Accurate measurement of the cluster mass function is a crucial element in efforts to constrain structure formation models, the normalisation of the matter power spectrum and the cosmological matter density, and the nature and evolution of dark energy. Large weak lensing surveys of ~20,000 galaxy clusters and groups will be key tools in the observational pursuit of that goal. These weak lensing studies often proceed by stacking the lensing signals of many clusters and groups binned by mass-correlated observables such as richness and luminosity; typically such analyses ignore the triaxial structure of dark matter halos on the assumption that the averaging of many shear signals within each mass bin makes its effects (as large as factors of two in mass model parameter estimates from individual clusters) negligible. We test this assumption and find that triaxiality can bias 3D virial mass estimates compared to those for a spherical population by a few percent if suboptimal mass estimators are used. This bias affects not only direct lensing constraints on the mass function but can also affect the scatter and normalization of the mass-observable relations derived from lensing that are so crucial to constraining the cluster mass function with large samples. However, we demonstrate that a careful choice of mass estimator can remove the bias very effectively if the lensing signals from a sufficient number of triaxial halos are averaged together, and further quantify that sufficient number for adequate shape averaging. We thus show that by choosing observable bins to contain an adequate number of halos and by utilizing a carefully chosen 3D mass estimator stacked weak-lensing analyses can give unbiased constraints on the triaxial mass function.
We present the optimal convergence and shear estimators for lensing reconstruction from the cosmic microwave background temperature field. This generalizes the deflection estimator, is sensitive to non-lensing modes, provides internal consistency checks, and is always at least as optimal. Previously, these estimators were only known in the squeezed limit. This paper decomposes convergence and shear fields into cosine and sine waves and the lensed correlation function is then Taylor expanded in the wave amplitudes. Maximizing the likelihood function gives the optimal estimators for the converge…
We introduce a new estimator of the CMB lensing power spectrum, together with its likelihood, based on iterative lensing reconstruction. Despite the increased complexity of the lensing maps, this estimator shares similarities with the standard quadratic estimator. Most importantly, it is unbiased towards the assumptions done on the noise and cosmology for the lensing reconstruction. This new spectrum estimator can double the constraints on the lensing amplitude compared to the quadratic estimator, while keeping numerical cost under control and being robust to errors.
We derive an estimator for the lensing potential from galaxy number counts which contains a linear and a quadratic term. We show that this estimator has a much larger signal-to-noise ratio than the corresponding estimator from intensity mapping. This is due to the additional lensing term in the number count angular power spectrum which is present already at linear order. We estimate the signal-to-noise ratio for future photometric surveys. Particularly at high redshifts, $z\gtrsim 1.5$, the signal to noise ratio can become of order 30. Therefore, the number counts in photometric surveys would …
Stacked lensing is a powerful means of measuring the average mass distribution around large-scale structure tracers. There are two stacked lensing estimators used in the literature, denoted as $ΔΣ$ and $γ_+$, which are related as $ΔΣ=Σ_{\rm cr}γ_+$, where $Σ_{\rm cr}(z_l,z_s)$ is the critical surface mass density for each lens-source pair ($z_l$ and $z_s$ are lens and source redshifts, respectively). In this paper we derive a formula for the covariance matrix of $ΔΣ$-estimator focusing on `weight' function to improve the signal-to-noise ($S/N$). We assume that the lensing fields and the distri…
I describe a method to estimate response matrices of Cosmic Microwave Background (CMB) lensing power spectra estimators to the true sky power under realistic conditions. Applicable to all lensing reconstruction pipelines based on quadratic estimators (QE), it uses a small number of Gaussian CMB Monte-Carlos and specially designed QE's in order to obtain sufficiently accurate matrices with little computational effort. This method may be used to improve the modelling of CMB lensing band-powers by incorporating at least some of the non-idealities encountered in CMB lensing reconstruction. These n…
In recent years, weak lensing of the cosmic microwave background (CMB) has emerged as a powerful tool to probe fundamental physics, such as neutrino masses, primordial non-Gaussianity, dark energy, and modified gravity. The prime target of CMB lensing surveys is the lensing potential, which is reconstructed from observed CMB temperature $T$ and polarization $E$ and $B$ fields. Until very recently, this reconstruction has been performed with quadratic estimators (QEs), which, although known to be suboptimal for high-sensitivity experiments, are numerically efficient, and useful to make forecast…
CMB lensing from current and upcoming wide-field CMB experiments such as AdvACT, SPT-3G and Simons Observatory relies heavily on temperature (vs. polarization). In this regime, foreground contamination to the temperature map produces significant lensing biases, which cannot be fully controlled by multi-frequency component separation, masking or bias hardening. In this letter, we split the standard CMB lensing quadratic estimator into a new set of optimal "multipole" estimators. On large scales, these multipole estimators reduce to the known magnification and shear estimators, and a new shear B…
This is the fourth in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. Here, we use measurements of weak gravitational lensing from the Weighing the Giants project to calibrate Chandra X-ray measurements of total mass that rely on the assumption of hydrostatic equilibrium. This comparison of X-ray and lensing masses provides a measurement of the combined bias of X-ray hydrostatic masses due to both astrophysical and instrumental sources. Assuming a fixed cosmology, and within a characteristic radius (r_2500) determined from the X-ray d…
Extragalactic foregrounds in temperature maps of the Cosmic Microwave Background (CMB) severely limit the ability of standard estimators to reconstruct the weak lensing potential. These foregrounds are not fully removable by multi-frequency cleaning or masking and can lead to large biases if not properly accounted for. For foregrounds made of a number of unclustered point sources, an estimator for the source amplitude can be derived and deprojected, removing any bias to the lensing reconstruction. We show with simulations that all of the extragalactic foregrounds in temperature can be approxim…
In this paper, we investigate whether galaxy assembly bias can reconcile the 20-40% disagreement between the observed galaxy projected clustering signal and the galaxy-galaxy lensing signal in the BOSS CMASS galaxy sample reported in Leauthaud et al. (2017). We use the suite of AbacusCosmos Lamda-CDM simulations at Planck best-fit cosmology and two flexible implementations of extended halo occupation distribution (HOD) models that incorporate galaxy assembly bias to build forward models and produce joint fits of the observed galaxy clustering signal and the galaxy-galaxy lensing signal. We fin…
Weak Lensing Peak Finding: Estimators, Filters, and Biases
剪切选择峰的大型目录最近已成为现实。为了正确解释这些峰的丰度和性质，有必要考虑到源星系之间以及与透镜的聚集效应。此外，在通量和尺寸有限的样品中透镜星系的首选导致与透镜场（透镜偏置）相关的表观源密度的波动。在本文中，我们研究这些问题的两个不同的选择剪切估计，这是目前常用的：全球归一化和局部归一化估计。虽然在原则上等同，在实践中，这些估计不同的系统效应，如透镜偏差和集群成员稀释。此外，我们发现，估计是统计上优越的取决于特定形状的滤波器用于峰值查找;次优选择的估计+滤波器组合可以导致抑制数量级的高峰。透镜偏置通常用于增加剪切峰的信噪比V;对于高峰值，增强可以大到Δ V ~ 1-2。由于峰丰度函数的陡度，这些提升可导致剪切峰丰度的显著增加。一篇配套论文（Rozo et al.，2010）在叠加弱透镜质量估计的背景下研究了这些相同的问题。
Weak gravitational lensing, the deflection of light by mass, is one of the best tools to constrain the growth of cosmic structure with time and reveal the nature of dark energy. I discuss the sources of systematic uncertainty in weak lensing measurements and their theoretical interpretation, including our current understanding and other options for future improvement. These include long-standing concerns such as the estimation of coherent shears from galaxy images or redshift distributions of galaxies selected based on photometric redshifts, along with systematic uncertainties that have receiv…
Polarization data will soon provide the best avenue for measurements of the CMB lensing potential, although it is potentially sensitive to several instrumental effects including beam asymmetry, polarization angle uncertainties, sky coverage, as well as analysis choices such as masking. We derive "bias-hardened" lensing estimators to mitigate these effects, at the expense of somewhat larger reconstruction noise, and test them numerically on simulated data. We find that the mean-field bias from masking is significant for the EE quadratic lensing estimator, however the bias-hardened estimator com…
This document was submitted as supporting material to an Engineering Change Proposal (ECP) for the Square Kilometre Array (SKA). This ECP requests gridded visibilities as an extra imaging data product from the SKA, in order to enable bespoke analysis techniques to measure source morphologies to the accuracy necessary for precision cosmology with radio weak lensing. We also discuss the properties of an SKA weak lensing data set and potential overlaps with other cosmology science goals.
We discuss detectability of the nonlinear growth of the large-scale structure in the cosmic microwave background (CMB) lensing. Lensing signals involved in CMB anisotropies have been measured from multiple CMB experiments, such as Atacama Cosmology Telescope (ACT), Planck, POLARBEAR, and South Pole Telescope (SPT). Reconstructed lensing signals are useful to constrain cosmology via their angular power spectrum, while detectability and cosmological application of their bispectrum induced by the nonlinear evolution are not well studied. Extending the analytic estimate of the galaxy lensing bispe…
We investigate the expected cosmological constraints from a combination of weak lensing and large-scale galaxy clustering using realistic redshift distributions. Introducing a systematic bias in the weak lensing redshift distributions (of 0.05 in redshift) produces a $>2σ$ bias in the recovered matter power spectrum amplitude and dark energy equation of state, for preliminary Stage III surveys. We demonstrate that these cosmological errors can be largely removed by marginalising over unknown biases in the assumed weak lensing redshift distributions, if we assume high quality redshift informati…
Accurate galaxy cluster mass measurements from the gravitational lensing of the cosmic microwave background temperature maps depend on mitigating potential biases from the cluster's own thermal Sunyaev-Zel'dovich (SZ) effect signal. Quadratic lensing estimators use a pair of maps to extract the lensing signal: a large scale gradient map and a small scale lensing map. The SZ bias can be eliminated by using an SZ-free map in the pair, with the gradient map being favored for signal-to-noise reasons. However, while this approach eliminates the bias, the SZ power in small scale lensing map adds ext…
We investigate the origin of $Λ$CDM parameter constraints in weak lensing, with a focus on the Hubble constant. We explain why current cosmic shear data are sensitive to the parameter combination $S_8 \propto σ_8 Ω_m^{0.5}$, improving upon previous studies through use of the halo model. Motivated by the ongoing discrepancy in measurements of the Hubble constant from high and low redshift, we explain why cosmic shear provides almost no constraint on $H_0$ by showing how the lensing angular power spectrum depends on physical length scales in the dark matter distribution. We derive parameter cons…
We develop a method of reconstructing the lensing field from lensed CMB temperature and polarization maps in real space as an alternative to the harmonic space estimators currently in use by extending an existing real space lensing estimator for temperature to polarization. Real space estimators have the advantage of being local in nature and they are thus equipped to deal with the nonuniform sky coverage, especially galactic cuts and point source excisions, found in experimental data. We characterize some of the properties and limitations of these estimators and test them on simulated maps wi…
Precise reconstruction of the cosmic microwave background lensing potential can be achieved with deep polarization surveys by iteratively removing lensing-induced $B$ modes. We introduce a lensing spectrum estimator and its likelihood for such optimal iterative reconstruction. Our modelling share similarities to the state-of-the-art likelihoods for quadratic estimator-based (QE) lensing reconstruction. In particular, we generalize the $N_L^{(0)}$ and $N_L^{(1)}$ lensing biases, and design a realization-dependent spectrum debiaser, making this estimator robust to uncertainties in the data model…
In this paper, we assemble a catalog of 118 strong gravitational lensing systems from SLACS, BELLS, LSD and SL2S surveys and use them to constrain the cosmic equation of state. In particular we consider two cases of dark energy phenomenology: $XCDM$ model where dark energy is modeled by a fluid with constant $w$ equation of state parameter and in Chevalier - Polarski - Linder (CPL) parametrization where $w$ is allowed to evolve with redshift: $w(z) = w_0 + w_1 \frac{z}{1+z}$. We assume spherically symmetric mass distribution in lensing galaxies, but relax the rigid assumption of SIS model in f…
On the cosmology dependence of the cluster weak-lensing mass bias
LMU Munich（慕尼黑大学）；INAF-Osservatorio Astronomico di Trieste（意大利天文学研究所的里雅斯特天文台）；Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理研究所）；Universität Innsbruck（因斯布鲁克大学）
Weak lensing has become an increasingly important tool in cosmology and the use of galaxy shapes to measure cosmic shear has become routine. The weak-lensing distortion tensor contains two other effects in addition to the two components of shear: the convergence and rotation. The rotation mode is not measurable using the standard cosmic shear estimators based on galaxy shapes, as there is no information on the original shapes of the images before they were lensed. Due to this, no estimator has been proposed for the rotation mode in cosmological weak-lensing surveys, and the rotation mode has n…
Ongoing and future wide-field galaxy surveys can be used to locate a number of clusters of galaxies with cosmic shear measurement alone. We study constraints on cosmological models using statistics of weak lensing selected galaxy clusters. We extend our previous theoretical framework to model the statistical properties of clusters in variants of cosmological models as well as in the standard $Λ$CDM model. Weak lensing selection of clusters does not rely on the conventional assumption such as the relation between luminosity and mass and/or hydrostatic equilibrium, but a number of observational …
We report a measurement of the power spectrum of cosmic microwave background (CMB) lensing from two seasons of Atacama Cosmology Telescope Polarimeter (ACTPol) CMB data. The CMB lensing power spectrum is extracted from both temperature and polarization data using quadratic estimators. We obtain results that are consistent with the expectation from the best-fit Planck LCDM model over a range of multipoles L=80-2100, with an amplitude of lensing A_lens = 1.06 +/- 0.15 (stat.) +/- 0.06 (sys.) relative to Planck. Our measurement of the CMB lensing power spectrum gives sigma_8 Omega_m^0.25 = 0.643 …
Double source lensing, with two sources lensed by the same foreground galaxy, involves the distance between each source and the lens and hence is a probe of the universe away from the observer. The double source distance ratio also reduces sensitivity to the lens model and has good complementarity with standard distance probes. We show that using this technique at high redshifts $z>1$, to be enabled by data from the Euclid satellite and other surveys, can give insights on dark energy, both in terms of $w_0$-$w_a$ and redshift binned density. We find a dark energy figure of merit of 245 from co…
Effect of gravitational magnification on the measurement of distance modulus of type Ia supernovae is presented. We investigate a correlation between magnification and Hubble residual to explore how the magnification affects the estimation of cosmological parameters. We estimate magnification of type Ia supernovae in two distinct methods: one is based on convergence mass reconstruction under the weak lensing limit and the other is based on the direct measurement from galaxies distribution. Both magnification measurements are measured from Subaru Hyper Suprime-Cam survey catalogue. For both mea…
Pinning down the total neutrino mass and the dark energy equation of state is a key aim for upcoming galaxy surveys. Weak lensing is a unique probe of the total matter distribution whose non-Gaussian statistics can be quantified by the one-point probability distribution function (PDF) of the lensing convergence. We calculate the convergence PDF on mildly non-linear scales from first principles using large-deviation statistics, accounting for dark energy and the total neutrino mass. For the first time, we comprehensively validate the cosmology-dependence of the convergence PDF model against lar…
We develop a Maximum Likelihood estimator (MLE) to measure the masses of galaxy clusters through the impact of gravitational lensing on the temperature and polarization anisotropies of the cosmic microwave background (CMB). We show that, at low noise levels in temperature, this optimal estimator outperforms the standard quadratic estimator by a factor of two. For polarization, we show that the Stokes Q/U maps can be used instead of the traditional E- and B-mode maps without losing information. We test and quantify the bias in the recovered lensing mass for a comprehensive list of potential sys…
Headline constraints on cosmological parameters from current weak lensing surveys are derived from two-point statistics that are known to be statistically sub-optimal, even in the case of Gaussian fields. We study the performance of a new fast implementation of the Quadratic Maximum Likelihood (QML) estimator, optimal for Gaussian fields, to test the performance of Pseudo-Cl estimators for upcoming weak lensing surveys and quantify the gain from a more optimal method. Through the use of realistic survey geometries, noise levels, and power spectra, we find that there is a decrease in the errors…
Mass calibration uncertainty is the largest systematic effect for using clusters of galaxies to constrain cosmological parameters. We present weak lensing mass measurements from the Canada-France-Hawaii Telescope Stripe 82 Survey for galaxy clusters selected through their high signal-to-noise thermal Sunyaev-Zeldovich (tSZ) signal measured with the Atacama Cosmology Telescope (ACT). For a sample of 9 ACT clusters with a tSZ signal-to-noise greater than five the average weak lensing mass is $\left(4.8\pm0.8\right)\,\times10^{14}\,\mathrm{M}_\odot$, consistent with the tSZ mass estimate of $\lef…
Despite the impressive success of the standard cosmological model, several anomalies defy its triumph. Among them is the so-called lensing anomaly: the Planck satellite observes stronger CMB gravitational lensing than expected. The role of neutrinos in this anomaly has been mostly overlooked, despite their key role in CMB lensing, because in the standard scenario they tend to increase the tension. Here, we show that this strongly depends on the assumed neutrino equation of state. We demonstrate that if neutrinos have yet undiscovered long-range interactions, the lensing pattern is significantl…
We explore synergies between the Nancy Grace Roman Space Telescope and CMB lensing data to constrain dark energy and modified gravity scenarios. A simulated likelihood analysis of the galaxy clustering and weak lensing data from the Roman Space Telescope High Latitude Survey combined with CMB lensing data from the Simons Observatory is undertaken, marginalizing over important astrophysical effects and calibration uncertainties. Included in the modeling are the effects of baryons on small-scale clustering, scale-dependent growth suppression by neutrinos, as well as uncertainties in the galaxy c…
Cosmology and Source Redshift Constraints from Galaxy Clustering and Tomographic Weak Lensing with HSC Y3 and SDSS using the Point-Mass Correction Model
