Gravitational Lens Image Research Articles

Synthetic gravitational lens image of the Sagittarius A* black hole with a thin disc model

ABSTRACT The images of Sagittarius A* published by the Event Horizon Telescope (ETH) Collaboration in 2022 present features that were associated with an emission ring consistent with what is expected from an accretion disc surrounding the supermassive black hole at the centre of our Galaxy. Here, we generate images of Sgr A* across different configurations of a simple accretion disc model that became successful, in our previous work, in reproducing the main features observed in M87*. Their best image, here reproduced in Fig. 1, suggests a geometric configuration of an inclined disc with three bright regions; which we have considered as our first configuration. Since we were not convinced with the results of this first configuration, we also explore in detail the case of nearly edge-on orientations which are a priori the expected geometry for a relaxed disc, as seen from the plane of the Galaxy. We have produced simulated images using an efficient ray tracing and geodesic deviation methodology that allows to account for deformation, relativistic, and magnification effects. We compare our synthetic images with the EHT images reconstructed with data from April 6 and 7 of 2017. We found that, although the EHT Collaboration seems to discard the image from April 6, our best suggested image resembles the output from the themis pipeline for April 6; which for us gives support for the edge-on configuration.

Pushing the limits of detectability: mixed dark matter from strong gravitational lenses.

One of the frontiers for advancing what is known about dark matter lies in using strong gravitational lenses to characterize the population of the smallest dark matter haloes. There is a large volume of information in strong gravitational lens images - the question we seek to answer is to what extent we can refine this information. To this end, we forecast the detectability of a mixed warm and cold dark matter scenario using the anomalous flux ratio method from strong gravitational lensed images. The halo mass function of the mixed dark matter scenario is suppressed relative to cold dark matter but still predicts numerous low-mass dark matter haloes relative to warm dark matter. Since the strong lensing signal receives a contribution from a range of dark matter halo masses and since the signal is sensitive to the specific configuration of dark matter haloes, not just the halo mass function, degeneracies between different forms of suppression in the halo mass function, relative to cold dark matter, can arise. We find that, with a set of lenses with different configurations of the main deflector and hence different sensitivities to different mass ranges of the halo mass function, the different forms of suppression of the halo mass function between the warm dark matter model and the mixed dark matter model can be distinguished with 40 lenses with Bayesian odds of 30:1.

Pixelated Reconstruction of Foreground Density and Background Surface Brightness in Gravitational Lensing Systems Using Recurrent Inference Machines

Modeling strong gravitational lenses in order to quantify distortions in the images of background sources and to reconstruct the mass density in foreground lenses has been a difficult computational challenge. As the quality of gravitational lens images increases, the task of fully exploiting the information they contain becomes computationally and algorithmically more difficult. In this work, we use a neural network based on the recurrent inference machine to reconstruct simultaneously an undistorted image of the background source and the lens mass density distribution as pixelated maps. The method iteratively reconstructs the model parameters (the image of the source and a pixelated density map) by learning the process of optimizing the likelihood given the data using the physical model (a ray-tracing simulation), regularized by a prior implicitly learned by the neural network through its training data. When compared to more traditional parametric models, the proposed method is significantly more expressive and can reconstruct complex mass distributions, which we demonstrate by using realistic lensing galaxies taken from the IllustrisTNG cosmological hydrodynamic simulation.

Strong gravitational lens image of the M87 black hole with a simple accreting matter model

ABSTRACT We study simulated images generated from an accretion disc surrounding the supermassive black hole hosted in the nearby galaxy M87. We approach the problem employing very simple accreting models inspired from magnetohydrodynamical simulations and introducing a new recipe for dealing with the combined integration of the geodesic and geodesic deviation equations in Kerr space–time, which allows for a convenient and efficient way to manage the system of equations. The geometry of the basic emission model is given by a two-temperature thin disc in the equatorial plane of the black hole supplemented by an asymmetric bar structure. We show that this configuration permits to generate the most salient features appearing in the EHT Collaboration images of M87 with impressive fidelity.

TDCOSMO

Time delay cosmography uses the arrival time delays between images in strong gravitational lenses to measure cosmological parameters, in particular the Hubble constantH0. 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 inferH0. We base the mock lenses on six quadruply imaged quasars that have delivered measurements of the Hubble constant, and quantify the additional uncertainties and/or bias on a lens-by-lens basis. We show that omitting dark substructure does not bias inferences ofH0. However, perturbations from substructure contribute an additional source of random uncertainty in the inferred value ofH0that scales as the square root of the lensing volume divided by the longest time delay. This additional source of uncertainty, for which we provide a fitting function, ranges from 0.7 − 2.4%. It may need to be incorporated in the error budget as the precision of cosmographic inferences from single lenses improves, and it sets a precision limit on inferences from single lenses.

PROBING THE INNER KILOPARSEC OF MASSIVE GALAXIES WITH STRONG GRAVITATIONAL LENSING

We examine the prospects of detecting demagnified images of gravitational lenses in observations of strongly lensed mm-wave molecular emission lines with ALMA. We model the lensing galaxies as a superposition of a dark matter component, a stellar component, and a central supermassive black hole and assess the detectability of the central images for a range of relevant parameters (e.g., stellar core, black hole mass, and source size). We find that over a large range of plausible parameters, future deep observations of lensed molecular lines with ALMA should enable detection of the central images at $\gtrsim 3\sigma$ significance. We use a Fisher analysis to examine the constraints that could be placed on these parameters in various scenarios and find that for large stellar cores, both the core size and the mass of the central SMBHs can be accurately measured. We also study the prospects for detecting binary SMBHs with such observations and find that only under rare conditions and with very long integrations ($\sim$40-hr) the masses of both SMBHs may be measured using the distortions of central images.

Effects of supermassive binary black holes on gravitational lenses

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 by black holes, we find that the cross section for at least one such additional image to have a magnification larger than $10^{-5}$ is comparable to the cross section for producing multiple-images in singular isothermal lenses. Such additional images may be detectable with high-resolution and large dynamic range maps of multiply-imaged systems from future facilities, such as the SKA. The probability of detecting at least one image (two images) with magnification above $10^{-3}$ is $\sim 0.2 \fBH$ ($\sim 0.05 \fBH$) in a multiply-imaged lens system, where $\fBH$ is the fraction of galaxies housing binary black holes. We also study the effects of SMBBHs on the core images when galaxies have shallower central density profiles (modelled as non-singular isothermal ellipsoids). We find that the cross section of the usually faint core images is further suppressed by SMBBHs. Thus their presence should also be taken into account when one constrains the core radius from the lack of central images in gravitational lenses.

Gravitational Lens Images Generated by Cosmic Strings

In this review paper the current understanding on the properties of cosmic strings is shortly outlined with spe- cial emphasis on the observational signatures which can be expected both in the optical, through gravitational lensing, and in the radio, through anisotropies in the cosmic microwave background. The experience gathered during the long term in- vestigation of the former candidate CSL-1 is also shortly summarized.

Deconvolution of HST images of the Cloverleaf gravitational lens

Archival HST/NICMOS-2 images of the Cloverleaf gravitational lens (H1413+117), a quadruply-imaged quasar, were analysed with a new method derived from the MCS deconvolution algorithm (Magain et al. 1998). This method is based on an iterative process which simultaneously allows us to determine the Point Spread Function (PSF) and to perform a deconvolution of images containing several point sources plus extended structures. As such, it is well-adapted to the processing of gravitational lens images, especially in the case of multiply-imaged quasars. Two sets of data were analysed: the first one, which was obtained through the F160W filter in 1997, basically corresponds to a continuum image, while the second one, obtained through the narrower F180M filter in 2003, is centered around the forbidden [Oiii] emission lines at the source redshift, thus probing the narrow-line region of the quasar. The deconvolution gives astrometric and photometric measurements in both filters and reveals the primary lensing galaxy as well as a partial Einstein ring. The high accuracy of the results is particularly important in order to model the lensing system and to reconstruct the source undergoing the strong lensing. The reliability of the method is checked on a synthetic image similar to H1413+117.

LENSVIEW: software for modelling resolved gravitational lens images

We have developed a new software tool, lensview, for modelling resolved gravitational lens images. Based on the lensmem algorithm, the software finds the best-fitting lens mass model and source brightness distribution using a maximum entropy constraint. The method can be used with any point spread function or lens model. We review the algorithm and introduce some significant improvements. We also investigate and discuss issues associated with the statistical uncertainties of models and model parameters and the issues of source plane size and source pixel size. We test the software on simulated optical and radio data to evaluate how well lens models can be recovered and with what accuracy. For optical data, lens model parameters can typically be recovered with better than 1 per cent accuracy, and the degeneracy between mass ellipticity and power law is reduced. For radio data, we find that systematic errors associated with using processed radio maps, rather than the visibilities, are of similar magnitude to the random errors. Hence analysing radio data in image space is still useful and meaningful. The software is applied to the optical arc HST J15433+5352 and the radio ring MG1549+3047 using a simple elliptical isothermal lens model. For HST J15433+5352, the Einstein radius is 0.525 ± 0.015 arcsec which probably includes a substantial convergence contribution from a neighbouring galaxy. For MG1549+3047, the model has Einstein radius 1.105 ± 0.005 arcsec and core radius 0.16 ± 0.03 arcsec. The total mass enclosed in the critical radius is 7.06 × 1010 M⊙ for our best model. We finish by discussing issues relating to modelling of resolved lens images for this method and some alternatives.

The lens and source of the optical Einstein ring gravitational lens ER 0047-2808

We perform a detailed analysis of the optical gravitational lens ER 0047-2808 imaged with the Wide Field Planetary Camera 2 on the Hubble Space Telescope. Using software specifically designed for the analysis of resolved gravitational lens systems, we focus on how the image alone can constrain the mass distribution in the lens galaxy. We find that the data are of sufficient quality to strongly constrain the lens model with no a priori assumptions about the source. Using a variety of mass models, we find statistically acceptable results for elliptical isothermal-like models with an Einstein radius of 1.17 arcsec. An elliptical power-law model (Σ∝R−β) for the surface mass density favours a slope slightly steeper than isothermal with β= 1.08 ± 0.03. Other models including a constant mass-to-light ratio (M/L), pure Navarro, Frenk & White halo and (surprisingly) an isothermal sphere with external shear are ruled out by the data. We find the galaxy light profile can only be fit with a Sérsic plus point-source model. The resulting total M/LB contained within the images is 4.7 h65± 0.3. In addition, we find the luminous matter is aligned with the total mass distribution within a few degrees. This is the first time a resolved optical gravitational lens image has been quantitatively reproduced using a non-parametric source. The source, reconstructed by the software, is revealed to have two bright regions, with an unresolved component inside the caustic and a resolved component straddling a fold caustic. The angular size of the entire source is ~0.1 arcsec and its (unlensed) Lyα flux is 3 × 10−17 erg s−1 cm−2.

Image reconstruction technique and optical monitoring of the QSO2237+0305 from Maidanak Observatory in 2002-2003

We have observed the gravitational lens system Q2237+0305 from the Maidanak Observatory over the period from August 2002 to November 2003. Here we report the results of our observations. We implemented a two-stage technique that has been developed specifically for the purpose of gravitational lens image reconstruction. The technique is based on the Tikhonov regularization approach and allows one to obtain astrometric and photometric characteristics of the gravitational lens system. Light curves with 78 data points for the four quasar components are obtained. Slow brightness variations over the observational period are found in all components. Images A, C, D have a tendency to decrease in brightness. Image B does not vary more than 0.05mag. The observations did not reveal evidence for large variations in brightness of the components due to microlensing effects. To provide an overall picture of the photometry behaviour, our data are combined with the Maidanak observations published for 1995 -- 2000.

Semilinear Gravitational Lens Inversion

We describe a new method for analyzing gravitational lens images, for the case in which the source light distribution is pixelized. The method is suitable for high-resolution, high signal-to-noise ratio (S/N) data of a multiply imaged extended source. For a given mass distribution, we show that the step of inverting the image to obtain the deconvolved pixelized source light distribution, and the uncertainties, is a linear one. This means that the only parameters of the nonlinear problem are those required to model the mass distribution. This greatly simplifies the search for a minimum χ2 fit to the data and speeds up the inversion. The method is extended in a straightforward way to include linear regularization. We apply the method to simulated Einstein ring images and demonstrate the effectiveness of the inversion for both the unregularized and regularized cases.

Variability of gravitational lens images, caused by variability of gravitational field of lens: binary systems and loops of cosmic strings

Variability of gravitational lens images, caused by variability of gravitational field of lens: binary systems and loops of cosmic strings

Measuring the Size of Quasar Broad‐Line Clouds through Time‐Delay Light‐Curve Anomalies of Gravitational Lenses

Intensive monitoring campaigns have recently attempted to measure the time delays between multiple images of gravitational lenses. Some of the resulting light-curves show puzzling low-level, rapid variability which is unique to individual images, superimposed on top of (and concurrent with) longer time-scale intrinsic quasar variations which repeat in all images. We demonstrate that both the amplitude and variability time-scale of the rapid light-curve anomalies, as well as the correlation observed between intrinsic and microlensed variability, are naturally explained by stellar microlensing of a smooth accretion disk which is occulted by optically-thick broad-line clouds. The rapid time-scale is caused by the high velocities of the clouds (~5x10^3 km/s), and the low amplitude results from the large number of clouds covering the magnified or demagnified parts of the disk. The observed amplitudes of variations in specific lenses implies that the number of broad-line clouds that cover ~10% of the quasar sky is ~10^5 per 4 pi steradian. This is comparable to the expected number of broad line clouds in models where the clouds originate from bloated stars.

Global Probes of the Impact of Baryons on Dark Matter Halos

The halo mass function, dn/dM, predicted by hierarchical clustering models can be measured indirectly using dynamical probes like the distribution of gravitational lens image separations, dn/dΔθ, or halo circular velocities, dn/dvc. These dynamical variables depend on the halo structure as well as the halo mass. Since baryonic physics, particularly cooling, significantly modifies the central density structure of dark matter halos, both observational distributions show a feature corresponding to the mass scale below which the baryons in the halo can cool (i.e., galaxies versus clusters). We use simplified but self-consistent models to show that the structural changes to the halos produced by the cooling baryons explain both distributions. Given a fixed halo mass function, matching the observed image separation distribution or local velocity function depends largely on Ωb through its effects on the cooling timescales. These baryonic effects on the halo structure also affect the evolution of the velocity function of galaxies with redshift.

The influence of central black holes on gravitational lenses

Recent observations indicate that many if not all galaxies host massive central black holes. In this paper we explore the influence of black holes on the lensing properties. We model the lens as an isothermal ellipsoid with a finite core radius plus a central black hole. We show that the presence of the black hole substantially changes the critical curves and caustics. If the black hole mass is above a critical value, then it will completely suppress the central images for all source positions. Realistic central black holes are likely to have masses below this critical value. Even in such subcritical cases, the black hole can suppress the central image when the source is inside a zone of influence, which depends on the core radius and black hole mass. In the subcritical cases, an additional image may be created by the black hole in some regions, which for some radio lenses may be detectable with high-resolution and large dynamic range VLBI maps. The presence of central black holes should also be taken into account when one constrains the core radius from the lack of central images in gravitational lenses.

CONSTRAINTS ON GALAXY EVOLUTION THROUGH GRAVITATIONAL LENSING STATISTICS

Explaining the formation and evolution of galaxies is one of the most challenging problems in observational cosmology. Many observations suggest that galaxies we see today could have evolved from the merging of smaller subsystems. Evolution of galaxies tells us how the mass or number density of the lens varies with cosmic time. Merging between the galaxies and the infall of surrounding mass into galaxies are two possible processes that can change the comoving number density of galaxies and/or their mass. We consider five different evolutionary models of galaxies. These models are: Non-evolutionary model, Guiderdoni and Volmerange model, fast merging, slow merging and mass accretion model. We study the gravitational lens image separation distribution function for these models of evolving galaxies. A comparison with data for lensed quasars taken from the HST snapshot survey rules out the fast merging model completely as this model produces a large number of small-separation lenses. It is possible that the mass accretion model and the non-evolutionary model of galaxies may be able to explain the small angle separations.

Two-dimensional Spectroscopy Reveals an Arc of Extended Emission in the Gravitational Lens System Q2237+0305

We present two-dimensional spectroscopy of the gravitational lens system Q2237+0305 (Einstein Cross) obtained with the INTEGRAL fiber system in subarcsecond seeing conditions. The four components of the system appear clearly separated in the continuum intensity maps. However, the intensity map of the C III] λ1909 line exhibits an arc of extended emission connecting the A, D, and B components. This result can be explained if, as is usually assumed, the continuum arises from a compact source ≲0.05 pc in extent in the nucleus of the object while the line emission comes from a much larger region. A lens model fitted to the positions of the four compact images also accounts for the arc morphology. In the framework of this model, the region generating the C III] λ1909 emission would have dimensions of about 400 h-1 pc across. We interpret the observed arc as a gravitational lens image of the extended narrow line region of the source.

Clusters Point to Never-Ending Universe

Until recently, the outlook for the expanding universe has varied with cosmological fashion. Now, a team of German and British researchers has simulated how the vast clusters of galaxies that bend the light of objects behind them should evolve over time in universes containing different densities of matter. They then compared the results to the number of gravitational lens images actually seen in the sky. The verdict: The simulation that best matches the observed lensing images is one that assumes a low-density, open universe.