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Register a new userMasked areas in shear peak statistics: a forward modeling approach
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The statistics of shear peaks have been shown to provide valuable cosmological information beyond the power spectrum, and will be an important constraint of models of cosmology with the large survey areas provided by forthcoming astronomical surveys. Surveys include masked areas due to bright stars, bad pixels etc, which must be accounted for in producing constraints on cosmology from shear maps. We advocate a forward-modeling approach, where the impact of masking (and other survey artifacts) are accounted for in the theoretical prediction of cosmological parameters, rather than removed from survey data. We use masks based on the Deep Lens Survey, and explore the impact of up to 37% of the survey area being masked on LSST and DES-scale surveys. By reconstructing maps of aperture mass, the masking effect is smoothed out, resulting in up to 14% smaller statistical uncertainties compared to simply reducing the survey area by the masked area. We show that, even in the presence of large survey masks, the bias in cosmological parameter estimation produced in the forward-modeling process is ~1%, dominated by bias caused by limited simulation volume. We also explore how this potential bias scales with survey area and find that small survey areas are more significantly impacted by the differences in cosmological structure in the data and simulated volumes, due to cosmic variance.
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Weak gravitational lensing analyses are fundamentally limited by the intrinsic, non-Gaussian distribution of galaxy shapes. We explore alternative statistics for samples of ellipticity measurements that are unbiased, efficient, and robust. We take the non-linear mapping of gravitational shear and the effect of noise into account. We then discuss how the distribution of individual galaxy shapes in the observed field of view can be modeled by fitting Fourier modes to the shear pattern directly. We simulated samples of galaxy ellipticities, using both theoretical distributions and real data for ellipticities and noise. We determined the possible bias $Delta e$, the efficiency $eta$ and the robustness of the least absolute deviations, the biweight, and the convex hull peeling estimators, compared to the canonical weighted mean. Using these statistics for regression, we have shown the applicability of direct Fourier mode fitting. These estimators can be unbiased in the absence of noise, and decrease noise bias by more than $sim 30%$. The convex hull peeling estimator distribution is centered around the underlying shear, and its bias least affected by noise. The least absolute deviations estimator to be the most efficient estimator in almost all cases, except in the Gaussian case, where its still competitive ($0.83<eta <5.1$) and therefore robust. These results hold when fitting Fourier modes, where amplitudes of variation in ellipticity are determined to the order of $10^{-3}$. The peak of the ellipticity distribution is a direct tracer of the underlying shear and unaffected by noise, and we have shown that estimators that are sensitive to a central cusp perform more efficiently, potentially reducing uncertainties by more than $50%$ and significantly decreasing noise bias.
Shear peak statistics has gained a lot of attention recently as a practical alternative to the two point statistics for constraining cosmological parameters. We perform a shear peak statistics analysis of the Dark Energy Survey (DES) Science Verification (SV) data, using weak gravitational lensing measurements from a 139 deg$^2$ field. We measure the abundance of peaks identified in aperture mass maps, as a function of their signal-to-noise ratio, in the signal-to-noise range $0<mathcal S / mathcal N<4$. To predict the peak counts as a function of cosmological parameters we use a suite of $N$-body simulations spanning 158 models with varying $Omega_{rm m}$ and $sigma_8$, fixing $w = -1$, $Omega_{rm b} = 0.04$, $h = 0.7$ and $n_s=1$, to which we have applied the DES SV mask and redshift distribution. In our fiducial analysis we measure $sigma_{8}(Omega_{rm m}/0.3)^{0.6}=0.77 pm 0.07$, after marginalising over the shear multiplicative bias and the error on the mean redshift of the galaxy sample. We introduce models of intrinsic alignments, blending, and source contamination by cluster members. These models indicate that peaks with $mathcal S / mathcal N>4$ would require significant corrections, which is why we do not include them in our analysis. We compare our results to the cosmological constraints from the two point analysis on the SV field and find them to be in good agreement in both the central value and its uncertainty. We discuss prospects for future peak statistics analysis with upcoming DES data.
The unprecedented amount and the excellent quality of lensing data that the upcoming ground- and space-based surveys will produce represent a great opportunity to shed light on the questions that still remain unanswered concerning our universe and the validity of the standard $Lambda$CDM cosmological model. Therefore, it is important to develop new techniques that can exploit the huge quantity of data that future observations will give us access to in the most effective way possible. For this reason, we decided to investigate the development of a new method to treat weak lensing higher order statistics, which are known to break degeneracy among cosmological parameters thanks to their capability of probing the non-Gaussian properties of the shear field. In particular, the proposed method directly applies to the observed quantity, i.e., the noisy galaxy ellipticity. We produced simulated lensing maps with different sets of cosmological parameters and used them to measure higher order moments, Minkowski functionals, Betti numbers, and other statistics related to graph theory. This allowed us to construct datasets with different size, precision, and smoothing. We then applied several machine learning algorithms to determine which method best predicts the actual cosmological parameters associated with each simulation. The best model resulted to be simple multidimensional linear regression. We used this model to compare the results coming from the different datasets and found out that we can measure with good accuracy the majority of the parameters that we considered. We also investigated the relation between each higher order estimator and the different cosmological parameters for several signal-to-noise thresholds and redshifts bins. Given the promising results, we consider this approach as a valuable resource, worth of further development.
In this paper we derive a full expression for the propagation of weak lensing shape measurement biases into cosmic shear power spectra including the effect of missing data. We show using simulations that terms higher than first order in bias parameters can be ignored and the impact of biases can be captured by terms dependent only on the mean of the multiplicative bias field. We identify that the B-mode power contains information on the multiplicative bias. We find that without priors on the residual multiplicative bias $delta m$ and stochastic ellipticity variance $sigma_e$ that constraints on the amplitude of the cosmic shear power spectrum are completely degenerate, and that when applying priors the constrained amplitude $A$ is slightly biased low via a classic marginalisation paradox. Using all-sky Gaussian random field simulations we find that the combination of $(1+2delta m)A$ is unbiased for a joint EE and BB power spectrum likelihood if the error and mean (precision and accuracy) of the stochastic ellipticity variance is known to better than $sigma(sigma_e)leq 0.05$ and $Deltasigma_eleq 0.01$, or the multiplicative bias is known to better than $sigma(m)leq 0.07$ and $Delta mleq 0.01$.
The statistics of peak counts in reconstructed shear maps contain information beyond the power spectrum, and can improve cosmological constraints from measurements of the power spectrum alone if systematic errors can be controlled. We study the effect of galaxy shape measurement errors on predicted cosmological constraints from the statistics of shear peak counts with the Large Synoptic Survey Telescope (LSST). We use the LSST image simulator in combination with cosmological N-body simulations to model realistic shear maps for different cosmological models. We include both galaxy shape noise and, for the first time, measurement errors on galaxy shapes. We find that the measurement errors considered have relatively little impact on the constraining power of shear peak counts for LSST.
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