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Register a new userMinkowski Functionals of Convergence Maps and the Lensing Figure of Merit
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Minkowski functionals (MFs) quantify the topological properties of a given field probing its departure from Gaussianity. We investigate their use on lensing convergence maps in order to see whether they can provide further insights on the underlying cosmology with respect to the standard second-order statistics, i.e., cosmic shear tomography. To this end, we first present a method to match theoretical predictions with measured MFs taking care of the shape noise, imperfections in the map reconstruction, and inaccurate description of the nonlinearities in the matter power spectrum and bispectrum. We validate this method against simulated maps reconstructed from shear fields generated by the MICE simulation. We then perform a Fisher matrix analysis to forecast the accuracy on cosmological parameters from a joint MFs and shear tomography analysis. It turns out that MFs are indeed helpful to break the $Omega_{rm m}$--$sigma_8$ degeneracy thus generating a sort of chain reaction leading to an overall increase of the Figure of Merit.
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The unprecedented quality, the increased dataset, and the wide area of ongoing and near future weak lensing surveys allows to move beyond the standard two points statistics thus making worthwhile to investigate higher order probes. As an interesting step towards this direction, we expolore the use of higher order moments (HOM) of the convergence field as a way to increase the lensing Figure of Merit (FoM). To this end, we rely on simulated convergence to first show that HOM can be measured and calibrated so that it is indeed possible to predict them for a given cosmological model provided suitable nuisance parameters are introduced and then marginalized over. We then forecast the accuracy on cosmological parameters from the use of HOM alone and in combination with standard shear power spectra tomography. It turns out that HOM allow to break some common degeneracies thus significantly boosting the overall FoM. We also qualitatively discuss possible systematics and how they can be dealt with.
Stage IV lensing surveys promise to make available an unprecedented amount of excellent data which will represent a huge leap in terms of both quantity and quality. This will open the way to the use of novel tools, which go beyond the standard second order statistics probing the high order properties of the convergence field. We discuss the use of Minkowski Functionals (MFs) as complementary probes to increase the lensing Figure of Merit (FoM), for a survey made out of a wide total area $A_{rm{tot}}$ imaged at a limiting magnitude $rm{mag_{W}}$ containing a subset of area $A_{rm{deep}}$ where observations are pushed to a deeper limiting magnitude $rm{mag_{D}}$. We present an updated procedure to match the theoretically predicted MFs to the measured ones, taking into account the impact of map reconstruction from noisy shear data. We validate this renewed method against simulated data sets with different source redshift distributions and total number density, setting these quantities in accordance with the depth of the survey. We can then rely on a Fisher matrix analysis to forecast the improvement in the FoM due to the joint use of shear tomography and MFs under different assumptions on $(A_{rm{tot}},,A_{rm{deep}},,rm{mag_{D}})$, and the prior on the MFs nuisance parameters. It turns out that MFs can provide a valuable help in increasing the FoM of the lensing survey, provided the nuisance parameters are known with a non negligible precision. What is actually more interesting is the possibility to compensate for the loss of FoM due to a cut in the multipole range probed by shear tomography, which makes the results more robust against uncertainties in the modeling of nonlinearities. This makes MFs a promising tool to both increase the FoM and make the constraints on the cosmological parameters less affected by theoretical systematic effects.
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.
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.
We study the morphology of convergence maps by perturbatively reconstructing their Minkowski Functionals (MFs). We present a systematics study using a set of three generalised skew-spectra as a function of source redshift and smoothing angular scale. Using an approach based on pseudo-$S_{ell}$s (PSL) we show how these spectra will allow reconstruction of MFs in the presence of an arbitrary mask and inhomogeneous noise in an unbiased way. Our theoretical predictions are based on a recently introduced fitting function to the bispectrum. We compare our results against state-of-the art numerical simulations and find an excellent agreement. The reconstruction can be carried out in a controlled manner as a function of angular harmonics $ell$ and source redshift $z_s$ which allows for a greater handle on any possible sources of non-Gaussianity. Our method has the advantage of estimating the topology of convergence maps directly using shear data. We also study weak lensing convergence maps inferred from Cosmic Microwave Background (CMB) observations; and we find that, though less significant at low redshift, the post-Born corrections play an important role in any modelling of the non-Gaussianity of convergence maps at higher redshift. We also study the cross-correlations of estimates from different tomographic bins.
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