to be valid for the range of angular scales probed by most current weak-lensing surveys, we show that the study of three generalized skewness parameters is equivalent to the study of the three MFs defined in two dimensions. We then extend these skewness parameters to three associated skew-spectra which carry more information about the convergence bispectrum than their one-point counterparts. We discuss various issues such as noise and incomplete sky coverage in the context of estimation of these skew-spectra from realistic data. Our technique provides an alternative to the pixel-space approaches typically used in the estimation of MFs, and it can be particularly useful in the presence of masks with non-trivial topology. Analytical modeling of weak lensing statistics relies on an accurate modeling of the statistics of underlying density distribution. We apply three different formalisms to model the underlying dark-matter bispectrum: the hierarchical ansatz, halo model and a fitting function based on numerical simulations; MFs resulting from each of these formalisms are computed and compared. We investigate the extent to witch late-time gravity-induced non-Gaussianity (to which weak lensing is primarily sensitive) can be separated from primordial non-Gaussianity and how this separation depends on source redshift and angular scale.
We generalize the concept of the ordinary skew-spectrum to probe the effect of non-Gaussianity on the morphology of Cosmic Microwave Background (CMB) maps in several domains: in real-space (where they are commonly known as cumulant-correlators), and in harmonic and needlet bases. The essential aim is to retain more information than normally contained in these statistics, in order to assist in determining the source of any measured non-Gaussianity, in the same spirit as Munshi & Heavens (2010) skew-spectra were used to identify foreground contaminants to the CMB bispectrum in Planck data. Using a perturbative series to construct the Minkowski Functionals (MFs), we provide a pseudo-Cl based approach in both harmonic and needlet representations to estimate these spectra in the presence of a mask and inhomogeneous noise. Assuming homogeneous noise we present approx- imate expressions for error covariance for the purpose of joint estimation of these spectra. We present specific results for four different models of primordial non-Gaussianity local, equilateral, orthogonal and enfolded models, as well as non-Gaussianity caused by unsubtracted point sources. Closed form results of next-order corrections to MFs too are obtained in terms of a quadruplet of kurt-spectra. We also use the method of modal decomposition of the bispectrum and trispectrum to reconstruct the MFs as an alternative method of reconstruction of morphological properties of CMB maps. Finally, we introduce the odd-parity skew-spectra to probe the odd-parity bispectrum and its impact on the morphology of the CMB sky. Although developed for the CMB, the generic results obtained here can be useful in other areas of cosmology.
Weak gravitational lensing is a powerful cosmological probe, with non--Gaussian features potentially containing the majority of the information. We examine constraints on the parameter triplet $(Omega_m,w,sigma_8)$ from non-Gaussian features of the weak lensing convergence field, including a set of moments (up to $4^{rm th}$ order) and Minkowski functionals, using publicly available data from the 154deg$^2$ CFHTLenS survey. We utilize a suite of ray--tracing N-body simulations spanning 91 points in $(Omega_m,w,sigma_8)$ parameter space, replicating the galaxy sky positions, redshifts and shape noise in the CFHTLenS catalogs. We then build an emulator that interpolates the simulated descriptors as a function of $(Omega_m,w,sigma_8)$, and use it to compute the likelihood function and parameter constraints. We employ a principal component analysis to reduce dimensionality and to help stabilize the constraints with respect to the number of bins used to construct each statistic. Using the full set of statistics, we find $Sigma_8equivsigma_8(Omega_m/0.27)^{0.55}=0.75pm0.04$ (68% C.L.), in agreement with previous values. We find that constraints on the $(Omega_m,sigma_8)$ doublet from the Minkowski functionals suffer a strong bias. However, high-order moments break the $(Omega_m,sigma_8)$ degeneracy and provide a tight constraint on these parameters with no apparent bias. The main contribution comes from quartic moments of derivatives.
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