Weak gravitational lensing perturbations have a non-negligible impact on strong lensing observables, and several degeneracies exist between the properties of the main lens, line of sight, and cosmology. In this work, we consider the impact of the line of sight on double-source-plane lenses (DSPLs), a rare class of lens systems in which two sources at different redshifts are lensed by the same foreground galaxy, and which enable competitive constraints on the dark energy equation of state. Generating and sampling statistically representative lines of sight from N-body simulations, we show that line-of-sight perturbations add a $\sim1\%$ uncertainty to measurements of the cosmological scaling factor $η$ (a ratio of angular diameter distance ratios), which is subdominant but non-negligible compared to the measurement error. We also show that the line-of-sight shear experienced by images of the two sources can differ significantly in both magnitude and direction. Including a line-of-sight error budget, we measure $w=-1.17^{+0.19}_{-0.21}$ from the Jackpot DSPL in combination with Planck. We show that the line of sight is expected to introduce an additional scatter in the constraints possible with a larger sample of DSPLs from Euclid, but that this scatter is subdominant compared to other sources of error.
We study the origin of absorption features on the blue side of the C IV broad emission line of the large-separation lensed quasar SDSS J1029+2623 at z_em ~ 2.197. The quasar images, produced by a foreground cluster of galaxies, have a maximum separation angle of ~ 22".5. The large angular separation suggests that the sight-lines to the quasar central source can go through different regions of outflowing winds from the accretion disk of the quasar, providing a unique opportunity to study the structure of outflows from the accretion disk, a key ingredient for the evolution of quasars as well as …
We explore the use of strong lensing by galaxy clusters to constrain the dark energy equation of state and its possible time variation. The cores of massive clusters often contain several multiply imaged systems of background galaxies at different redshifts. The locations of lensed images can be used to constrain cosmological parameters due to their dependence on the ratio of angular diameter distances. We employ Monte-Carlo simulations of cluster lenses, including the contribution from substructures, to assess the feasibility of this potentially powerful technique. At the present, parametric …
In strong gravitational lens systems, the light bending is usually dominated by one main galaxy, but may be affected by other mass along the line of sight (LOS). Shear and convergence can be used to approximate the contributions from less significant perturbers (e.g. those that are projected far from the lens or have a small mass), but higher order effects need to be included for objects that are closer or more massive. We develop a framework for multiplane lensing that can handle an arbitrary combination of tidal planes treated with shear and convergence and planes treated exactly (i.e., incl…
Data from 58 strong-lensing events surveyed by the Sloan Lens ACS Survey are used to estimate the projected galaxy mass inside their Einstein radii by two independent methods: stellar dynamics and strong gravitational lensing. We perform a joint analysis of these two estimates inside models with up to three degrees of freedom with respect to the lens density profile, stellar velocity anisotropy, and line-of-sight (LOS) external convergence, which incorporates the effect of the large-scale structure on strong lensing. A Bayesian analysis is employed to estimate the model parameters, evaluate th…
Line-of-sight shear in SLACS strong lenses II: validation tests with an extended sample
University of Cambridge（剑桥大学）；Kavli Institute for Cosmology, University of Cambridge（剑桥大学卡弗里宇宙学研究所）；Laboratoire Univers et Particules de Montpellier, CNRS & Université de Montpellier（蒙彼利埃大学与法国国家科学研究中心宇宙与粒子物理实验室）；University of Chicago（芝加哥大学）；Kavli Institute for Cosmological Physics, University of Chicago（芝加哥大学卡弗里宇宙物理学研究所）；Independent University, Bangladesh（孟加拉独立大学）
TDCOSMO XXXI: New techniques in line-of-sight studies of time delay lenses
CNRS & Université de Montpellier（法国国家科学研究中心与蒙彼利埃大学）；University of California, Los Angeles（加州大学洛杉矶分校）；University of California, Davis（加州大学戴维斯分校）；Argonne National Laboratory（阿贡国家实验室）；Technical University of Munich（慕尼黑工业大学）；Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理研究所）；Université de Genève（日内瓦大学）
Strong lensing provides a powerful means of investigating the nature of dark matter as it probes dark matter structure on sub-galactic scales. We present an extension of a forward modeling framework that uses flux ratios from quadruply imaged quasars (quads) to measure the shape and amplitude of the halo mass function, including line of sight (LOS) halos and main deflector subhalos. We apply this machinery to 50 mock lenses --- roughly the number of known quads --- with warm dark matter (WDM) mass functions exhibiting free-streaming cutoffs parameterized by the half-mode mass $m_{\rm{hm}}$. As…
We explore the weak lensing effect by line-of-sight halos and sub-halos with a mass of M < 10^7 solar mass in QSO-galaxy strong lens systems with quadruple images in a concordant LCDM universe. Using a polynomially fitted non-linear power spectrum P(k) obtained from N-body simulations that can resolve halos with a mass of M ~ 10^5 solar mass, or structures with a comoving wavenumber of k ~ 3*10^2 h/Mpc, we find that the ratio of magnification perturbation due to intervening halos to that of a primary lens is typically ~10 per cent and the predicted values agree well with the estimated values f…
We have been able to connect the statistics of the observed double image gravitational lenses to the general properties of the internal structure of dark matter haloes. Our analytical theory for the GNFW lenses with parametrized cusp slope (alpha) gives us a relation connecting the cusp slope of the lensing profile to the observed magnification ratio of the produced images and location of the optical axis. The relation does not depend on cosmology, total lens mass, concentration or redshifts of the the lens and the lensed object. Simple geometry of axially symmetric lensing and aforementioned …
We investigate the influence of matter along the line of sight and in the strong lens vicinity on the properties of quad image configurations and on the measurements of the Hubble constant (H0). We use simulations of light propagation in a nonuniform universe model with the distribution of matter in space based on the data from Millennium Simulation. For a given strong lens and haloes in its environment we model the matter distribution along the line of sight many times, using different combinations of precomputed deflection maps representing subsequent layers of matter on the path of rays. We…
Line-of-sight shear in SLACS strong lenses I: shear and mass model parametrisations
Institute of Astronomy, University of Cambridge（剑桥大学天文学研究所）；Kavli Institute for Cosmology, University of Cambridge（剑桥大学卡弗里宇宙学研究所）；Clare Hall（克莱尔学院）；Laboratoire Univers et Particules de Montpellier, CNRS & Université de Montpellier（蒙彼利埃大学与法国国家科学研究中心宇宙与粒子物理实验室）；Department of Astronomy & Astrophysics, University of Chicago（芝加哥大学天文与天体物理系）；Kavli Institute for Cosmological Physics, University of Chicago（芝加哥大学卡弗里宇宙物理学研究所）；Center for Astronomy, Space Science and Astrophysics, Independent University, Bangladesh（孟加拉独立大学天文、空间科学与天体物理中心）
We give a physical interpretation of the formalism intrinsic degeneracies of the gravitational lensing formalism that we derived on a mathematical basis in part IV of this series. We find that all degeneracies occur due to the partition of the mass density along the line of sight. Usually, it is partitioned into a background (cosmic) density and a foreground deflecting object. The latter can be further partitioned into a main deflecting object and perturbers. Weak deflecting objects along the line of sight are also added, either to the deflecting object or as a correction of the angular diamet…
Cosmology with the line-of-sight shear of strong gravitational lenses
Laboratoire Univers et Particules de Montpellier, CNRS & Université de Montpellier（蒙彼利埃宇宙与粒子实验室，法国国家科学研究中心与蒙彼利埃大学）；Institute of Astronomy, University of Cambridge（剑桥大学天文学研究所）；Kavli Institute for Cosmology, University of Cambridge（剑桥大学卡弗里宇宙学研究所）
We present an analysis of the line-of-sight structure toward a sample of ten strong lensing cluster cores. Structure is traced by groups that are identified spectroscopically in the redshift range, 0.1 $\leq$ z $\leq$ 0.9, and we measure the projected angular and comoving separations between each group and the primary strong lensing clusters in each corresponding line of sight. From these data we measure the distribution of projected angular separations between the primary strong lensing clusters and uncorrelated large scale structure as traced by groups. We then compare the observed distribut…
The precision reached by current and forthcoming strong-lensing observations requires to accurately model various perturbations to the main deflector. Hitherto, theoretical models have been developed to account for either cosmological line-of-sight perturbations, or isolated secondary lenses via the multi-plane lensing framework. This article proposes a general formalism to describe multiple lenses within an arbitrary space-time background. The lens equation, and the expressions of the amplification and time delays, are rigorously derived in that framework. Our results may be applied to a wide…
We present a theoretical estimate for a new observable: the cross-correlation between the Lyman-alpha flux fluctuations in quasar (QSO) spectra and the convergence of the cosmic microwave background (CMB) as measured along the same line-of-sight. As a first step toward the assessment of its detectability, we estimate the signal-to-noise ratio using linear theory. Although the signal-to-noise is small for a single line-of-sight and peaks at somewhat smaller redshifts than those probed by the Lyman-alpha forest, we estimate a total signal-to-noise of 9 for cross-correlating QSO spectra of SDSS-I…
We present a weak gravitational lensing measurement of the external convergence along the line of sight to the quadruply lensed quasar HE$\,$0435$-$1223. Using deep r-band images from Subaru-Suprime-Cam we observe galaxies down to a 3$σ$ limiting magnitude of $\sim 26$ mags resulting in a source galaxy density of 14 galaxies / arcmin$^2$ after redshift-based cuts. Using an inpainting technique and Multi-Scale Entropy filtering algorithm, we find that the region in close proximity to the lens has an estimated external convergence of $κ=-0.012^{+0.020}_{-0.013}$ and is hence marginally under-den…
Cluster gravitational lensing surveys like the Hubble Space Telescope Frontier Fields survey will detect distant galaxies 10-50 times fainter than any yet discovered. Using these surveys to measure the luminosity function of such faint, distant galaxies, however, requires that magnification maps built from the constraints of strongly-lensed images be accurate. For models that assume the cluster and nearby (correlated) structures are the only significant sources of lensing, a potential source of error in these maps comes from the fact that light rays also suffer weak deflections by uncorrelated…
We test whether the Tinker & Chen model of MgII absorption due to the gaseous halo around a galaxy can reproduce absorption in quasar pairs (both lensed and physical) and lensed triples and quads from the literature. These quasars exhibit absorption from a total of 38 MgII systems spanning z=0.043 - 2.066 with mean redshift <z>=1.099 and weighted mean rest-frame equivalent width of 0.87 Ang. Using the Tinker & Chen model to generate simulated sight-lines, we marginalize the unknown parameters of the absorbing galaxies: dark matter halo mass, impact parameter, and azimuthal angle on the sky. We…
Using new photometric and spectroscopic data in the fields of nine strong gravitational lenses that lie in galaxy groups, we analyze the effects of both the local group environment and line-of-sight galaxies on the lens potential. We use Monte Carlo simulations to derive the shear directly from measurements of the complex lens environment, providing the first detailed independent check of the shear obtained from lens modeling. We account for possible tidal stripping of the group galaxies by varying the fraction of total mass apportioned between the group dark matter halo and individual group g…
Galaxy-galaxy strong gravitational lenses have become a popular probe of dark matter (DM) by providing a window into structure formation on the smallest scales. In particular, the convergence power spectrum of subhalos within lensing galaxies has been suggested as a promising observable to study DM. However, the distances involved in strong-lensing systems are vast, and we expect the relevant volume to contain line-of-sight (LOS) halos that are not associated with the main lens. We develop a formalism to calculate the effect of LOS halos as an effective convergence power spectrum. The multi-le…
We explore the weak lensing effects by ministructures in the line-of-sight in a quadruply lensed quasar MG0414+0534 that shows an anomaly in the flux-ratios. We find that the observed flux-ratio anomaly can be explained by a presence of either a minifilament or a minivoid in the line-of-sight with a surface mass density of the order of 10^(8-9) h^(-1) solar mass /arcsec^2 without taking into account any subhalos in the lensing galaxy. The astrometric perturbation by a possible minifilament/minivoid is <~ 0.001 arcsec and the amplitudes of convergence perturbations due to these perturbers are ~…
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)…
We investigate the influence of the matter along the line of sight and in the lens environment on the image configurations, relative time delays, and the resulting models of strong gravitational lensing. The distribution of matter in space and properties of gravitationally bound haloes are based on the Millennium Simulation. In our numerical experiments we consider isolated lens in a uniform universe model and the same lens surrounded by close neighbours and/or objects close to the line of sight which gives four different descriptions of the light propagation. We compare the results of the len…
Cosmological parameter constraints from observations of time-delay lenses are becoming increasingly precise. However, there may be significant bias and scatter in these measurements due to, among other things, the so-called mass-sheet degeneracy. To estimate these uncertainties, we analyze strong lenses from the largest EAGLE hydrodynamical simulation. We apply a mass-sheet transformation to the radial density profiles of lenses, and by selecting lenses near isothermality, we find that the bias on H0 can be reduced to 5% with an intrinsic scatter of 10%, confirming previous results performed o…
Degeneracies and modelling choices in double-plane time-delay cosmography
Laboratoire Univers et Particules de Montpellier (LUPM), CNRS & Université de Montpellier（蒙彼利埃宇宙与粒子实验室（LUPM），法国国家科学研究中心与蒙彼利埃大学）；Université de Genève（日内瓦大学）；Institute for Particle Physics and Astrophysics, ETH Zurich（苏黎世联邦理工学院粒子物理与天体物理研究所）
A promising route for revealing the existence of dark matter structures on mass scales smaller than the faintest galaxies is through their effect on strong gravitational lenses. We examine the role of local, lens-proximate clustering in boosting the lensing probability relative to contributions from substructure and unclustered line-of-sight (LOS) halos. Using two cosmological simulations that can resolve halo masses of $M_{\rm halo} \simeq 10^{9}\ M_{\odot}$ (in a simulation box of length $L_{\rm box}{\sim}100\,{\rm Mpc}$) and $10^{7}\ M_{\odot}$ ($L_{\rm box}\sim20\,{\rm Mpc}$), we demonstra…
We use a sample of 17 strong gravitational lens systems from the BELLS GALLERY survey to quantify the amount of low-mass dark matter haloes within the lensing galaxies and along their lines of sight, and to constrain the properties of dark matter. Based on a detection criterion of 10$σ$, we report no significant detection in any of the lenses. Using the sensitivity function at the 10-$σ$ level, we have calculated the predicted number of detectable cold dark matter (CDM) line-of-sight haloes to be $μ_{l} = 1.17\pm1.08$, in agreement with our null detection. Assuming a detection sensitivity that…
Probing modified gravity with galaxy-cluster-lensed gravitational-wave time delays: impact of systematic effects
Imperial College（帝国理工学院）；Observatoire de Paris, Université PSL, Sorbonne Université, CNRS（巴黎天文台，巴黎文理研究大学，索邦大学，法国国家科学研究中心）；Alma Mater Studiorum Universita di Bologna（博洛尼亚大学）；INAF - Osservatorio di Astrofisica e Scienza dello Spazio di Bologna（意大利国家天体物理研究所博洛尼亚天文与空间科学观测站）；INFN - Sezione di Bologna（意大利国家核物理研究所博洛尼亚分部）
We investigate the possibility of constraining the dark energy equation of state by measuring the ratio of Einstein radii in a strong gravitational lens system with two source planes. This quantity is independent of the Hubble parameter and directly measures the growth of angular diameter distances as a function of redshift. We investigate the prospects for a single double source plane system and for a forecast population of systems discovered by re-observing a population of single source lenses already known from a photometrically selected catalogue such as CASSOWARY or from a spectroscopical…
We compare galaxy number counts in HST/ACS fields containing moderate-redshift (0.2<z<1.0) strong gravitational lenses with those in two control samples: (1) the first square degree of the COSMOS survey, comprising 259 ACS fields and (2) 20 "pure parallel" fields randomly located on the sky. Through a Bayesian analysis we determine the expectation values (mu_0) and confidence levels of the underlying number counts for a range of apertures and magnitude bins. Our analysis has produced the following results: (i) We infer that our control samples are not consistent, with the number counts in the …
With a fantastic sensitivity improving significantly over the advanced GW detectors, Einstein Telescope (ET) will be able to observe hundreds of thousand inspiralling double compact objects per year. By virtue of gravitational lensing effect, intrinsically unobservable faint sources can be observed by ET due to the magnification by intervening galaxies. We explore the possibility of observing such faint sources amplified by strong gravitational lensing. Following our previous work, we use the merger rates of DCO (NS-NS,BH-NS,BH-BH systems) as calculated by Dominik et al.(2013). It turns out th…
The magnifications of compact-source lenses are extremely sensitive to the presence of low mass dark matter halos along the entire sight line from the source to the observer. Traditionally, the study of dark matter structure in compact-source strong gravitational lenses has been limited to radio-loud systems, as the radio emission is extended and thus unaffected by microlensing which can mimic the signal of dark matter structure. An alternate approach is to measure quasar nuclear-narrow line emission, which is free from microlensing and present in virtually all quasar lenses. In this paper, we…
Strongly lensed systems are powerful probes of the distribution of dark matter on small scales. In this paper, we show that line-of-sight haloes between the source and the observers give rise to a distinct anisotropic signature in the two-point function of the effective lensing deflection field. We show in particular that the non-linear coupling between line-of-sight haloes and the main-lens plane imprints a characteristic quadrupole moment on this two-point function whose amplitude reflects the abundance of such haloes within the strongly lensed field. We discuss how, by taking ratios of diff…
In time-delay cosmography, three of the key ingredients are 1) determining the velocity dispersion of the lensing galaxy, 2) identifying galaxies and groups along the line of sight with sufficient proximity and mass to be included in the mass model, and 3) estimating the external convergence $κ_\mathrm{ext}$ from less massive structures that are not included in the mass model. We present results on all three of these ingredients for two time-delay lensed quasar systems, DES J0408-5354 and WGD 2038-4008. We use the Gemini, Magellan and VLT telescopes to obtain spectra to both measure the stella…
Inferring cosmological parameters from time-delay strong lenses requires a significant investment of telescope time; it is therefore tempting to focus on the systems with the brightest sources, the highest image multiplicities and the widest image separations. We investigate if this selection bias can influence the properties of the lenses studied and the cosmological parameters that are inferred. Using a population of lenses with ellipsoidal powerlaw density profiles, we build a sample of double and quadruple image systems. Assuming reasonable thresholds on image separation and flux, based on…
Strong lensing by intervening galaxies can produce multiple images of gravitational waves from sources at cosmological distances. These images acquire additional phase-shifts as the over-focused wavefront passes through itself along the line of sight. Time domain waveforms of Type-II images (associated with saddle points of the time delay) exhibit a non-trivial distortion from the unlensed waveforms. This phenomenon is in addition to the usual frequency-independent magnification, and happens even in the geometric limit where the wavelength is much shorter than the deflector's gravitational len…
Plasma lensing is the refraction of low-frequency electromagnetic rays due to cold free electrons in the universe. For sources at a cosmological distance, there is observational evidence of elongated, complex plasma structures along the line of sight requiring a multi-lens-plane description. To investigate the limits of single-plane plasma lensing, we set up a double-plane lens with a projected Gaussian electron density in each lens plane. We compare double-plane scenarios with corresponding effective single-plane configurations. Our results show how double-plane lenses can be distinguished fr…
We present results from a search for gravitationally lensed galaxies present in the Hubble Space Telescope (HST)/Wide Field Camera-3 (WFC3) images of the Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey (CANDELS). We present one bona fide lens system in UDS and two compact lens candidates in the GOODS-S field. The lensing system in UDS involves two background galaxies, one at z=1.847 lensed to an arc and a counterimage, and the second at a photometric redshift of z=2.32^{+0.10}_{-0.06} lensed to a double image. We reconstruct the lensed sources in the source plane and find in each of t…
We report upon the follow up of 34 candidate lensed quasars found in the Dark Energy Survey using NTT-EFOSC, Magellan-IMACS, KECK-ESI and SOAR-SAMI. These candidates were selected by a combination of double component fitting, morphological assessment and color analysis. Most systems followed up are indeed composed of at least one quasar image and 13 with two or more quasar images: two lenses, four projected binaries and seven Nearly Identical Quasar Pairs (NIQs). The two systems confirmed as genuine gravitationally lensed quasars are one quadruple at $z_s=1.713$ and one double at $z_s=1.515$. …
Gravitational wave (GW) experiments are entering their advanced stage which should soon open a new observational window on the Universe. Looking into this future, the Einstein Telescope (ET) was designed to have a fantastic sensitivity improving significantly over the advanced GW detectors. One of the most important astrophysical GW sources supposed to be detected by the ET in large numbers are double compact objects (DCO) and some of such events should be gravitationally lensed by intervening galaxies. We explore the prospects of observing gravitationally lensed inspiral DCO events in the ET.…
Time delay cosmography uses the arrival time delays between images in strong gravitational lenses to measure cosmological parameters, in particular the Hubble constant $H_0$. The lens models used in time delay cosmography omit dark matter subhalos and line-of-sight halos because their effects are assumed to be negligible. We explicitly quantify this assumption by analyzing mock lens systems that include full populations of dark matter subhalos and line-of-sight halos, applying the same modeling assumptions used in the literature to infer $H_0$. We base the mock lenses on six quadruply-imaged q…
In galaxy-galaxy strong gravitational lensing, Einstein rings are generated when the lensing galaxy has an axisymmetric lensing potential and the source galaxy is aligned with its symmetry centre along the line of sight. Using a Taylor expansion around the Einstein radius and eliminating the unknown source, I derive a set of analytic equations that determine differences of the deflection angle of the perturber weighted by the convergence of the axisymmetric lens and ratios of the convergences at the positions of the arcs from the measurable thickness of the arcs. In the same manner, asymmetrie…
We investigate the weak lensing effects of line-of-sight structures on quadruple images in quasar-galaxy strong lens systems based on N-body and ray-tracing simulations that can resolve halos with a mass of 10^5 solar mass. The intervening halos and voids disturb the magnification ratios of lensed images as well as their relative positions due to lensing. The magnification ratios typically change by O(10%) when the shifts of relative angular positions of lensed images are constrained to <0.004 arcsec. The constrained amplitudes of projected density perturbations due to line-of-sight structures…
Image distortion due to weak gravitational lensing is examined using a non-perturbative method of integrating the geodesic deviation and optical scalar equations along the null geodesics connecting the observer to a distant source. The method we develop continuously changes the shape of the pencil of rays from the source to the observer with no reference to lens planes in astrophysically relevant scenarios. We compare the projected area and the ratio of semi-major to semi-minor axes of the observed elliptical image shape for circular sources from the continuous, thick-lens method with the comm…
We investigate the weak lensing effect by line-of-sight structures with a surface mass density of <~10^8 solar mass/arcsec^2 in QSO-galaxy quadruple lens systems. Using high-resolution N-body simulations in warm dark matter (WDM) models and observed four quadruple lenses that show anomalies in the flux ratios, we obtain constraints on the mass of thermal WDM, m_WDM>= 1.3keV(95%CL) assuming that the density of the primary lens is described by a singular isothermal ellipsoid (SIE). The obtained constraint is consistent with those from Lyman-$α$ forests and the number counts of high-redshift gala…
We investigate how Einstein rings and magnified arcs are affected by small-mass dark-matter haloes placed along the line-of-sight to gravitational lens systems. By comparing the gravitational signature of line-of-sight haloes with that of substructures within the lensing galaxy, we derive a mass-redshift relation that allows us to rescale the detection threshold (i.e. lowest detectable mass) for substructures to a detection threshold for line-of-sight haloes at any redshift. We then quantify the line-of-sight contribution to the total number density of low-mass objects that can be detected thr…
We report on discovery results from a quasar lens search in the ATLAS public footprint, extending quasar lens searches to a regime without $u-$band or fiber-spectroscopic information, using a combination of data mining techniques on multi-band catalog magnitudes and image-cutout modelling. Spectroscopic follow-up campaigns, conducted at the 2.6m Nordic Optical Telescope (La Palma) and 3.6m New Technology Telescope (La Silla) in 2016, yielded seven pairs of quasars exhibiting the same lines at the same redshift and monotonic flux-ratios with wavelength (hereafter NIQs, Nearly Identical Quasar p…
