Strong gravitational lensing by groups or clusters of galaxies provides a powerful technique to measure the dark matter properties of individual lens galaxies. We study in detail the mass distribution of the satellite lens galaxy in the group-scale lens SL2S J08544-0121 by modelling simultaneously the spatially extended surface brightness distribution of the source galaxy and the lens mass distribution using Markov chain Monte Carlo methods. In particular, we measure the dark matter halo size of the satellite lens galaxy to be 6.0^{+2.9}_{-2.0} kpc with a fiducial velocity dispersion of 127^{+21}_{-12} km/s. This is the first time the size of an individual galaxy halo in a galaxy group has been measured using strong gravitational lensing without assumptions of mass following light. We verify the robustness of our halo size measurement using mock data resembling our lens system. Our measurement of the halo size is compatible with the estimated tidal radius of the satellite galaxy, suggesting that halos of galaxies in groups experience significant tidal stripping, a process that has been previously observed on galaxies in clusters. Our mass model of the satellite galaxy is elliptical with its major axis misaligned with that of the light by ~50 deg. The major axis of the total matter distribution is oriented more towards the centre of the host halo, exhibiting the radial alignment found in N-body simulations and observational studies of satellite galaxies. This misalignment between mass and light poses a significant challenge to modified Newtonian dynamics.
We investigate the validity of the approximate method to describe a strong gravitational lensing which was extended by Alard on the basis of a perturbative approach to an Einstein ring. Adopting an elliptical Navarro-Frenk-White (NFW) lens model, we demonstrate how the approximate method works, focusing on the shape of the image, the magnification, caustics, and the critical line. Simplicity of the approximate method enables us to investigate the lensing phenomena in an analytic way. We derive simple approximate formulas which characterise a lens system near the Einstein ring.
The deflection, potential, shear and magnification of a gravitational lens following an elliptical power law mass model are investigated. This mass model is derived from the circular power law profile through a rescaling of the axes, similar to the case of a singular isothermal ellipsoid. The resulting deflection can be calculated explicitly and given in terms of the Gaussian hypergeometric function. Analytic expressions for the remaining lensing properties are found as well. Because the power law profile lens contains a number of well-known lens models as special cases, the equivalence of the…
The Perturbative Approach (PA) introduced by \citet{alard07} provides analytic solutions for gravitational arcs by solving the lens equation linearized around the Einstein ring solution. This is a powerful method for lens inversion and simulations in that it can be used, in principle, for generic lens models. In this paper we aim to quantify the domain of validity of this method for three quantities derived from the linearized mapping: caustics, critical curves, and the deformation cross section (i.e. the arc cross section in the infinitesimal circular source approximation). We consider lens m…
We investigate a physical, composite alignment model for both spiral and elliptical galaxies and its impact on cosmological parameter estimation from weak lensing for a tomographic survey. Ellipticity correlation functions and angular ellipticity spectra for spiral and elliptical galaxies are derived on the basis of tidal interactions with the cosmic large-scale structure and compared to the tomographic weak lensing signal. We find that elliptical galaxies cause a contribution to the weak-lensing dominated ellipticity correlation on intermediate angular scales between $\ell\simeq40$ and $\ell\…
We derive the average mass profile of elliptical galaxies from the ensemble of 161 strong gravitational lens systems selected from several surveys, assuming that the mass profile scales with the stellar mass and effective radius of each lensing galaxy. The total mass profile is well fitted by a power-law ρ(r) \propto r^γwith best-fit slope γ= -2.11+/-0.05. The decomposition of the total mass profile into stellar and dark matter distributions is difficult due to a fundamental degeneracy between the stellar initial mass function (IMF) and the dark matter fraction f_DM. We demonstrate that this I…
Models with elliptical potentials (pseudo-elliptical) are often used in gravitational lensing applications. Nevertheless, they generally lead to nonphysical mass distributions in some regions. In this paper we revisit the physical limitations of the pseudo-elliptical Navarro-Frenk-White (PNFW) model, for a broad range of the potential ellipticity parameter ε and characteristic convergence κ_s focusing on the behavior of the mass distribution close to the tangential critical curve, where tangential arcs are expected to be formed. We investigate the shape of the mass distribution on this region …
Plasma lensing is the refraction of low-frequency electromagnetic rays due to free electrons in the interstellar medium. Although the phenomenon has a distinct similarity to gravitational lensing, particularly in its mathematical description, plasma lensing introduces other additional features, such as wavelength dependence, radial rather than tangential image distortions, and strong demagnification of background sources. Axisymmetrical models of plasma lenses have been well-studied in the literature, but density distributions with more complicated shapes can provide new and exotic image confi…
We demonstrate an efficient method to compute the strong-gravitational-lensing deflection angle and magnification for any elliptical surface-density profile. This method solves a numerical hurdle in lens modelling that has lacked a general solution for nearly three decades. The hurdle emerges because it is prohibitive to derive analytic expressions of the lensing quantities for most elliptical mass profiles. In our method, we first decompose an elliptical mass profile into Gaussian components. We introduce an integral transform that provides us with a fast and accurate algorithm for the Gaussi…
We have developed a new method(E-HOLICs) of estimating gravitational shear by adopting an elliptical weight function to measure background galaxy images in our previous paper. Following to the previous paper where isotropic Point Spread Function(PSF) correction is calculated, we consider an anisotropic PSF correction in this paper in order to apply E-HOLICs for real data. A an example, E-HOLICs is applied to Subaru data of massive and compact galaxy clusters A370, and is able to detect double peaks in the central region of the cluster consistent with the analysis of strong lensing. We also stu…
We use 118 strong gravitational lenses observed by the SLACS, BELLS, LSD and SL2S surveys to constrain the total mass profile and the profile of luminosity density of stars (light-tracers) in elliptical galaxies up to redshift $z \sim 1$. Assuming power-law density profiles for the total mass density, $ρ=ρ_0(r/r_0)^{-α}$, and luminosity density, $ν=ν_0(r/r_0)^{-δ}$, we investigate the power law index and its first derivative with respect to the redshift. Using Monte Carlo simulations of the posterior likelihood taking the Planck's best-fitted cosmology as a prior, we find $γ= 2.132\pm0.055$ wi…
We present equations for the gravitational lensing flexion expected for an elliptical lens mass distribution. These can be reduced to one-dimensional finite integrals, thus saving significant computing time over a full two-dimensional calculation. We estimate constraints on galaxy halo ellipticities for a range of potential future surveys, finding that the constraints from the two different types of flexion are comparable and are up to two orders of magnitude tighter than those from shear. Flexion therefore appears to be a very promising potential tool for constraining the shapes of galaxy hal…
The combination of strong gravitational lensing and stellar kinematics provides a powerful and robust method to investigate the mass and dynamical structure of early-type galaxies. We demonstrate this approach by analysing two massive ellipticals from the XLENS Survey for which both high-resolution HST imaging and X-Shooter spectroscopic observations are available. We adopt a flexible axisymmetric two-component mass model for the lens galaxies, consisting of a generalised NFW dark halo and a realistic self-gravitating stellar mass distribution. For both systems, we put constraints on the dark …
The gravitational lens system MG J0414+0534 is formed by an elliptical galaxy at redshift ~0.96 and a quasar at z~2.64. The system geometry is typical of lensing by an elliptical galaxy with the QSO close to and inside a fold caustic. It shows 4 images of the background source, and a partial Einstein ring is visible at optical wavelengths. It was observed with a global-VLBI array at 18 cm in June 2008. We present here the imaging results and a preliminary lens model constrained by these observations.
We present a microlensing analysis of 61 Chandra observations of 14 quadruply lensed quasars. X-ray flux measurements of the individual quasar images give a clean determination of the microlensing effects in the lensing galaxy and thus offer a direct assessment of the local fraction of stellar matter making up the total integrated mass along the lines of sight through the lensing galaxy. A Bayesian analysis of the ensemble of lensing galaxies gives a most likely local stellar fraction of 7%, with the other 93% in a smooth, dark matter component, at an average impact parameter R_c of 6.6 kpc fr…
We present new VLT observations of the closest-known strong-lensing galaxy, the sigma=330 km/s giant elliptical ESO325-G004. The low redshift of the lens (z_lens=0.035) results in arcs being formed at a small fraction of the effective radius, (R_Ein ~ R_Eff/4). At such small radii, stars dominate the lensing mass, so that lensing provides a direct probe of the stellar mass-to-light ratio, with only small corrections needed for dark matter. The redshift of the galaxy lensed by ESO325-G004 was unknown until now, so the lensing mass was not securely determined. Using X-SHOOTER, we measure a secur…
The Navarro-Frenk-White (NFW) density profile is often used to model gravitational lenses. For low values of the characteristic convergence ($κ_s \ll 1$) of this model - corresponding to galaxy and galaxy group mass scales - a high numerical precision is required in order to accurately compute several quantities in the strong lensing regime. An alternative for fast and accurate computations is to derive analytic approximations in this limit. In this work we obtain analytic solutions for several lensing quantities for elliptical (ENFW) and pseudo-elliptical (PNFW) NFW lens models on the typical…
If dark matter has a non-zero self-interaction cross-section, then dark matter halos of individual galaxies in cluster cores should experience a drag force from the ambient dark matter of the cluster, which will not affect the stellar components of galaxies, and thus will lead to a separation between the stellar and dark matter. If the cross-section is only a few decades below its current astrophysically determined upper limit, then kpc-scale separations should result. However, such separations will be observable only under very favorable conditions. Abell 3827 is a nearby late stage cluster m…
Using a large suite of galaxies with a variety of concentrations and metallicity gradients, we study the evolution of non-dissipative ("dry") equal mass mergers. Our purpose in generating these simulations is to explore how the metallicity gradient in dry mergers depends on the structure and metallicity gradients of the galaxies involved in the merger. Specifically, we would like to answer: Could dry mergers lead to metallicity gradients as observed in elliptical galaxies in the local Universe? Do dry mergers always lead to a flattening of the initial (i.e., pre-merger) gradient? From this mod…
We use high-resolution hydrodynamical simulations run with the EAGLE model of galaxy formation to study the differences between the properties of - and subsequently the lensing signal from - subhaloes of massive elliptical galaxies at redshift 0.2, in Cold and Sterile Neutrino (SN) Dark matter models. We focus on the two 7 keV SN models that bracket the range of matter power spectra compatible with resonantly-produced SN as the source of the observed 3.5 keV line. We derive an accurate parametrisation for the subhalo mass function in these two SN models relative to CDM, as well as the subhalo …
In a quadruply imaged lens system the angular distribution of images around the lens center is completely described by three relative angles. We show empirically that in the 3D space of these angles, spanning 180 x 180 x 90 degrees, quads from simple two-fold symmetric lenses of arbitrary radial density profile and arbitrary radially dependent ellipticity or external shear define a nearly invariant 2D surface. We give a fitting formula for the surface using SIS+elliptical lensing potential. Various circularly symmetric mass distributions with shear up to 0.4 deviate from it by typically, rms~0…
We use deep V-band surface photometry of five of the brightest elliptical galaxies in the Virgo cluster to search for diffuse tidal streams, shells, and plumes in their outer halos (r > 50 kpc). We fit and subtract elliptical isophotal models from the galaxy images to reveal a variety of substructure, with surface brightnesses in the range mu_V= 26-29 mag/arcsec^2. M49 possesses an extended, interleaved shell system reminiscent of the radial accretion of a satellite companion, while M89's complex system of shells and plumes suggests a more complicated accretion history involving either multipl…
We investigate how strong gravitational lensing can test contemporary models of massive elliptical (ME) galaxy formation, by combining a traditional decomposition of their visible stellar distribution with a lensing analysis of their mass distribution. As a proof of concept, we study a sample of three ME lenses, observing that all are composed of two distinct baryonic structures, a `red' central bulge surrounded by an extended envelope of stellar material. Whilst these two components look photometrically similar, their distinct lensing effects permit a clean decomposition of their mass structu…
Gravitational lensing shear has the potential to be the most powerful tool for constraining the nature of dark energy. However, accurate measurement of galaxy shear is crucial and has been shown to be non-trivial by the Shear TEsting Programme. Here we demonstrate a fundamental limit to the accuracy achievable by model-fitting techniques, if oversimplistic models are used. We show that even if galaxies have elliptical isophotes, model-fitting methods which assume elliptical isophotes can have significant biases if they use the wrong profile. We use noise-free simulations to show that on allowi…
Massive elliptical galaxies can display structures that deviate from a pure elliptical shape, such as a twist of the principal axis or variations in the axis ratio with galactocentric distance. Although satisfactory lens modeling is generally achieved without accounting for these azimuthal structures, the question about their impact on inferred lens parameters remains, in particular, on time delays as they are used in time-delay cosmography. This paper aims at characterizing these effects and quantifying their impact considering realistic amplitudes of the variations. We achieved this goal by …
In this article we study the well-known strong lensing system SDSS J1004+4112. Not only does it host a large-separation lensed quasar with measured time-delay information, but several other lensed galaxies have been identified as well. A previously developed strong lens inversion procedure that is designed to handle a wide variety of constraints, is applied to this lensing system and compared to results reported in other works. Without the inclusion of a tentative central image of one of the galaxies as a constraint, we find that the model recovered by the other constraints indeed predicts an …
We have discovered a strong lensing fossil group (J0454) at z=0.26, projected near the well-studied cluster MS0451-0305. Using multicolour Subaru/Suprime-Cam and CFHT/Megaprime imaging together with Keck spectroscopy we identify member galaxies. A VLT/FORS2 spectrum was taken to determine the redshifts of the brightest elliptical and the lensed arc. Using HST/ACS images we determine the group's weak lensing signal and model the strong lens system. This is the first time that a fossil group is analysed with lensing methods. The X-ray luminosity and temperature are derived from XMM-Newton data. …
We present the first resolved mid-IR (11 micron) observations of the four-image quasar lens H1413+117 using the Michelle camera on Gemini North. All previous observations (optical, near-IR, and radio) of this lens show a "flux anomaly," where the image flux ratios cannot be explained by a simple, central lens galaxy. We attempt to reproduce the mid-IR flux ratios, which are insensitive to extinction and microlensing, by modeling the main lens as a singular isothermal ellipsoid. This model fails to reproduce the flux ratios. However, we can explain the flux ratios simply by adding to the model …
A Salpeter IMF and an NFW halo: Disentangling the dark and stellar mass of an elliptical galaxy through precise lens modelling of a double-source-plane system
University of Portsmouth（朴茨茅斯大学）；The University of Sydney（悉尼大学）
The positions of images produced by the gravitational lensing of background sources provide unique insight in to galaxy-lens mass distribution. However, even quad images of extended sources are not able to fully characterize the central regions of the host galaxy. Most previous work has focused either on the radial density profile of the lenses or localized substructure clumps. Here, we concentrate on the azimuthal mass asymmetries near the image circle. The motivation for considering such mass inhomogeneities is that the transition between the central stellar dominated region and the outer da…
Correlations of galaxy ellipticities with large-scale structure, due to galactic tidal interactions, provide a potentially significant contaminant to measurements of cosmic shear. However, these intrinsic alignments are still poorly understood for galaxies at the redshifts typically used in cosmic shear analyses. For spiral galaxies, it is thought that tidal torquing is significant in determining alignments resulting in zero correlation between the intrinsic ellipticity and the gravitational potential in linear theory. Here, we calculate the leading-order correction to this result in the tidal…
Using isophotal radius correlations for a sample of 2MASS ellipticals, we have constructed a series of template surface brightness profiles to describe the profile shapes of ellipticals as a function of luminosity. The templates are a smooth function of luminosity, yet are not adequately matched to any fitting function supporting the view that ellipticals are weakly non-homologous with respect to structure. Through comparison to the templates, it is discovered that ellipticals are divided into two families; those well matched to the templates and a second class of ellipticals with distinctly s…
We derive dynamical and gravitational lensing properties of local sources in the Hassan-Rosen bimetric gravity theory. Observations of elliptical galaxies rule out values of the effective length-scale of the theory, in units of the Hubble radius, in the interval 10^-6 < lambda_g/r_H < 10^-3, unless the proportionality constant between the metrics at the background level is far from unity, in which case general relativity is effectively restored for local sources. In order to have background solutions resembling the concordance cosmological model, without fine-tuning of the parameters of the mo…
The subject of this paper is to build a physical model describing shape and size correlations of galaxies due to weak gravitational lensing and due to direct tidal interaction of elliptical galaxies with gravitational fields sourced by the cosmic large-scale structure. Setting up a linear intrinsic alignment model for elliptical galaxies which parameterises the reaction of the galaxy to an external tidal shear field is controlled by the velocity dispersion, we predict intrinsic correlations and cross-correlations with weak lensing for both shapes and sizes, juxtaposing both types of spectra wi…
The first resolved, multiply imaged supernova Type Ia, iPTF16geu, was observed 4 years ago, five decades after such systems were first envisioned. Because of the unique properties of the source, these systems hold a lot of promise for the study of galaxy structure and cosmological parameters. However, this very first example presented modelers with a few puzzles. It was expected that to explain image fluxes a contribution from microlensing by stars would be required, but to accommodate the magnitude of microlensing, the density slope of the elliptical power law lens model had to be quite shall…
The stellar velocity anisotropy of strong lensing massive elliptical galaxies and its role in the inference of the Hubble parameter $H_0$ using spatially resolved kinematics
American Museum of Natural History（美国自然历史博物馆）；The Graduate Center of the City University of New York（纽约市立大学研究生中心）；Lehman College of the CUNY（纽约市立大学雷曼学院）；Borough of Manhattan Community College, City University of New York（纽约市立大学曼哈顿社区学院）
We present long-baseline ALMA observations of the strong gravitational lens H-ATLAS J090740.0-004200 (SDP.9), which consists of an elliptical galaxy at $z_{\mathrm{L}}=0.6129$ lensing a background submillimeter galaxy into two extended arcs. The data include Band 6 continuum observations, as well as CO $J$=6$-$5 molecular line observations, from which we measure an updated source redshift of $z_{\mathrm{S}}=1.5747$. The image morphology in the ALMA data is different from that of the HST data, indicating a spatial offset between the stellar, gas, and dust component of the source galaxy. We mode…
In the context of gravitational lensing, the density profile of lensing galaxies is often considered to be perfectly elliptical. Potential angular structures are generally ignored, except to explain flux ratios anomalies. Surprisingly, the impact of azimuthal structures on extended images of the source has not been characterized, nor its impact on the H0 inference. We address this task by creating mock images of a point source embedded in an extended source, lensed by an elliptical galaxy on which multipolar components are added to emulate boxy/discy isodensity contours. Modeling such images w…
Galaxy-galaxy lensing is an essential tool for probing dark matter halos and constraining cosmological parameters. While galaxy-galaxy lensing measurements usually rely on shear, weak-lensing magnification contains additional constraining information. Using the fundamental plane (FP) of elliptical galaxies to anchor the size distribution of a background population is one method that has been proposed for performing a magnification measurement. We present a formalism for using the FP residuals of elliptical galaxies to jointly estimate the foreground mass and background redshift errors for a st…
Gauss-Hermite and Gauss-Laguerre ("shapelet") decompositions of images have become important tools in galaxy modeling, particularly for the purpose of extracting ellipticity and morphological information from astronomical data. However, the standard shapelet basis functions cannot compactly represent galaxies with high ellipticity or large Sersic index, and the resulting underfitting bias has been shown to present a serious challenge for weak-lensing methods based on shapelets. We present here a new convolution relation and a compound "multi-scale" shapelet basis to address these problems, and…
The Cheshire Cat is a relatively poor group of galaxies dominated by two luminous elliptical galaxies surrounded by at least four arcs from gravitationally lensed background galaxies that give the system a humorous appearance. Our combined optical/X-ray study of this system reveals that it is experiencing a line of sight merger between two groups with a roughly equal mass ratio with a relative velocity of ~1350 km/s. One group was most likely a low-mass fossil group, while the other group would have almost fit the classical definition of a fossil group. The collision manifests itself in a bimo…
Galaxy lenses are frequently modeled as an elliptical mass distribution with external shear and isothermal spheres to account for secondary and line-of-sight galaxies. There is statistical evidence that some fraction of observed quads are inconsistent with these assumptions, and require a dipole-like contribution to the mass with respect to the light. Simplifying assumptions about the shape of mass distributions can lead to the incorrect recovery of parameters such as $H_0$. We create several tests of synthetic quad populations with different deviations from an elliptical shape, then fit them …
Strong gravitational lensing offers a compelling test of the cold dark matter paradigm, as it allows for subhaloes with masses of $\sim10^{9}$ M$_\odot$ and below to be detected. We test commonly-used techniques for detecting subhaloes superposed in images of strongly lensed galaxies. For the lens we take a simulated galaxy in a $\sim10^{13}$ M$_\odot$ halo grown in a high-resolution cosmological hydrodynamical simulation, which we view from two different directions. Though the resolution is high, we note the simulated galaxy still has an artificial core which adds additional complexity to the…
