Weak Lensing Surveys Research Articles

Cosmology with Galaxy Cluster Weak Lensing: Statistical Limits and Experimental Design

Abstract We forecast constraints on the amplitude of matter clustering σ 8(z) achievable with the combination of cluster weak lensing and number counts, in current and next-generation weak lensing surveys. We advocate for an approach, analogous to galaxy–galaxy lensing, in which the observables in each redshift bin are the mean number counts and the mean weak lensing profile of clusters above a mass proxy threshold. The primary astrophysical nuisance parameter is the logarithmic scatter between the mass proxy and true mass near the threshold. For surveys similar to the Dark Energy Survey (DES), the Roman Space Telescope High Latitude Survey (HLS), and the Rubin Observatory Legacy Survey of Space and Time (LSST), we forecast aggregate precision on σ 8 of 0.26%, 0.24%, and 0.10%, respectively, if the mass–observable scatter is known externally to . These constraints would be degraded by about 20% for in the case of DES or HLS and for for LSST. A 1 month observing program with Roman Space Telescope targeting ∼2500 massive clusters could achieve a ∼ 0.5% constraint on σ 8(z = 0.7) on its own, or a ∼ 0.33% constraint in combination with the HLS. Realizing the constraining power of clusters Requires accurate knowledge of the mass–observable relation and stringent control of systematics. We provide analytic approximations to our numerical results that allow for easy scaling to other survey assumptions or other methods of cluster mass estimation.

Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys

ABSTRACT We investigate whether a Gaussian likelihood is sufficient to obtain accurate parameter constraints from a Euclid-like combined tomographic power spectrum analysis of weak lensing, galaxy clustering, and their cross-correlation. Testing its performance on the full sky against the Wishart distribution, which is the exact likelihood under the assumption of Gaussian fields, we find that the Gaussian likelihood returns accurate parameter constraints. This accuracy is robust to the choices made in the likelihood analysis, including the choice of fiducial cosmology, the range of scales included, and the random noise level. We extend our results to the cut sky by evaluating the additional non-Gaussianity of the joint cut-sky likelihood in both its marginal distributions and dependence structure. We find that the cut-sky likelihood is more non-Gaussian than the full-sky likelihood, but at a level insufficient to introduce significant inaccuracy into parameter constraints obtained using the Gaussian likelihood. Our results should not be affected by the assumption of Gaussian fields, as this approximation only becomes inaccurate on small scales, which in turn corresponds to the limit in which any non-Gaussianity of the likelihood becomes negligible. We nevertheless compare against N-body weak lensing simulations and find no evidence of significant additional non-Gaussianity in the likelihood. Our results indicate that a Gaussian likelihood will be sufficient for robust parameter constraints with power spectra from stage IV weak lensing surveys.

The Atacama Cosmology Telescope: A Catalog of >4000 Sunyaev–Zel’dovich Galaxy Clusters

Abstract We present a catalog of 4195 optically confirmed Sunyaev–Zel’dovich (SZ) selected galaxy clusters detected with signal-to-noise ratio >4 in 13,211 deg2 of sky surveyed by the Atacama Cosmology Telescope (ACT). Cluster candidates were selected by applying a multifrequency matched filter to 98 and 150 GHz maps constructed from ACT observations obtained from 2008 to 2018 and confirmed using deep, wide-area optical surveys. The clusters span the redshift range 0.04 < z < 1.91 (median z = 0.52). The catalog contains 222 z > 1 clusters, and a total of 868 systems are new discoveries. Assuming an SZ signal versus mass-scaling relation calibrated from X-ray observations, the sample has a 90% completeness mass limit of M 500c > 3.8 × 1014 M ⊙, evaluated at z = 0.5, for clusters detected at signal-to-noise ratio >5 in maps filtered at an angular scale of 2.′4. The survey has a large overlap with deep optical weak-lensing surveys that are being used to calibrate the SZ signal mass-scaling relation, such as the Dark Energy Survey (4566 deg2), the Hyper Suprime-Cam Subaru Strategic Program (469 deg2), and the Kilo Degree Survey (825 deg2). We highlight some noteworthy objects in the sample, including potentially projected systems, clusters with strong lensing features, clusters with active central galaxies or star formation, and systems of multiple clusters that may be physically associated. The cluster catalog will be a useful resource for future cosmological analyses and studying the evolution of the intracluster medium and galaxies in massive clusters over the past 10 Gyr.

Self-calibration of weak lensing systematic effects using combined two- and three-point statistics

ABSTRACT We investigate the prospects for using the weak lensing bispectrum alongside the power spectrum to control systematic uncertainties in a Euclid-like survey. Three systematic effects are considered: the intrinsic alignment of galaxies, uncertainties in the means of tomographic redshift distributions, and multiplicative bias in the measurement of the shear signal. We find that the bispectrum is very effective in mitigating these systematic errors. Varying all three systematics simultaneously, a joint power spectrum and bispectrum analysis reduces the area of credible regions for the cosmological parameters Ωm and σ8 by a factor of 90 and for the two parameters of a time-varying dark energy equation of state by a factor of almost 20, compared with the baseline approach of using the power spectrum alone and of imposing priors consistent with the accuracy requirements specified for Euclid. We also demonstrate that including the bispectrum self-calibrates all three systematic effects to the stringent levels required by the forthcoming generation of weak lensing surveys, thereby reducing the need for external calibration data.

κTNG: effect of baryonic processes on weak lensing with IllustrisTNG simulations

ABSTRACT We study the effect of baryonic processes on weak lensing (WL) observables with a suite of mock WL maps, the κTNG, based on the cosmological hydrodynamic simulations IllustrisTNG. We quantify the baryonic effects on the WL angular power spectrum, one-point probability distribution function (PDF), and number counts of peaks and minima. We also show the redshift evolution of the effects, which is a key to distinguish the effect of baryons from fundamental physics such as dark energy, dark matter, and massive neutrinos. We find that baryonic processes reduce the small-scale power, suppress the tails of the PDF, peak and minimum counts, and change the total number of peaks and minima. We compare our results to existing semi-analytical models and hydrodynamic simulations, and discuss the source of discrepancies. The κTNG suite includes 10 000 realizations of $5 \times 5 \, \mathrm{deg}^2$ maps for 40 source redshifts up to zs = 2.6, well covering the range of interest for existing and upcoming WL surveys. We also produce the κTNG-Dark suite of maps, generated based on the corresponding dark matter-only IllustrisTNG simulations. Our mock maps are not only suitable for developing analytical models that incorporate the effect of baryons, but also particularly useful for studies that rely on mass maps, such as non-Gaussian statistics and machine learning with convolutional neural networks. The suite of mock maps is publicly available at Columbia Lensing (http://columbialensing.org).

Tightening weak lensing constraints on the ellipticity of galaxy-scale dark matter haloes

Cosmological simulations predict that galaxies are embedded into triaxial dark matter haloes, which appear approximately elliptical in projection. Weak gravitational lensing allows us to constrain these halo shapes and thereby test the nature of dark matter. Weak lensing has already provided robust detections of the signature of halo flattening at the mass scales of groups and clusters, whereas results for galaxies have been somewhat inconclusive. Here we combine data from five weak lensing surveys (NGVSLenS, KiDS/KV450, CFHTLenS, CS82, and RCSLenS, listed in order of most to least constraining) in order to tighten observational constraints on galaxy-scale halo ellipticity for photometrically selected lens samples. We constrain fh, the average ratio between the aligned component of the halo ellipticity and the ellipticity of the light distribution, finding fh = 0.303−0.079+0.080 for red lens galaxies and fh = 0.217−0.159+0.160 for blue lens galaxies when assuming elliptical Navarro-Frenk-White density profiles and a linear scaling between halo ellipticity and galaxy ellipticity. Our constraints for red galaxies constitute the currently most significant (3.8σ) systematics-corrected detection of the signature of halo flattening at the mass scale of galaxies. Our results are in good agreement with expectations from the Millennium Simulation that apply the same analysis scheme and incorporate models for galaxy–halo misalignment. Assuming these misalignment models and the analysis assumptions stated above are correct, our measurements imply an average dark matter halo ellipticity for the studied red galaxy samples of ⟨|ϵh|⟩ = 0.174 ± 0.046, where |ϵh| = (1 − q)/(1 + q) relates to the ratio q = b/a of the minor and major axes of the projected mass distribution. Similar measurements based on larger upcoming weak lensing data sets can help to calibrate models for intrinsic galaxy alignments, which constitute an important source of systematic uncertainty in cosmological weak lensing studies.

Cross-correlating radio continuum surveys and CMB lensing: constraining redshift distributions, galaxy bias, and cosmology

ABSTRACT We measure the harmonic-space auto-power spectrum of the galaxy overdensity in the LOFAR Two-metre Sky Survey (LoTSS) first data release and its cross-correlation with the map of the lensing convergence of the cosmic microwave background (CMB) from the Planck collaboration. We report a ∼5σ detection of the cross-correlation. We show that the combination of the clustering power spectrum and CMB lensing cross-correlation allows us to place constraints on the high-redshift tail of the redshift distribution, one of the largest sources of uncertainty in the use of continuum surveys for cosmology. Our analysis shows a preference for a broader redshift tail than that predicted by the photometric redshifts contained in the LoTSS value-added catalogue, as expected, and more compatible with predictions from simulations and spectroscopic data. Although the ability of CMB lensing to constrain the width and tail of the redshift distribution could also be valuable for the analysis of current and future photometric weak lensing surveys, we show that its performance relies strongly on the redshift evolution of the galaxy bias. Assuming the redshift distribution predicted by the Square Kilometre Array Design simulations, we use our measurements to place constraints on the linear bias of radio galaxies and the amplitude of matter inhomogeneities σ8, finding $\sigma _8=0.69^{+0.14}_{-0.21}$ assuming the galaxy bias scales with the inverse of the linear growth factor, and $\sigma _8=0.79^{+0.17}_{-0.32}$ assuming a constant bias.

Cosmological forecast for non-Gaussian statistics in large-scale weak lensing surveys

Cosmic shear data contains a large amount of cosmological information encapsulated in the non-Gaussian features of the weak lensing mass maps. Weak lensing studies mostly rely on two-point statistics to constrain cosmology from cosmic shear data, that do not capture all of this information. Additional non-Gaussian information can be extracted using non-Gaussian statistics. We compare the constraining power in the Ωm–σ8 plane of three map-based non-Gaussian statistics with the angular power spectrum, namely; peak counts, minimum counts and Minkowski functionals. We further analyze the impact of tomography and systematic effects originating from galaxy intrinsic alignments, multiplicative shear bias and photometric redshift systematics. We forecast the performance of the statistics for a stage-3-like weak lensing survey, spanning an area of 5000 deg2 and restrict ourselves to scales ⩾ 10 arcmin to avoid baryonic effects. The study follows a forward modelling scheme to predict the statistics at different cosmologies based on N-Body simulations. We find, that in our setup, the considered non-Gaussian statistics provide tighter constraints than the angular power spectrum. The peak counts show the greatest potential, increasing the figure-of-Merit (FoM) in the Ωm–σ8 plane by a factor of about 6, while the minimum counts and the Minkowski functionals yield an increase by a factor of about 3 and 2, respectively. A combined analysis using all non-Gaussian statistics in addition to the power spectrum increases the FoM by a factor of 9 and reduces the error on S8 by ≈ 30%. We find that the importance of tomography is diminished when combining non-Gaussian statistics with the angular power spectrum. The non-Gaussian statistics indeed profit less from tomography and the minimum counts and Minkowski functionals add some robustness against galaxy intrinsic alignment in a non-tomographic setting. We further find that a combination of the angular power spectrum and the non-Gaussian statistics allows us to apply conservative scale cuts in the analysis, thus helping to minimize the impact of baryonic and relativistic effects, while conserving the cosmological constraining power. We make the code that was used to conduct this analysis publicly available to simplify performing such analyses in the future.

Minimizing the impact of scale-dependent galaxy bias on the joint cosmological analysis of large-scale structures

ABSTRACT We present a mitigation strategy to reduce the impact of non-linear galaxy bias on the joint ‘3 × 2pt’ cosmological analysis of weak lensing and galaxy surveys. The Ψ-statistics that we adopt are based on Complete Orthogonal Sets of E/B Integrals. As such they are designed to minimize the contributions to the observable from the smallest physical scales where models are highly uncertain. We demonstrate that Ψ-statistics carry the same constraining power as the standard two-point galaxy clustering and galaxy–galaxy lensing statistics, but are significantly less sensitive to scale-dependent galaxy bias. Using two galaxy bias models, motivated by halo model fits to data and simulations, we quantify the error in a standard 3 × 2pt analysis where constant galaxy bias is assumed. Even when adopting conservative angular scale cuts, that degrade the overall cosmological parameter constraints, we find of order 1σ biases for Stage III surveys on the cosmological parameter S8 = σ8(Ωm/0.3)α. This arises from a leakage of the smallest physical scales to all angular scales in the standard two-point correlation functions. In contrast, when analysing Ψ-statistics under the same approximation of constant galaxy bias, we show that the bias on the recovered value for S8 can be decreased by a factor of ∼2, with less conservative scale cuts. Given the challenges in determining accurate galaxy bias models in the highly non-linear regime, we argue that 3 × 2pt analyses should move towards new statistics that are less sensitive to the smallest physical scales.

Photo-z outlier self-calibration in weak lensing surveys

Calibrating photometric redshift errors in weak lensing surveys with external data is extremely challenging. We show that both Gaussian and outlier photo-z parameters can be self-calibrated from the data alone. This comes at no cost for the neutrino masses, curvature and dark energy equation of state w0, but with a 65% degradation when both w0 and wa are varied. We perform a realistic forecast for the Vera Rubin Observatory (VRO) Legacy Survey of Space and Time (LSST) 3× 2 analysis, combining cosmic shear, projected galaxy clustering and galaxy—galaxy lensing. We confirm the importance of marginalizing over photo-z outliers. We examine a subset of internal cross-correlations, dubbed “null correlations”, which are usually ignored in 3× 2 analyses. Despite contributing only ∼ 10% of the total signal-to-noise, these null correlations improve the constraints on photo-z parameters by up to an order of magnitude. Using the same galaxy sample as sources and lenses dramatically improves the photo-z uncertainties too. Together, these methods add robustness to any claim of detected new Physics, and reduce the statistical errors on cosmology by 15% and 10% respectively. Finally, including CMB lensing from an experiment like Simons Observatory or CMB-S4 improves the cosmological and photo-z posterior constraints by about 10%, and further improves the robustness to systematics. To give intuition on the Fisher forecasts, we examine in detail several toy models that explain the origin of the photo-z self-calibration. Our Fisher code LaSSI (Large-Scale Structure Information), which includes the effect of Gaussian and outlier photo-z, shear multiplicative bias, linear galaxy bias, and extensions to LCDM, is publicly available at \\href{https://github.com/EmmanuelSchaan/LaSSI}{https://github.com/EmmanuelSchaan/LaSSI}.

Cross-correlation between Subaru Hyper Suprime-Cam Galaxy Weak Lensing and Planck Cosmic Microwave Background Lensing

Abstract Cross-correlations between galaxy weak lensing (WL) and cosmic microwave background (CMB) lensing are powerful tools to probe matter fluctuations at intermediate redshifts and to detect residual systematics in either probe. In this paper, we study the cross-correlation of galaxy WL from the Hyper Suprime-Cam Subaru Strategic Program (HSC) first data release and CMB lensing from the final Planck data release, for HSC source galaxies at 0.3 ≤ z ≤ 1.5. HSC is the deepest Stage-III galaxy WL survey, and provides a great opportunity to study the high-redshift universe. It also presents new challenges related to its exceptionally high source density, such as source blending. The cross-correlation signal is measured at a significance level of 3.1σ. The amplitude of our best-fit model with respect to the best-fit 2018 Planck cosmology is A = 0.81 ± 0.25, consistent with A = 1. Our result is also consistent with previous CMB lensing and galaxy WL cross-correlation studies using different surveys. We perform tests with respect to the WL B-modes, the point-spread-function, photometric redshift errors, and thermal Sunyaev–Zel’dovich leakage, and find no significant evidence of residual systematics.

Optimizing tomography for weak gravitational lensing surveys

ABSTRACT The subject of this paper is optimization of weak lensing tomography: we carry out numerical minimization of a measure of total statistical error as a function of the redshifts of the tomographic bin edges by means of a Nelder–Mead algorithm in order to optimize the sensitivity of weak lensing with respect to different optimization targets. Working under the assumption of a Gaussian likelihood for the parameters of a w0wa CDM (cold dark matter) model and using euclid’s conservative survey specifications, we compare an equipopulated, equidistant, and optimized bin setting and find that in general the equipopulated setting is very close to the optimal one, while an equidistant setting is far from optimal and also suffers from the ad hoc choice of a maximum redshift. More importantly, we find that nearly saturated information content can be gained using already few tomographic bins. This is crucial for photometric redshift surveys with large redshift errors. We consider a large range of targets for the optimization process that can be computed from the parameter covariance (or equivalently, from the Fisher matrix), extend these studies to information entropy measures such as the Kullback–Leibler divergence and conclude that in many cases equipopulated binning yields results close to the optimum, which we support by analytical arguments.

A synthetic Roman Space Telescope High-Latitude Imaging Survey: simulation suite and the impact of wavefront errors on weak gravitational lensing

ABSTRACT The Nancy Grace Roman Space Telescope (Roman) mission is expected to launch in the mid-2020s. Its weak lensing program is designed to enable unprecedented systematics control in photometric measurements, including shear recovery, point spread function (PSF) correction, and photometric calibration. This will enable exquisite weak lensing science and allow us to adjust to and reliably contribute to the cosmological landscape after the initial years of observations from other concurrent Stage IV dark energy experiments. This potential requires equally careful planning and requirements validation as the mission prepares to enter its construction phase. We present a suite of image simulations based on galsim that are used to construct a complex, synthetic Roman weak lensing survey that incorporates realistic input galaxies and stars, relevant detector non-idealities, and the current reference 5-yr Roman survey strategy. We present a first study to empirically validate the existing Roman weak lensing requirements flowdown using a suite of 12 matched image simulations, each representing a different perturbation to the wavefront or image motion model. These are chosen to induce a range of potential static and low- and high-frequency time-dependent PSF model errors. We analyse the measured shapes of galaxies from each of these simulations and compare them to a reference, fiducial simulation to infer the response of the shape measurement to each of these modes in the wavefront model. We then compare this to existing analytic flowdown requirements, and find general agreement between the empirically derived response and that predicted by the analytic model.

Sparse Bayesian mass-mapping with uncertainties: Full sky observations on the celestial sphere

ABSTRACT To date weak gravitational lensing surveys have typically been restricted to small fields of view, such that the flat-sky approximation has been sufficiently satisfied. However, with Stage IV surveys (e.g. LSST and Euclid) imminent, extending mass-mapping techniques to the sphere is a fundamental necessity. As such, we extend the sparse hierarchical Bayesian mass-mapping formalism presented in previous work to the spherical sky. For the first time, this allows us to construct maximum a posteriori spherical weak lensing dark-matter mass-maps, with principled Bayesian uncertainties, without imposing or assuming Gaussianty. We solve the spherical mass-mapping inverse problem in the analysis setting adopting a sparsity promoting Laplace-type wavelet prior, though this theoretical framework supports all log-concave posteriors. Our spherical mass-mapping formalism facilitates principled statistical interpretation of reconstructions. We apply our framework to convergence reconstruction on high resolution N-body simulations with pseudo-Euclid masking, polluted with a variety of realistic noise levels, and show a significant increase in reconstruction fidelity compared to standard approaches. Furthermore, we perform the largest joint reconstruction to date of the majority of publicly available shear observational data sets (combining DESY1, KiDS450, and CFHTLens) and find that our formalism recovers a convergence map with significantly enhanced small-scale detail. Within our Bayesian framework we validate, in a statistically rigorous manner, the community’s intuition regarding the need to smooth spherical Kaiser-Squires estimates to provide physically meaningful convergence maps. Such approaches cannot reveal the small-scale physical structures that we recover within our framework.

Void halo mass function: A promising probe of neutrino mass

Cosmic voids, the underdense regions in the universe, are particularly sensitive to diffuse density components such as cosmic neutrinos. This sensitivity is enhanced by the match between void sizes and the free-streaming scale of massive neutrinos. Using the massive neutrino simulations massivenus, we investigate the effect of neutrino mass on dark matter halos as a function of environment. We find that the halo mass function depends strongly on neutrino mass and that this dependence is more pronounced in voids than in high-density environments. An observational program that measured the characteristic mass of the most massive halos in voids should be able to place novel constraints on the sum of the masses of neutrinos $\ensuremath{\sum}{m}_{\ensuremath{\nu}}$. The neutrino mass effect in the simulations is quite strong: In a ${512}^{3}\text{ }\text{ }{h}^{\ensuremath{-}3}\text{ }{\mathrm{Mpc}}^{3}$ survey, the mean mass of the 1000 most massive halos in the void interiors is $(4.82\ifmmode\pm\else\textpm\fi{}0.11)\ifmmode\times\else\texttimes\fi{}{10}^{12}\text{ }\text{ }{h}^{\ensuremath{-}1}\text{ }{M}_{\ensuremath{\bigodot}}$ for $\ensuremath{\sum}{m}_{\ensuremath{\nu}}=0.6\text{ }\text{ }\mathrm{eV}$ and $(8.21\ifmmode\pm\else\textpm\fi{}0.13)\ifmmode\times\else\texttimes\fi{}{10}^{12}\text{ }\text{ }{h}^{\ensuremath{-}1}\text{ }{M}_{\ensuremath{\bigodot}}$ for $\ensuremath{\sum}{m}_{\ensuremath{\nu}}=0.1\text{ }\text{ }\mathrm{eV}$. Subaru (SuMIRe), Euclid and WFIRST will have both spectroscopic and weak lensing surveys. Covering volumes at least 50 times larger than our simulations, they should be sensitive probes of neutrino mass through void substructure.

Accessing the high- ℓ frontier under the reduced shear approximation with k -cut cosmic shear

The precision of Stage IV cosmic shear surveys will enable us to probe smaller physical scales than ever before, however, model uncertainties from baryonic physics and non-linear structure formation will become a significant concern. The $k$-cut method -- applying a redshift-dependent $\ell$-cut after making the Bernardeau-Nishimichi-Taruya transform -- can reduce sensitivity to baryonic physics; allowing Stage IV surveys to include information from increasingly higher $\ell$-modes. Here we address the question of whether it can also mitigate the impact of making the reduced shear approximation; which is also important in the high-$\kappa$, small-scale regime. The standard procedure for relaxing this approximation requires the repeated evaluation of the convergence bispectrum, and consequently can be prohibitively computationally expensive when included in Monte Carlo analyses. We find that the $k$-cut cosmic shear procedure suppresses the $w_0w_a$CDM cosmological parameter biases expected from the reduced shear approximation for Stage IV experiments, when $\ell$-modes up to $5000$ are probed. The maximum cut required for biases from the reduced shear approximation to be below the threshold of significance is at $k = 5.37 \, h{\rm Mpc}^{-1}$. With this cut, the predicted $1\sigma$ constraints increase, relative to the case where the correction is directly computed, by less than $10\%$ for all parameters. This represents a significant improvement in constraints compared to the more conservative case where only $\ell$-modes up to 1500 are probed, and no $k$-cut is used. We also repeat this analysis for a hypothetical, comparable kinematic weak lensing survey. The key parts of code used for this analysis are made publicly available.

Cosmological consequences of intrinsic alignments supersample covariance

ABSTRACT We examine cosmological constraints from high-precision weak-lensing surveys including supersample covariance (SSC) due to the finite survey volume. Specifically, we focus on the contribution of beat coupling in the intrinsic alignments as a part of full cosmic shear signal under flat-sky approximation. The SSC-effect grows by going to lower redshift bin and indicates considerable footprint on the intermediate and high multipoles for cumulative signal-to-noise ratio (SNR). The SNR is reduced by $\approx 10{{\ \rm per\ cent}}$ as a consequence of including the intrinsic alignment SSC, for the full cosmic shear signal, depending on the amplitude of intrinsic alignments, the ellipticity dispersion, and the survey redshift ranges, while the contribution of photometric redshift error can be ignored in the cumulative SNR. Using the Fisher-matrix formalism, we find that the impact of large modes beyond the volume of the surveys on the small modes alters the intrinsic alignments. However, corresponding impact on the cosmological parameters’ estimation is marginal compared to that of for gravitational weak lensing, particularly, when all available redshift bins are considered. Our results also demonstrate that including SSC-effect on the intrinsic alignments in the analytical covariance matrix of full cosmic shear leads to increase marginally the confidence interval for σ8 by $\approx 10{{\ \rm per\ cent}}$ for a sample with almost high intrinsic alignment amplitude.

Fast estimation of aperture mass statistics – I. Aperture mass variance and an application to the CFHTLenS data

ABSTRACT We explore an alternative method to the usual shear correlation function approach for the estimation of aperture mass statistics in weak lensing survey data. Our approach builds on the direct estimator method. In this paper, to test and validate the methodology, we focus on the aperture mass dispersion. After computing the signal and noise for a weighted set of measured ellipticites we show how the direct estimator can be made into a linear order algorithm that enables a fast and efficient computation. We then investigate the applicability of the direct estimator approach in the presence of a real survey mask with holes and chip gaps. For this we use a large ensemble of full ray-tracing mock simulations. By using various weighting schemes for combining information from different apertures we find that inverse variance weighting the individual aperture estimates with an aperture completeness greater than 70 per cent yields an answer that is in close agreement with the correlation function approach. We then apply this approach to the CFHTLenS as a pilot scheme and find that our method recovers to high accuracy the official result for the variance of both the E- and B-mode signal. We then explore the cosmological information content of the direct estimator using the Fisher information approach. We show that there is a only modest loss in cosmological information from the rejection of apertures that are of low completeness. This method unlocks the door to efficient methods for recovering higher order aperture mass statistics in linear order operations.

Higher order spectra of weak lensing convergence maps in parametrized theories of modified gravity

ABSTRACT We compute the low-ℓ limit of the family of higher order spectra for projected (2D) weak lensing convergence maps. In this limit these spectra are computed to an arbitrary order using tree-level perturbative calculations. We use the flat-sky approximation and Eulerian perturbative results based on a generating function approach. We test these results for the lower order members of this family, i.e. the skew- and kurt-spectra against state-of-the-art simulated all-sky weak lensing convergence maps and find our results to be in very good agreement. We also show how these spectra can be computed in the presence of a realistic sky-mask and Gaussian noise. We generalize these results to 3D and compute the equal-time higher order spectra. These results will be valuable in analysing higher order statistics from future all-sky weak lensing surveys such as the Euclid survey at low-ℓ modes. As illustrative examples, we compute these statistics in the context of the Horndeski and beyond Horndeski theories of modified gravity. They will be especially useful in constraining theories such as the Gleyzes–Langlois–Piazza–Vernizzi (GLPV) theories and degenerate higher order scalar-tensor theories as well as the commonly used normal-branch of Dvali–Gabadadze–Porrati model, clustering quintessence models and scenarios with massive neutrinos.

A hydrodynamical halo model for weak-lensing cross correlations

On the scale of galactic haloes, the distribution of matter in the cosmos is affected by energetic, non-gravitational processes, the so-called baryonic feedback. A lack of knowledge about the details of how feedback processes redistribute matter is a source of uncertainty for weak-lensing surveys, which accurately probe the clustering of matter in the Universe over a wide range of scales. We developed a cosmology-dependent model for the matter distribution that simultaneously accounts for the clustering of dark matter, gas, and stars. We informed our model by comparing it to power spectra measured from theBAHAMASsuite of hydrodynamical simulations. In addition to considering matter power spectra, we also considered spectra involving the electron-pressure field, which directly relates to the thermal Sunyaev-Zel’dovich (tSZ) effect. We fitted parameters in our model so that it can simultaneously model both matter and pressure data and such that the distribution of gas as inferred from tSZ has an influence on the matter spectrum predicted by our model. We present two variants, one that matches the feedback-induced suppression seen in the matter–matter power spectrum at the percent level and a second that matches the matter–matter data to a slightly lesser degree (≃2%). However, the latter is able to simultaneously model the matter–electron pressure spectrum at the ≃15% level. We envisage our models being used to simultaneously learn about cosmological parameters and the strength of baryonic feedback using a combination of tSZ and lensing auto- and cross-correlation data.