A new stochastic approach to cumulative weak lensing
Kimmo Kainulainen, Valerio Marra
备注：
20 pages, 11 figures; replaced to match the version accepted for publication in Phys. Rev. D. The turboGL package [v0.3] can be downloaded at http://www.turbogl.org/
We study the weak gravitational lensing effects caused by a stochastic distribution of dark matter halos. We develop a simple approach to calculate the magnification probability distribution function which allows us to easily compute the magnitude bias and dispersion for an arbitrary data sample and a given universe model. As an application we consider the effects of single-mass large-scale cosmic inhomogeneities to the SNe magnitude-redshift relation, and conclude that such structures could bias the PDF enough to affect the extraction of cosmological parameters from the limited size of present-day SNe data samples. We also release turboGL, a simple and very fast (<= 1s) Mathematica code based on the method here presented.
A stochastic gravitational wave background (SGWB) will affect the CMB anisotropies via weak lensing. Unlike weak lensing due to large scale structure which only deflects photon trajectories, a SGWB has an additional effect of rotating the polarization vector along the trajectory. We study the relative importance of these two effects, deflection \& rotation, specifically in the context of E-mode to B-mode power transfer caused by weak lensing due to SGWB. Using weak lensing distortion of the CMB as a probe, we derive constraints on the spectral energy density ($Ω_{GW}$) of the SGWB, sourced at …
Gravitational waves (GWs) are subject to gravitational lensing in the same way as electromagnetic radiation. However, to date, no unequivocal observation of a lensed GW transient has been reported. Independently, GW observatories continue to search for the stochastic GW signal which is produced by many transient events at high redshift. We exploit a surprising connection between the lensing of individual transients and limits to the background radiation produced by the unresolved population of binary back hole mergers: we show that it constrains the fraction of individually resolvable lensed b…
In the advent of large scale surveys, individually modelling strong-gravitational lenses and their counterpart time-delays in order to precisely measure $H_0$ will become computationally expensive, and highly complex. A complimentary approach is to study the cumulative distribution function (CDF) of time-delays where the global population of lenses is modelled along with $H_0$. In this paper we use a suite of hydro-dynamical simulations to estimate the CDF of time-delays from doubly-imaged quasars for a realistic distribution of lenses. We find that the CDFs exhibit large amounts of halo-halo …
On the scale of the light beams subtended by small sources, e.g. supernovae, matter cannot be accurately described as a fluid, which questions the applicability of standard cosmic lensing to those cases. In this article, we propose a new formalism to deal with small-scale lensing as a diffusion process: the Sachs and Jacobi equations governing the propagation of narrow light beams are treated as Langevin equations. We derive the associated Fokker-Planck-Kolmogorov equations, and use them to deduce general analytical results on the mean and dispersion of the angular distance. This formalism is …
The anisotropies of the Stochastic Gravitational-Wave Background (SGWB) produced by merging compact binaries constitute a possible new probe of the Large-Scale Structure (LSS). However, the significant shot noise contribution caused by the discreteness of the GW sources and the poor angular resolution of the instruments hamper the detection of the intrinsic anisotropies induced by the LSS. In this work, we investigate the potential of cross-correlating forthcoming high precision measurements of the SGWB energy density and the Cosmic Microwave Background (CMB) lensing convergence to mitigate th…
General relativity predicts that the rotational momentum flux of matter twists the spacetime via a vector gravitomagnetic (frame-dragging) field, which remains undetected in cosmology. This vector field induces an additional gravitational lensing effect; at the same time, the momentum field sources the kinetic Sunyaev-Zel'dovich (kSZ) effect. The common origin of these two effects allows us to probe the gravitomagnetic signal via their cross-correlations. In this paper, we explore the possibility of detecting the gravitomagnetic field in $Λ$CDM by cross-correlating the weak-lensing convergence…
Strong lensing of gravitational waves is more likely for distant sources but predicted event rates are highly uncertain with many astrophysical origins proposed. Here we open a new avenue to estimate the event rate of strongly lensed systems by exploring the amplitude of the stochastic gravitational wave background (SGWB). This method can provide a direct upper bound on the high redshift binary coalescing rates, which can be translated into an upper bound on the expected rate of strongly lensed systems. We show that from the ongoing analysis of the Laser Interferometer Gravitational-wave Obser…
We revise and extend the stochastic approach to cumulative weak lensing (hereafter the sGL method) first introduced in Ref. [1]. Here we include a realistic halo mass function and density profiles to model the distribution of mass between and within galaxies, galaxy groups and galaxy clusters. We also introduce a modeling of the filamentary large-scale structures and a method to embed halos into these structures. We show that the sGL method naturally reproduces the weak lensing results for the Millennium Simulation. The strength of the sGL method is that a numerical code based on it can comput…
A stochastic gravitational wave background (SGWB) would gravitationally lens the cosmic microwave background (CMB) photons. We find that the lensing due to gravitational waves(GW) is more efficient as compared to lensing due to scalar density perturbations. Though the effect of lensing due to GW is found to effect all the four CMB power spectra, its effect is most prominently seen in the CMB polarization power spectra. This suggests that the measurements of the CMB angular power spectra could be used to constraining the energy density ($Ω_{GW}$) of the SGBW. In our analysis we find that the mo…
Mass clumps in gravitational lens galaxies can perturb lensed images in characteristic ways. Strong lens flux ratios have been used to constrain the amount of dark matter substructure in lens galaxies, and various other observables have been considered as additional probes of substructure. We study the general theory of lensing with stochastic substructure in order to understand how lensing observables depend on the mass function and spatial distribution of clumps. We find that magnification perturbations are mainly sensitive to the total mass in substructure projected near the lensed images; …
Sky masking is unavoidable in wide-field weak lensing observations. We study how masks affect the measurement of statistics of matter distribution probed by weak gravitational lensing. We first use 1000 cosmological ray-tracing simulations to examine in detail the impact of masked regions on the weak lensing Minkowski Functionals (MFs). We consider actual sky masks used for a Subaru Suprime-Cam imaging survey. The masks increase the variance of the convergence field and the expected values of the MFs are biased. The bias then affects the non-Gaussian signals induced by the gravitational growth…
We study the impact of baryonic processes and massive neutrinos on weak lensing peak statistics that can be used to constrain cosmological parameters. We use the BAHAMAS suite of cosmological simulations, which self-consistently include baryonic processes and the effect of massive neutrino free-streaming on the evolution of structure formation. We construct synthetic weak lensing catalogues by ray-tracing through light-cones, and use the aperture mass statistic for the analysis. The peaks detected on the maps reflect the cumulative signal from massive bound objects and general large-scale stru…
Cross-correlations between the lensing of the cosmic microwave background (CMB) and other tracers of large-scale structure provide a unique way to reconstruct the growth of dark matter, break degeneracies between cosmology and galaxy physics, and test theories of modified gravity. We detect a cross-correlation between DESI-like luminous red galaxies (LRGs) selected from DECaLS imaging and CMB lensing maps reconstructed with the Planck satellite at a significance of $S/N = 27.2$ over scales $\ell_{\rm min} = 30$, $\ell_{\rm max} = 1000$. To correct for magnification bias, we determine the slope…
The halo model (HM) describes the inhomogeneous universe as a collection of halos. The full nonlinear power spectrum of the universe is well approximated by the HM, whose prediction can be easily computed without lengthy numerical simulations. This makes the HM a useful tool in cosmology. Here we explore the lensing properties of the HM by use of the stochastic gravitational lensing (sGL) method. We obtain for the case of point sources exact and simple integral expressions for the expected value and variance of the lensing convergence, which encode detailed information about the internal halo …
The scatter in the apparent magnitude of type Ia supernovae induced by stochastic gravitational lensing is highly dependent on the nonlinear growth of cosmological structure. In this paper, we show that such a dependence can potentially be employed to gain significant information about the mass clustering at small scales. While the mass clustering ultimately hinges on cosmology, here we demonstrate that, upon obtaining more precise observational measurements through future cosmological surveys, the lensing dispersion can very effectively be used to gain information on the poorly understood ast…
In the theory of structure formation, galaxies are biased tracers of the underlying matter density field. The statistical relation between galaxy and matter density field is commonly referred as galaxy bias. In this paper, we test the linear bias model with weak-lensing and galaxy clustering measurements in the 2 square degrees COSMOS field (Scoville et al. 2007). We estimate the bias of galaxies between redshifts z=0.2 and z=1, and over correlation scales between R=0.2 h^-1 Mpc and R=15 h^-1 Mpc. We focus on three galaxy samples, selected in flux (simultaneous cuts I_814W < 26.5 and K_s < 24)…
The weak gravitational lensing distortion of distant galaxy images (defined as sources) probes the projected large-scale matter distribution in the Universe. To improve quality in the 3D mass mapping using 3D-lensing, we combine the lensing information with the spatial clustering of a population of galaxies that trace the matter density with a known galaxy bias (defined as tracers). For our minimum variance estimator, merely all the second-order bias of the tracers has to be known, which can in principle be self-consistently constrained in the data by lensing techniques. This synergy introduce…
Upcoming wide-area weak lensing surveys are expensive both in time and cost and require an optimal survey design in order to attain maximum scientific returns from a fixed amount of available telescope time. The super-sample covariance (SSC), which arises from unobservable modes that are larger than the survey size, significantly degrades the statistical precision of weak lensing power spectrum measurement even for a wide-area survey. Using the 1000 mock realizations of the log-normal model, which approximates the weak lensing field for a $Λ$-dominated cold dark matter model, we study an optim…
The baryon acoustic oscillation (BAO) feature in the two-point correlation function of galaxies supplies a standard ruler to probe the expansion history of the Universe. We study here several galaxy selection schemes, aiming at building an emission-line galaxy (ELG) sample in the redshift range $0.6<z<1.7$, that would be suitable for future BAO studies, providing a highly biased galaxy sample. We analyse the angular galaxy clustering of galaxy selections at the redshifts 0.5, 0.7, 0.8, 1 and 1.2 and we combine this analysis with a halo occupation distribution (HOD) model to derive the properti…
The weak lensing power spectrum is a powerful tool to probe cosmological parameters. Additionally, lensing peak counts contain cosmological information beyond the power spectrum. Both of these statistics can be affected by the preferential selection of source galaxies in patches of the sky with high magnification, as well as by the dilution in the source galaxy surface density in such regions. If not accounted for, these biases introduce systematic errors for cosmological measurements. Here we quantify these systematic errors, using convergence maps from a suite of ray-tracing N-body simulatio…
We study the impact of lensing magnification on the observed three-dimensional galaxy clustering in redshift space. We used the RayGal suite of N-body simulations, from which we extracted samples of dark matter particles and haloes in the redshift regime of interest for future large redshift surveys. Several magnitude-limited samples were built that reproduce various levels of magnification bias ranging from s = 0 to s = 1.2, where s is the logarithmic slope of the cumulative magnitude number counts, in three redshift intervals within 1 < z < 1.95. We studied the two-point correlation function…
We study how well the Gaussian approximation is valid for computing the covariance matrices of the convergence power and bispectrum in weak gravitational lensing analyses. We focus on its impact on the cosmological parameter estimations by comparing the results with and without non-Gaussian error contribution in the covariance matrix. We numerically derive the covariance matrix as well as the cosmology dependence of the spectra from a large set of N-body simulations performed for various cosmologies and carry out Fisher matrix forecasts for tomographic weak lensing surveys with three source re…
A long standing question in cosmology is whether gravitational lensing changes the distance-redshift relation $D(z)$ or the mean flux density of sources. Interest in this has been rekindled by recent studies in non-linear relativistic perturbation theory that find biases in both the area of a surface of constant redshift and in the mean distance to this surface, with a fractional bias in both cases on the order of the mean squared convergence $\langle κ^2 \rangle$. Any such area bias could alter CMB cosmology, and the corresponding bias in mean flux density could affect supernova cosmology. He…
We present a novel approach for a combined analysis of X-ray and gravitational lensing data and apply this technique to the merging galaxy cluster MACS J0416.1$-$2403. The method exploits the information on the intracluster gas distribution that comes from a fit of the X-ray surface brightness, and then includes the hot gas as a fixed mass component in the strong lensing analysis. With our new technique, we can separate the collisional from the collision-less diffuse mass components, thus obtaining a more accurate reconstruction of the dark matter distribution in the core of a cluster. We intr…
Peak counts have been shown to be an excellent tool to extract the non-Gaussian part of the weak lensing signal. Recently, we developped a fast stochastic forward model to predict weak-lensing peak counts. Our model is able to reconstruct the underlying distribution of observables for analyses. In this work, we explore and compare various strategies for constraining parameter using our model, focusing on the matter density $Ω_\mathrm{m}$ and the density fluctuation amplitude $σ_8$. First, we examine the impact from the cosmological dependency of covariances (CDC). Second, we perform the analys…
We address the amount of information in the non-Gaussian regime of weak lensing surveys by modelling all relevant covariances of the power spectra and bispectra, using 1000 ray-tracing simulation realizations for a Lambda-CDM model and an analytical halo model. We develop a formalism to describe the covariance matrices of power spectra and bispectra of all triangle configurations. In addition to the known contributions which extend up to six-point correlation functions, we propose a new contribution `the halo sample variance (HSV)' arising from the coupling of the lensing Fourier modes with la…
We use the mock catalog of galaxies, constructed based on the COSMOS galaxy catalog including information on photometric redshifts (photo-z) and SED types of galaxies, in order to study how to define a galaxy subsample suitable for weak lensing tomography feasible with optical (and NIR) multi-band data. Since most of useful cosmological information arises from the sample variance limited regime for upcoming lensing surveys, a suitable subsample can be obtained by discarding a large fraction of galaxies that have less reliable photo-z estimations. We develop a method to efficiently identify pho…
We present optimized source galaxy selection schemes for measuring cluster weak lensing (WL) mass profiles unaffected by cluster member dilution from the Subaru Hyper Suprime-Cam Strategic Survey Program (HSC-SSP). The ongoing HSC-SSP survey will uncover thousands of galaxy clusters to $z\lesssim1.5$. In deriving cluster masses via WL, a critical source of systematics is contamination and dilution of the lensing signal by cluster {members, and by foreground galaxies whose photometric redshifts are biased}. Using the first-year CAMIRA catalog of $\sim$900 clusters with richness larger than 20 f…
Secondary contributions to the anisotropy of the Cosmic Microwave Background (CMB), such as the integrated Sachs-Wolfe (ISW) effect, the thermal Sunyaev-Zel'dovich effect (tSZ), and the effect of gravitational lensing, have distinctive non-Gaussian signatures, and full descriptions therefore require information beyond that contained in their power spectra. In this paper we use the recently introduced skew-spectra associated with the Minkowski Functionals (MF) to probe the topology of CMB maps to probe the secondary non-Gaussianity as a function of beam-smoothing in order to separate various co…
We derive an accurate mass distribution of the galaxy cluster MACS J1206.2-0847 (z=0.439) from a combined weak-lensing distortion, magnification, and strong-lensing analysis of wide-field Subaru BVRIz' imaging and our recent 16-band Hubble Space Telescope observations taken as part of the Cluster Lensing And Supernova survey with Hubble (CLASH) program. We find good agreement in the regions of overlap between several weak and strong lensing mass reconstructions using a wide variety of modeling methods, ensuring consistency. The Subaru data reveal the presence of a surrounding large scale struc…
High peaks in weak lensing (WL) maps originate dominantly from the lensing effects of single massive halos. Their abundance is therefore closely related to the halo mass function and thus a powerful cosmological probe. On the other hand, however, besides individual massive halos, large-scale structures (LSS) along lines of sight also contribute to the peak signals. In this paper, with ray tracing simulations, we investigate the LSS projection effects. We show that for current surveys with a large shape noise, the stochastic LSS effects are subdominant. For future WL surveys with source galaxie…
We study the sensitivity of weak lensing surveys to the effects of catastrophic redshift errors - cases where the true redshift is misestimated by a significant amount. To compute the biases in cosmological parameters, we adopt an efficient linearized analysis where the redshift errors are directly related to shifts in the weak lensing convergence power spectra. We estimate the number Nspec of unbiased spectroscopic redshifts needed to determine the catastrophic error rate well enough that biases in cosmological parameters are below statistical errors of weak lensing tomography. While the stra…
Based on a large group/cluster catalog recently constructed from the DESI Legacy Imaging Surveys DR9 using an extended halo-based group finder, we measure and model the group-galaxy weak lensing signals for groups/clusters in a few redshift bins within redshift range $0.1 \leqslant z<0.6$. Here, the background shear signals are obtained based on the DECaLS survey shape catalog derived with the \textsc{Fourier\_Quad} method. We divide the lens samples into 5 equispaced redshift bins and 7 mass bins, which allow us to probe the redshift and mass dependence of the lensing signals and hence the re…
Bye binormal: analysing the joint PDF of galaxy density and weak lensing convergence
Ludwig-Maximilians Universität München（慕尼黑大学）；Excellence Cluster ORIGINS（ORIGINS卓越集群）；Universität Bielefeld（比勒费尔德大学）；Newcastle University（纽卡斯尔大学）；University of Cambridge（剑桥大学）
We investigate the information on cosmology contained in Gaussianised weak gravitational lensing convergence fields. Employing Box-Cox transformations to determine optimal transformations to Gaussianity, we develop analytical models for the transformed power spectrum, including effects of noise and smoothing. We find that optimised Box-Cox transformations perform substantially better than an offset logarithmic transformation in Gaussianising the convergence, but both yield very similar results for the signal-to-noise and parameter constraints. None of the transformations is capable of eliminat…
We formulate the concept of non-linear and stochastic galaxy biasing in the framework of halo occupation statistics. Using two-point statistics in projection, we define the galaxy bias function, b_g(r_p), and the galaxy-dark matter cross-correlation function, R_{gm}(r_p), where r_p is the projected distance. We use the analytical halo model to predict how the scale dependence of b_g and R_{gm}, over the range 0.1 Mpc/h < r_p < 30 Mpc/h, depends on the non-linearity and stochasticity in halo occupation models. In particular we quantify the effect due to the presence of central galaxies, the ass…
From Hubble Frontier Fields photometry, and data from the Multi Unit Spectroscopic Explorer on the Very Large Telescope, we build the Fundamental Plane (FP) relation for the early-type galaxies of the cluster Abell S1063. We use this relation to develop an improved strong lensing model of the total mass distribution of the cluster, determining the velocity dispersions of all 222 cluster members included in the model from their measured structural parameters. Fixing the hot gas component from X-ray data, the mass density distributions of the diffuse dark matter haloes are optimised by comparing…
Strong gravitational lensing (SL) has emerged as a very accurate probe of the mass distribution of cluster- and galaxy-scale dark matter (DM) haloes in the inner regions of galaxy clusters. The derived properties of DM haloes can be compared to the predictions of high-resolution cosmological simulations, providing us with a test of the Standard Cosmological Model. The usual choice of simple power-law scaling relations to link the total mass of members with their luminosity is one of the possible inherent systematics within SL models of galaxy clusters, and thus on the derived cluster masses. U…
