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 relation enables us to define a threshold value alpha_CSL for the cusp slope, independent from location of the optical axis. The threshold cusp slope value alpha=alpha_CSL is the shallowest slope for the inner part of the GNFW profile that can produce the observed magnification ratio with any lensing configuration. We use distribution of these threshold values in a statistical study of the double image lenses in order to limit the possible cusp slope values, and identify whether there exists a population of haloes with similar profiles. Our theoretical fit indicates that within our sample of double image gravitational lenses, most of the haloes have cusp slope alpha=-1.95 +/- 0.02. We have also found an indication of a second population of lenses with a cusp slope value alpha=-1.49 +/- 0.09. We estimate that there is about 99 per cent probability that the observed feature in the threshold value limit distribution is produced by the second population of lenses, with their own characteristic density profile.
Many distant objects can only be detected, or become more scientifically valuable, if they have been highly magnified by strong gravitational lensing. We use EAGLE and BAHAMAS, two recent cosmological hydrodynamical simulations, to predict the probability distribution for both the lens mass and lens redshift when point sources are highly magnified by gravitational lensing. For sources at a redshift of two, we find the distribution of lens redshifts to be broad, peaking at z=0.6. The contribution of different lens masses is also fairly broad, with most high-magnification lensing due to lenses w…
The dominant uncertainty in the current measurement of the Hubble constant ($H_0$) with strong gravitational lensing time delays is attributed to uncertainties in the mass profiles of the main deflector galaxies. Strongly lensed supernovae (glSNe) can provide, in addition to measurable time delays, lensing magnification constraints when knowledge about the unlensed apparent brightness of the explosion is imposed. We present a hierarchical Bayesian framework to combine a dataset of SNe that are not strongly lensed and a dataset of strongly lensed SNe with measured time delays. We jointly constr…
I summarise recent results on multi-wavelength properties of distant lensed galaxies, with a particular focus on Herschel. Submm surveys have already resulted in a breakthrough discovery of an extremely efficient selection technique for strong gravitational lenses. Benefitting from the gravitational magnification boost, blind mm-wave redshifts have been demonstrated on IRAM, SMA and GBT, and follow-up emission line detections have been made of water, [OIII], [CII] and other species, revealing the PDR/XDR/CRDR conditions. I also discuss HST imaging of submm lenses, lensed galaxy reconstruction,…
It is well known that the sum of signed magnifications is invariant for mass lens systems. In this paper, we discuss the signed magnification sums of general spherical lens models including the singular isothermal sphere, the Schwarzschild lens and the Ellis wormhole, the last of which is an example of the traversable wormholes of the Morris-Thorne class. We show that the signed magnication sums are a very useful tool to distinguish exotic lens objects. For example, we show that one can distinguish the Ellis wormholes from the Schwarzschild lens with the signed magnification sums.
Bright submm-selected galaxies have been found to be a rich source of strong gravitational lenses. However, strong gravitational lensing of extended sources leads inevitably to differential magnification. In this paper I quantify the effect of differential magnification on simulated far-infrared and submm surveys of strong gravitational lenses, using a foreground population of Navarro-Frenk-White plus de Vaucouleurs' density profiles, with a model source resembling the Cosmic Eyelash and QSO J1148+5251. Some emission line diagnostics are surprisingly unaffected by differential magnification ef…
In this work, we mainly study the magnification relations of quad lens models for cusp, fold and cross configurations. By dividing and ray-tracing in different image regions, we numerically derive the positions and magnifications of the four images for a point source lying inside of the astroid caustic. Then, based on the magnifications, we calculate the signed cusp and fold relations for the singular isothermal elliptical lenses. The signed fold relation map has positive and negative regions, and the positive region is usually larger than the negative region as has been confirmed before. It c…
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 …
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…
The Euclid space telescope will observe ~10^5 strong galaxy-galaxy gravitational lens events in its wide field imaging survey over around half the sky, but identifying the gravitational lenses from their observed morphologies requires solving the difficult problem of reliably separating the lensed sources from contaminant populations, such as tidal tails, as well as presenting challenges for spectroscopic follow-up redshift campaigns. Here I present alternative selection techniques for strong gravitational lenses in both Euclid and the Square Kilometer Array, exploiting the strong magnificatio…
Weak lensing is one of the best available diagnostic tools to measure the total density profiles of distant clusters of galaxies. Unfortunately, it suffers from the well-known mass-sheet degeneracy, so that weak lensing analyses cannot lead to fully reliable determinations of the total mass of the clusters. One possible way to set the relevant scale of the density profile would be to make a direct measurement of the magnification produced by the clusters as gravitational lenses. In this paper we revisit a suggestion made a few years ago for this general purpose, based on the use of the Fundame…
We give the lens equation for light deflections caused by point mass condensations in an otherwise spatially homogeneous and flat universe. We assume the signal from a distant source is deflected by a single condensation before it reaches the observer. We call this deflector an embedded lens because the deflecting mass is part of the mean density. The embedded lens equation differs from the conventional lens equation because the deflector mass is not simply an addition to the cosmic mean. We prescribe an iteration scheme to solve this new lens equation and use it to compare our results with st…
Recent observations indicate that many if not all galaxies host massive central black holes (BHs). In this paper we explore the influence of supermassive binary black holes (SMBBHs) on their actions as gravitational lenses. When lenses are modelled as singular isothermal ellipsoids, binary black holes change the critical curves and caustics differently as a function of distance. Each black hole can in principle create at least one additional image, which, if observed, provides evidence of black holes. By studying how SMBBHs affect the cumulative distribution of magnification for images created…
Wide-field optical imaging surveys will contain tens of thousands of new strong gravitational lenses. Some of these will have new and unusual image configurations, and so will enable new applications: for example, systems with high image multiplicity will allow more detailed study of galaxy and group mass distributions, while high magnification is needed to super-resolve the faintest objects in the high redshift universe. Inspired by a set of six unusual lens systems [including five selected from the Sloan Lens ACS (SLACS) and Strong Lensing Legacy (SL2S) surveys, plus the cluster Abell 1703],…
Extending over three Hubble Space Telescope (HST) cycles, the Hubble Frontier Fields (HFF) initiative constitutes the largest commitment ever of HST time to the exploration of the distant Universe via gravitational lensing by massive galaxy clusters. We here present models of the mass distribution in the six HFF cluster lenses, derived from a joint strong- and weak-lensing analysis anchored by a total of 88 multiple-image systems identified in existing HST data. The resulting maps of the projected mass distribution and of the gravitational magnification effectively calibrate the HFF clusters a…
Magnification bias is a gravitational lensing effect that is normally overlooked because it is considered sub-optimal in comparison with the lensing shear. Thanks to the demonstrated optimal characteristics of the sub-millimetre galaxies (SMGs) for lensing analysis, in this work we were able to measure the magnification bias produced by a sample of QSOs acting as lenses, $0.2<z<1.0$, on the SMGs observed by Herschel at $1.2<z<4.0$. Two different methodologies were successfully applied: the traditional cross-correlation function approach and the Davis-Peebles estimator through stacking techniqu…
We report lensing magnifications, extinction, and time-delay estimates for the first resolved, multiply-imaged Type Ia supernova iPTF16geu, at $z = 0.409$, using $Hubble\,Space\,Telescope$ ($HST$) observations in combination with supporting ground-based data. Multi-band photometry of the resolved images provides unique information about the differential dimming due to dust in the lensing galaxy. Using $HST$ and Keck AO reference images taken after the SN faded, we obtain a total lensing magnification for iPTF16geu of $μ= 67.8^{+2.6}_{-2.9}$, accounting for extinction in the host and lensing ga…
We review five often used quad lens models, each of which has analytical solutions and can produce four images at most. Each lens model has two parameters, including one that describes the intensity of non-dimensional mass density, and the other one that describes the deviation from the circular lens. In our recent work, we have found that the cusp and the fold summations are not equal to 0, when a point source infinitely approaches a cusp or a fold from inner side of the caustic. Based on the magnification invariant theory, which states that the sum of signed magnifications of the total image…
In the final paper of this series, we extend our results on magnification invariants to the infinite family of A, D, E caustic singularities. We prove that for families of general mappings between planes exhibiting any caustic singularity of the A, D, E family, and for a point in the target space lying anywhere in the region giving rise to the maximum number of lensed images (real pre-images), the total signed magnification of the lensed images will always sum to zero. The proof is algebraic in nature and relies on the Euler trace formula.
Compound strong gravitational lensing is a rare phenomenon, but a handful of such lensed systems are likely to be discovered in forthcoming surveys. In this work, we use a double SIS lens model to analytically understand how the properties of the system impact image multiplicity for the final source. We find that up to six images of a background source can form, but only if the second lens is multiply imaged by the first and the Einstein radius of the second lens is comparable to, but does not exceed that of the first. We then build a model of compound lensing masses in the Universe, using SIE…
Magnification changes the observed number counts of galaxies on the sky. This biases the observed tangential shear profiles around galaxies, the so-called galaxy-galaxy lensing (GGL) signal, and the related excess mass profile. Correspondingly, inference of physical quantities, such as the mean mass profile of halos around galaxies, are affected by magnification effects. We use simulated shear and galaxy data of the Millennium Simulation to quantify the effect on shear and mass estimates from magnified lens and source number counts. The former are due to the large-scale matter distribution in …
With the increase in the number of observed gravitational wave (GW) signals, detecting strongly lensed GWs by galaxies has become a real possibility. Lens galaxies also contain microlenses (e.g., stars and black holes), introducing further frequency-dependent modulations in the strongly lensed GW signal within the LIGO frequency range. The multiple lensed signals in a given lens system have different underlying macro-magnifications ($|μ|$) and are located in varied microlens densities ($Σ_\bullet$), leading to different levels of microlensing distortions. This work quantifies the fraction of s…
We present the discovery of an extremely bright and extended lensed source from the second Red Sequence Cluster Survey (RCS2). RCSGA 032727-132609 is spectroscopically confirmed as a giant arc and counter-image of a background galaxy at $z=1.701$, strongly-lensed by the foreground galaxy cluster RCS2 032727-132623 at $z=0.564$. The giant arc extends over $\sim 38$\,\arcsec and has an integrated $g$-band magnitude of 19.15, making it $\sim 20$ times larger and $\sim 4$ times brighter than the prototypical lensed galaxy MS1512-cB58. This is the brightest distant lensed galaxy in the Universe kno…
We present estimates for the size and the logarithmic slope of the disk temperature profile of the lensed quasar Q2237+0305, independent of the component velocities. These estimates are based on six epochs of multi-wavelength narrowband images from the Nordic Optical Telescope. For each pair of lensed images and each photometric band, we determine the microlensing amplitude and chromaticity using pre-existing mid-IR photometry to define the baseline for no microlensing magnification. A statistical comparison of the combined microlensing data (6 epochs $\times$ 5 narrow bands $\times$ 6 image p…
We present a Bayesian framework to account for the magnification bias from both strong and weak gravitational lensing in estimates of high-redshift galaxy luminosity functions. We illustrate our method by estimating the $z\sim8$ UV luminosity function using a sample of 97 Y-band dropouts (Lyman break galaxies) found in the Brightest of Reionizing Galaxies (BoRG) survey and from the literature. We find the luminosity function is well described by a Schechter function with characteristic magnitude of $M^\star = -19.85^{+0.30}_{-0.35}$, faint-end slope of $α= -1.72^{+0.30}_{-0.29}$, and number de…
Acting as powerful gravitational lenses, the strong lensing galaxy clusters of the deep Hubble Frontier Fields (HFF) program permit access to lower-luminosity galaxies lying at higher redshifts than hitherto possible. We analyzed the HFF to measure the volume density of Lyman-break galaxies at $z > 4.75$ by identifying a complete and reliable sample up to $z \simeq 10$. A marked deficit of such galaxies was uncovered in the highly magnified regions of the clusters relative to their outskirts, implying that the magnification of the sky area dominates over additional faint galaxies magnified abo…
With increasing sensitivities of the current ground-based gravitational-wave (GW) detectors, the prospects of detecting a strongly lensed GW signal are going to be high in the coming years. When such a signal passes through an intervening lensing galaxy or galaxy cluster, the embedded stellar-mass microlenses lead to interference patterns in the signal that may leave observable signatures. In this work, we present an extensive study of these wave effects in the LIGO/Virgo frequency band ($10$-$10^4$ Hz) due to the presence of the microlens population in galaxy-scale lenses for the first time. …
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…
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…
In 2016, the first strongly lensed Type Ia supernova, iPTF16geu at redshift $z=0.409$ with four resolved images arranged symmetrically around the lens galaxy at $z=0.2163$, was discovered. Here, refined observations of iPTF16geu, including the time delay between images, are used to decrease uncertainties in the lens model, including the the slope of the projected surface density of the lens galaxy, $Σ\propto r^{1-η}$, and to constrain the universal expansion rate $H_0$. Imaging with HST provides an upper limit on the slope $η$, in slight tension with the steeper density profiles indicated by i…
We report the discovery of a multiply-imaged gravitationally lensed Type Ia supernova, iPTF16geu (SN 2016geu), at redshift $z=0.409$. This phenomenon could be identified because the light from the stellar explosion was magnified more than fifty times by the curvature of space around matter in an intervening galaxy. We used high spatial resolution observations to resolve four images of the lensed supernova, approximately 0.3" from the center of the foreground galaxy. The observations probe a physical scale of $\sim$1 kiloparsec, smaller than what is typical in other studies of extragalactic gra…
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…
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…
LensWatch. II. Improved Photometry and Time-delay Constraints on the Strongly Lensed Type Ia Supernova 2022qmx ("SN Zwicky") with HST Template Observations
Galaxy-cluster gravitational lenses can magnify background galaxies by a total factor of up to ~50. Here we report an image of an individual star at redshift z=1.49 (dubbed "MACS J1149 Lensed Star 1 (LS1)") magnified by >2000. A separate image, detected briefly 0.26 arcseconds from LS1, is likely a counterimage of the first star demagnified for multiple years by a >~3 solar-mass object in the cluster. For reasonable assumptions about the lensing system, microlensing fluctuations in the stars' light curves can yield evidence about the mass function of intracluster stars and compact objects, inc…
The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an a…
The quadruple image configurations of gravitational lenses with vanishing ellipticity are examined. Even though such lenses asymptotically approach circularity, the configurations are stable if the position of the source relative to the vanishing diamond caustic is held constant. The configurations are the solutions of a quartic equation, an "Asymptotically Circular Lens Equation" (ACLE), parameterized by a single complex quantity. Several alternative parameterizations are examined. Relative magnifications of the images are derived. When a non-vanishing quadrupole, in the form of an external s…
SN 2022riv in RX J2129: Discovery, Spectroscopic Classification, and Microlensing of a Strongly Lensed Type Ia Supernova from JWST and HST Observations
University of Minnesota（明尼苏达大学）；Oklahoma State University（俄克拉荷马州立大学）；Space Telescope Science Institute（太空望远镜科学研究所）；Chiba University（千叶大学）；Instituto de Física de Cantabria（坎塔布里亚物理研究所）
Axions are a viable candidate for Cold Dark Matter (CDM) which should generically form minihalos of sub-planetary masses from white-noise isocurvature density fluctuations if the Peccei-Quinn phase transition occurs after inflation. Despite being denser than the larger halos formed out of adiabatic fluctuations from inflation, axion minihalos have surface densities much smaller than the critical value required for gravitational lensing to produce multiple images or high magnification, and hence are practically undetectable as lenses in isolation. However, their lensing effect can be enhanced w…
We model the strong lensing effect in the galaxy cluster PSZ1 G311.65-18.48 (z=0.443) with an improved version of the hybrid method WSLAP+. We extend the number of constraints by including the position of critical points, which are combined with the classic positional constraints of the lensed galaxies. We pay special attention to a transient candidate source (Tr) previously discovered in the giant Sunburst arc (z=2.37). Our lens model predicts Tr to be within a fraction of an arcsecond from the critical curve, having a larger magnification factor than previously found, but still not large eno…
