This article introduces a family of analytical functions of the form x^ν K_ν(x), where K_ν is the incomplete Bessel function of the third kind. This family of functions can describe the density profile, projected and integrated light profiles and the gravitational potentials of galaxies. For the proper choice of parameters, these functions accurately approximate Sersic functions over a range of indices and are good fits to galaxy light profiles. With an additional parameter corresponding to a galaxy core radius, these functions can fit galaxy like M87 over a factor of 100,000 in radius. Unlike Sersic profiles, these functions have simple analytical 2-dimensional and 3-dimensional Fourier transforms, so they are easily convolved with spatially varying point spread function and are well suited for photometric and lensing analysis. We use these functions to estimate the effects of seeing on lensing measurements and show that high S/N measurements, even when the PSF is larger than the galaxy effective radius, should be able to recover accurate estimates of lensing distortions by weighting light in the outer isophotes that are less effected by seeing.
I present an estimator for the angular cross-correlation of two tracers of the cosmological large-scale structure that utilizes redshift information to isolate separate physical contributions. The estimator is derived by solving the Limber equation for a re-weighting of the foreground tracer that nulls either clustering or lensing contributions to the cross-correlation function. Applied to future photometric surveys, the estimator can enhance the measurement of gravitational lensing magnification effects to provide a competitive independent constraint on the dark energy equation of state.
We investigate the spectro-photometric variability of quasars due to lensing of small mass substructure (from several tens to several hundreds solar masses). The aim of this paper is to explore the milli/microlensing influence on the flux anomaly observed between images of a lensed quasar in different spectral bands and possible influence of small mass structure lensing of non-macrolensed quasars.We find that spectro-photometric variability may be also caused by lensing of small mass diffuse structure and can produce the flux anomaly which is sometimes seen in different images of a lensed quas…
Accurate weak-lensing analysis requires not only accurate measurement of galaxy shapes but also precise and unbiased measurement of galaxy redshifts. The photometric redshift technique appears as the only possibility to determine the redshift of the background galaxies used in the weak-lensing analysis. Using the photometric redshift quality, simple shape measurement requirements, and a proper sky model, we explore what could be an optimal weak-lensing dark energy mission based on FoM calculation. We found that photometric redshifts reach their best accuracy for the bulk of the faint galaxy po…
We present a new measurement of structure growth at $z \simeq 0.08$ obtained by correlating the cosmic microwave background (CMB) lensing potential map from the \textit{Planck} satellite with the angular distribution of the 2MASS Photometric Redshift galaxies. After testing for, and finding no evidence for systematic effects, we calculate the angular auto- and cross-power spectra. We combine these spectra to estimate the amplitude of structure growth using the bias-independent $D_G$ estimator introduced by Giannantonio et al. 2016. We find that the relative amplitude of $D_G$ with respect to t…
Exploring Cosmological Constraints of the Void-Lensing Cross-Correlation in the CSST Photometric Survey
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of Astronomy and Space Sciences, University of Chinese Academy of Sciences(UCAS)（中国科学院大学天文与空间科学学院）；Science Center for China Space Station Telescope, National Astronomical Observatories, Chinese Academy of Science（中国科学院国家天文台中国空间站望远镜科学中心）
We study the importance of gravitational lensing in the modelling of the number counts of galaxies. We confirm previous results for photometric surveys, showing that lensing cannot be neglected in a survey like LSST since it would infer a significant shift of cosmological parameters. For a spectroscopic survey like SKA2, we find that neglecting lensing in the monopole, quadrupole and hexadecapole of the correlation function also induces an important shift of parameters. For $Λ$CDM parameters, the shift is moderate, of the order of 0.6$σ$ or less. However, for a model-independent analysis, that…
Weak gravitational lensing is a valuable probe of galaxy formation and cosmology. Here we quantify the effects of using photometric redshifts (photo-z) in galaxy-galaxy lensing, for both sources and lenses, both for the immediate goal of using galaxies with photo-z as lenses in the Sloan Digital Sky Survey (SDSS) and as a demonstration of methodology for large, upcoming weak lensing surveys that will by necessity be dominated by lens samples with photo-z. We calculate the bias in the lensing mass calibration as well as consequences for absolute magnitude (i.e., k-corrections) and stellar mass …
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…
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 weak lensing mass estimates of clusters are needed in order to calibrate mass proxies for the cosmological exploitation of galaxy cluster surveys. Such measurements require accurate knowledge of the redshift distribution of the weak lensing source galaxies. In this context, we investigate the accuracy of photometric redshifts (photo-$z$s) computed by the 3D-HST team for the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey fields, which provide a relevant photometric reference data set for deep weak lensing studies. Through the comparison to spectroscopic redshifts and ph…
We present a method that accurately propagates residual uncertainties in photometric redshift distributions into the cosmological inference from weak lensing measurements. The redshift distributions of tomographic redshift bins are parameterised using a flexible modified Gaussian mixture model. We fit this model to pre-calibrated redshift distributions and implement an analytic marginalisation over the potentially several hundred redshift nuisance parameters in the weak lensing likelihood, which is demonstrated to accurately recover the cosmological posterior. By iteratively fitting cosmologic…
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 …
Weak lensing surveys are reaching sensitivities at which uncertainties in the galaxy redshift distributions n(z) from photo-z errors degrade cosmological constraints. We use ray-tracing simulations and a simple treatment of photo-z errors to assess cosmological parameter biases from uncertainties in n(z) in an LSST-like survey. We use the power spectrum and the abundance of lensing peaks to infer cosmological parameters, and find that the former is somewhat more resilient to photo-z errors. We place conservative lower limits on the survey size at which different types of photo-z errors degrade…
We describe a methodology to probe gravity with the cosmic microwave background (CMB) lensing convergence $κ$, specifically by measuring $E_G$, the ratio of the Laplacian of the gravitational scalar potential difference with the velocity divergence. Using CMB lensing instead of galaxy-galaxy lensing avoids intrinsic alignments while also lacking a hard limit on the lens redshift and significant uncertainties in the source plane. We model $E_G$ for general relativity and modified gravity, finding that $E_G$ for $f(R)$ gravity should be scale-dependent due to the scale-dependence of the growth r…
The observed brightness of Type Ia supernovae is affected by gravitational lensing caused by the mass distribution along the line of sight, which introduces an additional dispersion into the Hubble diagram. We look for evidence of lensing in the SuperNova Legacy Survey 3-year data set. We investigate the correlation between the residuals from the Hubble diagram and the gravitational magnification based on a modeling of the mass distribution of foreground galaxies. A deep photometric catalog, photometric redshifts, and well established mass luminosity relations are used. We find evidence of a l…
The masses of galaxy clusters can be measured using data obtained exclusively from wide photometric surveys in one of two ways: directly from the amplitude of the weak lensing signal or, indirectly, through the use of scaling relations calibrated using binned lensing measurements. In this paper, we build on a recently proposed idea and implement an alternative method based on the radial profile of the satellite distribution. This technique relies on splashback, a feature associated with the apocenter of recently accreted galaxies that offers a clear window into the phase-space structure of clu…
We study the effect of diffuse intracluster light on the critical surface mass density estimated from photometric redshifts of lensing source galaxies, and the resulting bias in a weak lensing measurement of galaxy cluster mass. Under conservative assumptions, we find the bias to be negligible for imaging surveys like the Dark Energy Survey (DES) with a recommended scale cut of >=200 kpc distance from cluster centers. For significantly deeper source catalogs from present and future surveys like the Large Synoptic Survey Telescope (LSST) program, more conservative scale and source magnitude cut…
Weak gravitational lensing is becoming a mature technique for constraining cosmological parameters, and future surveys will be able to constrain the dark energy equation of state $w$. When analyzing galaxy surveys, redshift information has proven to be a valuable addition to angular shear correlations. We forecast parameter constraints on the triplet $(Ω_m,w,σ_8)$ for an LSST-like photometric galaxy survey, using tomography of the shear-shear power spectrum, convergence peak counts and higher convergence moments. We find that redshift tomography with the power spectrum reduces the area of the …
Photo-z errors, especially catastrophic errors, are a major uncertainty for precision weak lensing cosmology. We find that the shear-(galaxy number) density and density-density cross correlation measurements between photo-z bins, available from the same lensing surveys, contain valuable information for self-calibration of the scattering probabilities between the true-z and photo-z bins. The self-calibration technique we propose does not rely on cosmological priors nor parameterization of the photo-z probability distribution function, and preserves all of the cosmological information available …
We study how the addition of on-board optical photometric bands to future space-based weak lensing instruments could affect the photometric redshift estimation of galaxies, and hence improve estimations of the dark energy parameters through weak lensing. Basing our study on the current proposed Euclid configuration and using a mock catalog of galaxy observations, various on-board options are tested and compared with the use of ground-based observations from the Large Synoptic Survey Telescope (LSST) and Pan-STARRS. Comparisons are made through the use of the dark energy Figure of Merit, which …
Weak-Lensing Shear Response for Photometric Redshift-Based Tomographic Binning
Brookhaven National Laboratory（布鲁海文国家实验室）；University of Pittsburgh（匹兹堡大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；Carnegie Mellon University（卡内基梅隆大学）
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…
Cosmological galaxy surveys aim at mapping the largest volumes to test models with techniques such as cluster abundance, cosmic shear correlations or baryon acoustic oscillations (BAO), which are designed to be independent of galaxy bias. Here we explore an alternative route to constrain cosmology: sampling more moderate volumes with the cross-correlation of photometric and spectroscopic surveys. We consider the angular galaxy-galaxy autocorrelation in narrow redshift bins and its combination with different probes of weak gravitational lensing (WL) and redshift space distortions (RSD). Includi…
We describe a new method for measuring galaxy magnification due to weak gravitational lensing. Our method makes use of a tight scaling relation between galaxy properties that are modified by gravitational lensing, such as apparent size, and other properties that are not, such as surface brightness. In particular, we use a version of the well-known fundamental plane relation for early type galaxies. This modified "photometric fundamental plane" replaces velocity dispersions with photometric galaxy properties, thus obviating the need for spectroscopic data. We present the first detection of magn…
We study the impact of neglecting lensing magnification in galaxy clustering analyses for future galaxy surveys, considering the LambdaCDM model and two extensions: massive neutrinos and modifications of General Relativity. Our study focuses on the biases on the constraints and on the estimation of the cosmological parameters. We perform a comprehensive investigation of these two effects for the upcoming photometric and spectroscopic galaxy surveys Euclid and SKA for different redshift binning configurations. We also provide a fitting formula for the magnification bias of SKA. Our results show…
The coherent physical alignment of galaxies is an important systematic for gravitational lensing studies as well as a probe of the physical mechanisms involved in galaxy formation and evolution. We develop a formalism for treating this intrinsic alignment (IA) in the context of galaxy-galaxy lensing and present an improved method for measuring IA contamination, which can arise when sources physically associated with the lens are placed behind the lens due to photometric redshift scatter. We apply the technique to recent Sloan Digital Sky Survey (SDSS) measurements of Luminous Red Galaxy lenses…
We report weak-lensing masses for 51 of the most X-ray luminous galaxy clusters known. This cluster sample, introduced earlier in this series of papers, spans redshifts 0.15 < z_cl < 0.7, and is well suited to calibrate mass proxies for current cluster cosmology experiments. Cluster masses are measured with a standard `color-cut' lensing method from three-filter photometry of each field. Additionally, for 27 cluster fields with at least five-filter photometry, we measure high-accuracy masses using a new method that exploits all information available in the photometric redshift posterior probab…
Photo-z error is one of the major sources of systematics degrading the accuracy of weak lensing cosmological inferences. Zhang et al. (2010) proposed a self-calibration method combining galaxy-galaxy correlations and galaxy-shear correlations between different photo-z bins. Fisher matrix analysis shows that it can determine the rate of photo-z outliers at a level of 0.01-1% merely using photometric data and do not rely on any prior knowledge. In this paper, we develop a new algorithm to implement this method by solving a constrained nonlinear optimization problem arising in the self-calibratio…
The convolution of galaxy images by the point-spread function (PSF) is the dominant source of bias for weak gravitational lensing studies, and an accurate estimate of the PSF is required to obtain unbiased shape measurements. The PSF estimate for a galaxy depends on its spectral energy distribution (SED), because the instrumental PSF is generally a function of the wavelength. In this paper we explore various approaches to determine the resulting `effective' PSF using broad-band data. Considering the Euclid mission as a reference, we find that standard SED template fitting methods result in bia…
The cosmological peculiar velocity field (deviations from the pure Hubble flow) of matter carries significant information on dark energy, dark matter and the underlying theory of gravity on large scales. Peculiar motions of galaxies introduce systematic deviations between the observed galaxy redshifts z and the corresponding cosmological redshifts z_cos. A novel method for estimating the angular power spectrum of the peculiar velocity field based on observations of galaxy redshifts and apparent magnitudes m (or equivalently fluxes) is presented. This method exploits the fact that a mean relati…
Photometric redshifts are a key tool to extract as much information as possible from planned cosmic shear experiments. In this work we aim to test the performances that can be achieved with observations in the near-infrared from space and in the optical from the ground. This is done by performing realistic simulations of multi-band observations of a patch of the sky, and submitting these mock images to software usually applied to real images to extract the photometry and then a redshift estimate for each galaxy. In this way we mimic the most relevant sources of uncertainty present in real data…
We develop a set of machine-learning based cosmological emulators, to obtain fast model predictions for the $C(\ell)$ angular power spectrum coefficients characterising tomographic observations of galaxy clustering and weak gravitational lensing from multi-band photometric surveys (and their cross-correlation). A set of neural networks are trained to map cosmological parameters into the coefficients, achieving a speed-up $\mathcal{O}(10^3)$ in computing the required statistics for a given set of cosmological parameters, with respect to standard Boltzmann solvers, with an accuracy better than $…
We present a weak lensing analysis of the cluster of galaxies RXC J2248.7-4431, a massive system at z=0.3475 with prominent strong lensing features covered by the HST/CLASH survey (Postman et al. 2012). Based on UBVRIZ imaging from the WFI camera at the MPG/ESO-2.2m telescope, we measure photometric redshifts and shapes of background galaxies. The cluster is detected as a mass peak at 5sigma significance. Its density can be parametrised as an NFW profile (Navarro et al. 1996) with two free parameters, the mass M_200m=(33.1+9.6-6.8)x10^14Msol and concentration c_200m=2.6+1.5-1.0. We discover a …
To combine information from measurements of the redshift-space power spectrum from spectroscopic data with angular weak lensing, galaxy clustering and galaxy-galaxy lensing power spectra from photometric surveys (i.e. the $3 \times 2$ point statistics), we must account for the covariance between the two probes. Currently any covariance between the two types of measurements is neglected as existing photometric and spectroscopic surveys largely probe different cosmological volumes. This will cease to be the case as data arrives from Stage-IV surveys. In this paper we derive an analytic expressio…
The galaxy cluster Abell 781 West has been viewed as a challenge to weak gravitational lensing mass calibration, as Cook and dell'Antonio (2012) found that the weak lensing signal-to-noise in three independent sets of observations was consistently lower than expected from mass models based on X-ray and dynamical measurements. We correct some errors in statistical inference in Cook and dell'Antonio (2012) and show that their own results agree well with the dynamical mass and exhibit at most 2.2--2.9$σ$ low compared to the X-ray mass, similar to the tension between the dynamical and X-ray masses…
Intrinsic alignments of galaxies have been shown to contaminate weak gravitational lensing observables on linear scales, $r>$ 10 $h^{-1}$Mpc, but studies of alignments in the non-linear regime have thus far been inconclusive. We present an estimator for extracting the intrinsic alignment signal of galaxies around stacked clusters of galaxies from multiband imaging data. Our estimator removes the contamination caused by galaxies that are gravitationally lensed by the clusters and scattered in redshift space due to photometric redshift uncertainties. It uses posterior probability distributions f…
The magnification effect of gravitational lensing is a powerful probe of the distribution of matter in the universe, yet it is frequently overlooked due to the fact that its signal to noise is smaller than that of lensing shear. Because its systematic errors are quite different from those of shear, magnification is nevertheless an important approach with which to study the distribution of large scale structure. We present lensing mass profiles of spectroscopic luminous red galaxies (LRGs) and galaxy clusters determined through measurements of the weak lensing magnification of photometric LRGs …
Cosmic microwave background (CMB) lensing is an integrated effect whose kernel is greater than half the peak value in the range $1<z<5$. Measuring this effect offers a powerful tool to probe the large-scale structure of the Universe at high redshifts. With the increasing precision of ongoing CMB surveys, other statistics than the lensing power spectrum, in particular the lensing bi-spectrum, will be measured at high statistical significance. This will provide ways to improve the constraints on cosmological models and lift degeneracies. Following on an earlier paper, we test analytical predicti…
We determine the accuracy of galaxy redshift distributions as estimated from photometric redshift probability distributions $p(z)$. Our method utilises measurements of the angular cross-correlation between photometric galaxies and an overlapping sample of galaxies with spectroscopic redshifts. We describe the redshift leakage from a galaxy photometric redshift bin $j$ into a spectroscopic redshift bin $i$ using the sum of the $p(z)$ for the galaxies residing in bin $j$. We can then predict the angular cross-correlation between photometric and spectroscopic galaxies due to intrinsic galaxy clus…
Nonlinear redshift-space distortions, the Finger-of-God (FoG) effect, can complicate the interpretation of the galaxy power spectrum. Here, we demonstrate the method proposed by Hikage et al. (2012) to use complimentary observations to directly constrain this effect on the data. We use catalogs of Luminous Red Galaxies (LRGs) and photometric galaxies from the SDSS DR7 to measure the redshift-space power spectrum of LRGs, the cross-correlation of LRGs with the shapes of background photometric galaxies (galaxy-galaxy weak lensing), and the projected cross-correlation of LRGs with photometric gal…
In this paper we use deep CFHT and SUBARU $uBVRIz$ archival images of the Abell 383 cluster (z=0.187) to estimate its mass by weak lensing. To this end, we first use simulated images to check the accuracy provided by our KSB pipeline. Such simulations include both the STEP 1 and 2 simulations, and more realistic simulations of the distortion of galaxy shapes by a cluster with a Navarro-Frenk-White (NFW) profile. From such simulations we estimate the effect of noise on shear measurement and derive the correction terms. The R-band image is used to derive the mass by fitting the observed tangenti…
High precision cosmological distance measurements towards individual objects such as time delay gravitational lenses or type Ia supernovae are affected by weak lensing perturbations by galaxies and groups along the line of sight. In time delay gravitational lenses, "external convergence," kappa, can dominate the uncertainty in the inferred distances and hence cosmological parameters. In this paper we attempt to reconstruct kappa, due to line of sight structure, using a simple halo model. We use mock catalogues from the Millennium Simulation, and calibrate and compare our reconstructed P(kappa)…
Weak gravitational lensing on a cosmological scales can provide strong constraints both on the nature of dark matter and the dark energy equation of state. Most current weak lensing studies are restricted to (two-dimensional) projections, but tomographic studies with photometric redshifts have started, and future surveys offer the possibility of probing the evolution of structure with redshift. In future we will be able to probe the growth of structure in 3D and put tighter constraints on cosmological models than can be achieved by the use of galaxy redshift surveys alone. Earlier studies in t…
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. We show that 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. We find that particularly at high redshifts, $z\gtrsim 1.5$, the signal to noise ratio can become of order 30. We therefore claim that number c…
Anisotropy and tracer-profile assumptions in aperture-based strong-lens dynamics: Conditional inference from supernova distance ratios and unresolved stellar kinematics
Dali University（大理大学）；Xi’an Jiaotong University（西安交通大学）
Galaxies and their dark matter halos populate a complicated filamentary network around large, nearly empty regions known as cosmic voids. Cosmic voids are usually identified in spectroscopic galaxy surveys, where 3D information about the large-scale structure of the Universe is available. Although an increasing amount of photometric data is being produced, its potential for void studies is limited since photometric redshifts induce line-of-sight position errors of $\sim50$ Mpc/$h$ or more that can render many voids undetectable. In this paper we present a new void finder designed for photometr…
The Cluster Lensing And Supernovae survey with Hubble (CLASH) is an Hubble Space Telescope (HST) Multi-Cycle Treasury program observing 25 massive galaxy clusters. CLASH observations are carried out in 16 bands from UV to NIR to derive accurate and reliable estimates of photometric redshifts. We present the CLASH photometric redshifts and study the photometric redshift accuracy of the arcs in more detail for the case of MACS1206.2-0847. We use the publicly available Le Phare and BPZ photometric redshift codes on 17 CLASH galaxy clusters. Using Le Phare code for objects with StoN>=10, we reach …
Highly precise weak lensing shear measurement is required for statistical weak gravitational lensing analysis such as cosmic shear measurement to achieve severe constraint on the cosmological parameters. For this purpose, the accurate shape measurement of background galaxies is absolutely important in which any systematic error in the measurement should be carefully corrected. One of the main systematic error comes from photon noise which is Poisson noise of flux from the atmosphere(noise bias). We investigate how the photon noise makes a systematic error in shear measurement within the framew…
Here we present a number of improvements to weak lensing 3D power spectrum analysis, 3D cosmic shear, that uses the shape and redshift information of every galaxy to constrain cosmological parameters. We show how photometric redshift probability distributions for individual galaxies can be directly included in this statistic with no averaging. We also include the Limber approximation, considerably simplifying full 3D cosmic shear analysis, and we investigate its range of applicability. Finally we show the relationship between weak lensing tomography and the 3D cosmic shear field itself; the st…
We explore strategies to extract cosmological constraints from a joint analysis of cosmic shear, galaxy-galaxy lensing, galaxy clustering, cluster number counts and cluster weak lensing. We utilize the CosmoLike software to simulate results from an LSST like data set, specifically, we 1) compare individual and joint analyses of the different probes, 2) vary the selection criteria for lens and source galaxies, 3) investigate the impact of blending, 4) investigate the impact of the assumed cosmological model in multi-probe covariances, 6) quantify information content as a function of scales, and…
