Gravitational Lensing Research Articles

Gravitational lensing in more realistic dark matter halo models

Gravitational lensing in more realistic dark matter halo models

A simple model of a gravitational lens from geometric optics

We propose a simple geometric optics analog of a gravitational lens with a refractive index equal to one at large distances and scaling like n(r)2=1+C2/r2, where C is a constant. We obtain the equation for ray trajectories from Fermat's principle of least time and the Euler equation. Our model yields a very simple ray trajectory equation. The optical rays bending, reflecting, and looping around the lens are all described by a single trigonometric function in polar coordinates. Optical rays experiencing fatal attraction are described by a hyperbolic function. We use our model to illustrate the formation of Einstein rings and multiple images.

Theoretical wavelet ℓ1-norm from one-point probability density function prediction

Context. Weak gravitational lensing, which results from the bending of light by matter along the line of sight, is a potent tool for exploring large-scale structures, particularly in quantifying non-Gaussianities. It is a pivotal objective for upcoming surveys. In the realm of current and forthcoming full-sky weak-lensing surveys, convergence maps, which represent a line-of-sight integration of the matter density field up to the source redshift, facilitate field-level inference. This provides an advantageous avenue for cosmological exploration. Traditional two-point statistics fall short of capturing non-Gaussianities, necessitating the use of higher-order statistics to extract this crucial information. Among the various available higher-order statistics, the wavelet ℓ1 -norm has proven its efficiency in inferring cosmology. However, the lack of a robust theoretical framework mandates reliance on simulations, which demand substantial resources and time. Aims. Our novel approach introduces a theoretical prediction of the wavelet ℓ1-norm for weak-lensing convergence maps that is grounded in the principles of large-deviation theory. This method builds upon recent work and offers a theoretical prescription for an aperture mass one-point probability density function. Methods. We present for the first time a theoretical prediction of the wavelet ℓ1-norm for convergence maps that is derived from the theoretical prediction of their one-point probability distribution. Additionally, we explored the cosmological dependence of this prediction and validated the results on simulations. Results. A comparison of our predicted wavelet ℓ1 -norm with simulations demonstrates a high level of accuracy in the weakly nonlinear regime. Moreover, we show its ability to capture cosmological dependence. This paves the way for a more robust and efficient parameter-inference process.

Microlensing analysis of 14.5-year light curves in SDSS J1004+4112: Quasar accretion disk size and intracluster stellar mass fraction

Context. The gravitational lens system SDSS J1004+4112 was the first known example of a quasar lensed by a galaxy cluster. The interest in this system has been renewed following the publication of r-band light curves spanning 14.5 years and the determination of the time delays between the four brightest quasar images. Aims. We constrained the quasar accretion disk size and the fraction of the lens mass in stars using the signature of microlensing in the quasar image light curves. Methods. We built the six possible histograms of microlensing magnitude differences between the four quasar images and compared them with simulated model histograms, using a χ2 test to infer the model parameters. Results. We infer a quasar disk half-light radius of R1/2 = (0.70 ± 0.04)RE = (6.4 ± 0.4) √M/0.3M⊙ light-days at 2407 Å in the rest frame and stellar mass fractions at the quasar image positions of αA > 0.059, αB = 0.056+0.021-0.027, αC = 0.030+0.031-0.021, and αD = 0.072+0.034-0.016. Conclusions. The inferred disk size is broadly compatible with most previous estimates, and the stellar mass fractions are within the expected ranges for galaxy clusters. In the region where image C lies, the stellar mass fraction is compatible with a stellar contribution from the brightest cluster galaxy, galaxy cluster members, and intracluster light, but the values at images B, D, and especially A are slightly larger, possibly suggesting the presence of extra stellar components.

A deconstruction of methods to derive one-point lensing statistics

Gravitational lensing is a crucial tool for exploring cosmic phenomena, providing insights into galaxy clustering, dark matter, and dark energy. Given the substantial computational demands of N-body simulations, approximate methods like 𝙿𝙸𝙽𝙾𝙲𝙲𝙷𝙸𝙾 and 𝚝𝚞𝚛𝚋𝚘𝙶𝙻 have been proposed as viable alternatives for simulating lensing probability density functions (PDFs). This paper evaluates these methods and their effectiveness across both weak and strong lensing regimes, with a focus in the context where baryonic effects are negligible. Our comparative analysis reveals that these methods are effective for applications where lensing is mild, such as the majority of sources of electromagnetic and gravitational waves. However, both 𝙿𝙸𝙽𝙾𝙲𝙲𝙷𝙸𝙾 and 𝚝𝚞𝚛𝚋𝚘𝙶𝙻 break down for large values of convergence and magnification due to their loss of accuracy in capturing small-scale nonlinear matter fields, owing to oversimplified assumptions about internal halo structures and reliance on perturbation theory. 𝙿𝙸𝙽𝙾𝙲𝙲𝙷𝙸𝙾 yields second-to-fourth moments of the lensing PDFs, which are 6–10% smaller than those resulting from N-body simulations in regimes where baryonic effects are minimal. These findings aim to inform future studies on gravitational lensing of point sources, which are increasingly relevant with upcoming supernova and gravitational wave datasets.

HOLISMOKES. XI. Evaluation of supervised neural networks for strong-lens searches in ground-based imaging surveys

While supervised neural networks have become state of the art for identifying the rare strong gravitational lenses from large imaging data sets, their selection remains significantly affected by the large number and diversity of non-lens contaminants. This work evaluates and compares systematically the performance of neural networks in order to move towards a rapid selection of galaxy-scale strong lenses with minimal human input in the era of deep, wide-scale surveys. We used multiband images from PDR2 of the Hyper-Suprime Cam (HSC) Wide survey to build test sets mimicking an actual classification experiment, with 189 securely-identified strong lenses from the literature over the HSC footprint and 70\,910 non-lens galaxies in COSMOS covering representative lens-like morphologies. Multiple networks were trained on different sets of realistic strong-lens simulations and non-lens galaxies, with various architectures and data preprocessing, mainly using the deepest $gri$-bands. Most networks reached excellent area under the Receiver Operating Characteristic (ROC) curves on the test set of 71,099 objects, and we determined the ingredients to optimize the true positive rate for a total number of false positives equal to zero or 10 $ and TPR$_ $). The overall performances strongly depend on the construction of the ground-truth training data and they typically, but not systematically, improve using our baseline residual network architecture presented in HOLISMOKES VI. TPR$_ $ tends to be higher for ResNets (simeq 10--40<!PCT!>) compared to AlexNet-like networks or G-CNNs. Improvements are found when (1) applying random shifts to the image centroids, (2) using square-root scaled images to enhance faint arcs, (3) adding $z$-band to the otherwise used $gri$-bands, or (4) using random viewpoints of the original images. In contrast, we find no improvement when adding $g - i$ difference images (where alpha is a tuned constant) to subtract emission from the central galaxy. The most significant gain is obtained with committees of networks trained on different data sets, with a moderate overlap between populations of false positives. Nearly-perfect invariance to image quality can be achieved by using realistic PSF models in our lens simulation pipeline, and by training networks either with large number of bands, or jointly with the PSF and science frames. Overall, we show the possibility to reach a $ as high as 60<!PCT!> for the test sets under consideration, which opens promising perspectives for pure selection of strong lenses without human input using the Rubin Observatory and other forthcoming ground-based surveys.

Searching for Dark Matter Based on Gravitational Lensing

Gravitational lensing is a powerful astronomical tool in which scholars can accurately predict the distribution of dark matter in massive objects by observing the bending effects of light in the gravitational fields of huge objects (e.g., galaxies or galaxy clusters). Since dark matter does not emit directly, or is strongly interacts with ordinary matter, gravitational lensing gives us a unique view of observing and measuring dark matter. This study introduces some principles of gravitational lensing effect to provide favorable evidence in the study of dark matter and other celestial bodies (including an engineering study in the focal region of solar gravitational lensing (SGL) and other experiments). This research will see how the properties of the clear and focused gravitational lens are applied to celestial observations, and how they are captured by the detector. Strong gravitational lensing can better show distant galaxies (including high redshift) around the dark matter distribution, and through the several basic quantities in gravitational lens analytical and numerical calculation and analysis, to simulate the center of the supermassive black hole, and gravitational lensing image and model of dark matter mass can be detected and dark matter has the key evidences of the interaction. It reveals the intrinsic and distribution of dark matter, thus driving the understanding of the universe’s evolution and its fundamental components. Therefore, gravitational lensing has an irreplaceable value and a far-reaching influence in exploring the unsolved mystery of dark matter.

Analysis of the Current Status and Means of Studying Gravitational Lensing

Lens in physics is a kind of mirror that deflects light and results in a deflated and distorted image of the light-emitting object. Hence, the phenomenon of a massive celestial object deflecting light to form a distorted, magnified image of a luminous object is well known as gravitational lensing. In this paper, a brief summary of the concept and the status quo of the research and methodology related to it is rendered. This study offers a review of the overall founding history of the concept, and presents the current advances in relevant research. Later, the principles of generation and construction modeling of the concept, basic methodology are demonstrated. Subsequently, the applications of gravitational lensing in dark matter research, celestial body relationship research and validation of research results will be illustrated with examples of recent research. Then, the potential discrepancies in the use of gravitational lensing and future prospects are discussed in short. These results intended to help scholars who lack an understanding of the concept to have a primer on the field of gravitational lensing.

Spectroscopic analysis of the strongly lensed SN Encore: Constraints on cosmic evolution of Type Ia supernovae

Abstract Strong gravitational lensing magnifies the light from a background source, allowing us to study these sources in detail. Here, we study the spectra of a z = 1.95 lensed Type Ia supernova SN Encore for its brightest Image A, taken 39 days apart. We infer the spectral age with template matching using the supernova identification (SNID) software and find the spectra to be at 29.0 ±5.0 and 37.4 ±2.8 rest-frame days post maximum respectively, consistent with separation in the observer frame after accounting for time-dilation. Since SNe Ia measure dark energy properties by providing relative distances between low- and high-z SNe, it is important to test for evolution of spectroscopic properties. Comparing the spectra to composite low-z SN Ia spectra, we find strong evidence for similarity between the local sample and SN Encore. The line velocities of common SN Ia spectral lines, Si II 6355 and Ca II NIR triplet are consistent with the distribution for the low-z sample as well as other lensed SNe Ia, e.g. iPTF16geu (z = 0.409)and SN H0pe (z = 1.78). The consistency between the low-z sample and lensed SNe at high-z suggests no obvious cosmic evolution demonstrating their using as high-z distance indicators, though this needs to be confirmed/refuted via a larger sample. We also find that the spectra of SN Encore match the predictions for explosion models very well. With future large samples of lensed SNe Ia e.g. with the Vera C. Rubin Observatory, spectra at such late phases will be important to distinguish between different explosion scenarios.

Analogy of space-time as an elastic medium - Estimation of a creep coefficient of space from space data via the MOND theory and the gravitational lensing effect - the ball cluster and via time data from the GPS effect- comparison, discussion and implication of the results for dark matter and Einstein's field equation

Analogy of space-time as an elastic medium - Estimation of a creep coefficient of space from space data via the MOND theory and the gravitational lensing effect - the ball cluster and via time data from the GPS effect- comparison, discussion and implication of the results for dark matter and Einstein's field equation

Modeling and Subtracting Diffuse Cluster Light in JWST Images: A Relation between the Spatial Distribution of Globular Clusters, Dwarf Galaxies, and Intracluster Light in the Lensing Cluster SMACS 0723

We present a methodology for modeling and removing light from cluster galaxies and intracluster light (ICL) from James Webb Space Telescope images of gravitational lensing clusters. We apply our method to Webb’s First Deep Field the SMACS 0723 Early Release Observations and use the ICL-subtracted images to select a sample of globular clusters (GCs) and dwarf galaxies within the cluster. We compare the spatial distributions of these two samples with our models of the galaxy and ICL light, finding significant similarities. In particular, we find that GCs trace the diffuse ICL, while dwarf galaxies are centrally concentrated near the cluster center We quantify the relationship between the surface density of compact sources and total cluster light, demonstrating a significant, tight correlation. We repeat our methodology and compare distributions of GCs with the dark matter surface density and find a comparable result. Our findings suggest a common origin for GCs and diffuse ICL, with stripping from massive galaxies as they merge with the cluster being a plausible scenario.

Survey of Gravitationally lensed Objects in HSC Imaging (SuGOHI) − X. Strong Lens Finding in The HSC-SSP using Convolutional Neural Networks

Abstract We apply a novel model based on convolutional neural networks (CNN) to identify gravitationally-lensed galaxies in multi-band imaging of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) Survey. The trained model is applied to a parent sample of 2 350 061 galaxies selected from the ∼ 800 deg2 Wide area of the HSC-SSP Public Data Release 2. The galaxies in HSC Wide are selected based on stringent pre-selection criteria, such as multiband magnitudes, stellar mass, star formation rate, extendedness limit, photometric redshift range, etc. The trained CNN assigns a score from 0 to 1, with 1 representing lenses and 0 representing non-lenses. Initially, the CNN selects a total of 20 241 cutouts with a score greater than 0.9, but this number is subsequently reduced to 1 522 cutouts after removing definite non-lenses for further visual inspection. We discover 43 grade A (definite) and 269 grade B (probable) strong lens candidates, of which 97 are completely new. In addition, we also discover 880 grade C (possible) lens candidates, 289 of which are known systems in the literature. We identify 143 candidates from the known systems of grade C that had higher confidence in previous searches. Our model can also recover 285 candidate galaxy-scale lenses from the Survey of Gravitationally lensed Objects in HSC Imaging (SuGOHI), where a single foreground galaxy acts as the deflector. Even though group-scale and cluster-scale lens systems are not included in the training, a sample of 32 SuGOHI-c (i.e., group/cluster-scale systems) lens candidates is retrieved. Our discoveries will be useful for ongoing and planned spectroscopic surveys, such as the Subaru Prime Focus Spectrograph project, to measure lens and source redshifts in order to enable detailed lens modelling.

Lensing Point-spread Function of Coherent Astrophysical Sources and Nontrivial Wave Effects

Most research on astrophysical lensing has been conducted using the geometric optics framework, where there exists a clear concept of lensing images. However, wave optics effects can be important for coherent sources, e.g., pulsars, fast radio bursts, and gravitational waves observed at long wavelengths. There, the concept of lensing images needs an extension. We introduce the concept of the “lensing point-spread function” (LPSF), the smoothed flux density distribution of a coherent point source after being lensed, as a generalization of the lensing image concept at finite frequencies. The frequency-dependent LPSF captures the gradual change of the flux density distribution of the source from discrete geometric images at high frequencies to a smooth distribution at low frequencies. It complements other generalizations of lensing images, notably the imaginary images and the Lefschetz thimbles. Being a footprint of a lensing system, the LPSF is useful for theoretical studies of lensing. Using the LPSF, we identify a frequency range with nontrivial wave effects, where both geometric optics and perturbative wave optics fail, and determine this range to be ∣κ∣−1 ≲ ν ≲ 10, with κ and ν being the dimensionless lens amplitude and the reduced observing frequency, respectively. Observation of LPSFs with nontrivial wave effects requires either very close-by lenses or very large observing wavelengths. The potential possibilities are the lensing of gravitational waves, the plasma lensing of Milky Way pulsars, and lensing by the solar gravitational lens.

A Survey of Dynamical and Gravitational Lensing Tests in Scale Invariance: The Fall of Dark Matter?

We first briefly review the adventure of scale invariance in physics, from Galileo Galilei, Weyl, Einstein, and Feynman to the revival by Dirac (1973) and Canuto et al. (1977). In the way that the geometry of space–time can be described by the coefficients gμν, a gauging condition given by a scale factor λ(xμ) is needed to express the scaling. In general relativity (GR), λ=1. The “Large Number Hypothesis” was taken by Dirac and by Canuto et al. to fix λ. The condition that the macroscopic empty space is scale-invariant was further preferred (Maeder 2017a), the resulting gauge is also supported by an action principle. Cosmological equations and a modified Newton equation were then derived. In short, except in extremely low density regions, the scale-invariant effects are largely dominated by Newtonian effects. However, their cumulative effects may still play a significant role in cosmic evolution. The theory contains no “adjustment parameter”. In this work, we gather concrete observational evidence that scale-invariant effects are present and measurable in astronomical objects spanning a vast range of masses (0.5 M⊙< M <1014M⊙) and an equally impressive range of spatial scales (0.01 pc < r < 1 Gpc). Scale invariance accounts for the observed excess in velocity in galaxy clusters with respect to the visible mass, the relatively flat/small slope of rotation curves in local galaxies, the observed steep rotation curves of high-redshift galaxies, and the excess of velocity in wide binary stars with separations above 3000 kau found in Gaia DR3. Last but not least, we investigate the effect of scale invariance on gravitational lensing. We show that scale invariance does not affect the geodesics of light rays as they pass in the vicinity of a massive galaxy. However, scale-invariant effects do change the inferred mass-to-light ratio of lens galaxies as compared to GR. As a result, the discrepancies seen in GR between the total lensing mass of galaxies and their stellar mass from photometry may be accounted for. This holds true both for lenses at high redshift like JWST-ER1 and at low redshift like in the SLACS sample. Of note is that none of the above observational tests require dark matter or any adjustable parameter to tweak the theory at any given mass or spatial scale.

Fractional Einstein–Gauss–Bonnet Scalar Field Cosmology

Our paper introduces a new theoretical framework called the Fractional Einstein–Gauss–Bonnet scalar field cosmology, which has important physical implications. Using fractional calculus to modify the gravitational action integral, we derived a modified Friedmann equation and a modified Klein–Gordon equation. Our research reveals non-trivial solutions associated with exponential potential, exponential couplings to the Gauss–Bonnet term, and a logarithmic scalar field, which are dependent on two cosmological parameters, m and α0=t0H0 and the fractional derivative order μ. By employing linear stability theory, we reveal the phase space structure and analyze the dynamic effects of the Gauss–Bonnet couplings. The scaling behavior at some equilibrium points reveals that the geometric corrections in the coupling to the Gauss–Bonnet scalar can mimic the behavior of the dark sector in modified gravity. Using data from cosmic chronometers, type Ia supernovae, supermassive Black Hole Shadows, and strong gravitational lensing, we estimated the values of m and α0, indicating that the solution is consistent with an accelerated expansion at late times with the values α0=1.38±0.05, m=1.44±0.05, and μ=1.48±0.17 (consistent with Ωm,0=0.311±0.016 and h=0.712±0.007), resulting in an age of the Universe t0=19.0±0.7 [Gyr] at 1σ CL. Ultimately, we obtained late-time accelerating power-law solutions supported by the most recent cosmological data, and we proposed an alternative explanation for the origin of cosmic acceleration other than ΛCDM. Our results generalize and significantly improve previous achievements in the literature, highlighting the practical implications of fractional calculus in cosmology.

Optics equation provides approximation of gravitational lenses for students

Straighforward ray trajectory equation uses trigonometric and hyperbolic functions to model curves in space-time, including Einstein rings and fatal attraction near black holes.

Reconciling concentration to virial mass relations

The concentration--virial mass (c-M) relation is a fundamental scaling relation within the standard cold dark matter (Lambda CDM) framework well established in numerical simulations. However, observational constraints of this relation are hampered by the difficulty of characterising the properties of dark matter haloes. Recent comparisons between simulations and observations have suggested a systematic difference of the c-M relation, with higher concentrations in the latter. In this work, we undertake detailed comparisons between simulated galaxies and observations of a sample of strong-lensing galaxies. We explore several factors of the comparison with strong gravitational lensing constraints, including the choice of the generic dark matter density profile, the effect of radial resolution, the reconstruction limits of observed versus simulated mass profiles, and the role of the initial mass function in the derivation of the dark matter parameters. Furthermore, we show the dependence of the c-M relation on reconstruction and model errors through a detailed comparison of real and simulated gravitational lensing systems. An effective reconciliation of simulated and observed c-M relations can be achieved if one considers less strict assumptions on the dark matter profile, for example, by changing the slope of a generic NFW profile or focusing on rather extreme combinations of stellar-to-dark matter distributions. A minor effect is inherent to the applied method: fits to the NFW profile on a less well-constrained inner mass profile yield slightly higher concentrations and lower virial masses.

Euclid II. The VIS instrument

This paper presents the specification, design, and development of the Visible Camera (VIS) on the European Space Agency's mission. VIS is a large optical-band imager with a field of view of 0.54 deg$^2$ sampled at with an array of 609 Megapixels and a spatial resolution of . It will be used to survey approximately 14 000 deg$^2$ of extragalactic sky to measure the distortion of galaxies in the redshift range $z=0.1$--1.5 resulting from weak gravitational lensing, one of the two principal cosmology probes leveraged by With photometric redshifts, the distribution of dark matter can be mapped in three dimensions, and the extent to which this has changed with look-back time can be used to constrain the nature of dark energy and theories of gravity. The entire VIS focal plane will be transmitted to provide the largest images of the Universe from space to date, specified to reach AB with a signal-to-noise ratio S/N in a single broad E (r+i+z)$ band over a six-year survey. The particularly challenging aspects of the instrument are the control and calibration of observational biases, which lead to stringent performance requirements and calibration regimes. With its combination of spatial resolution, calibration knowledge, depth, and area covering most of the extra-Galactic sky, VIS will also provide a legacy data set for many other fields. This paper discusses the rationale behind the conception of VIS and describes the instrument design and development, before reporting the prelaunch performance derived from ground calibrations and brief results from the in-orbit commissioning. VIS should reach fainter than AB =25$ with $ S/N 10$ for galaxies with a full width at half maximum of in a diameter aperture over the Wide Survey, and $m_ AB for a Deep Survey that will cover more than 50 deg$^2$. The paper also describes how the instrument works with the telescope and survey, and with the science data processing, to extract the cosmological information.

Gravitational lensing around a dual-charged stringy black hole in plasma background

One of the strongest tools to verify the predictions of general relativity (GR) has been the gravitational lensing around various compact objects. Using a dual charged stringy black hole produced from dilaton-Maxwell gravity, we investigate the impact of the plasma parameter on gravitational lensing and black hole shadow in this study. Detailed investigations are performed to mark the impact of the homogeneous and non-homogeneous plasma environment on the electric and magnetic charge parameters of stringy black hole. In order to compare the results, we have also considered the vacuum scenario of the dual charged stringy black hole. Our results show that the effect of homogeneous plasma environment is much stronger in comparison to vacuum for the case of electrically charged stringy black hole. However, in the case of magnetically charged stringy black hole, the deflection angle gets decreased in presence of the homogeneous plasma medium. It has been observed that the radius of the shadow increases in a non-homogeneous plasma environment for electrically charged stringy black hole, whereas it decreases for magnetically charged stringy black hole in presence of the same plasma environment. This study aims to investigate how different plasma environments influence these fascinating astrophysical phenomena.

Underdetermination in classic and modern tests of general relativity

Canonically, ‘classic’ tests of general relativity (GR) include perihelion precession, the bending of light around stars, and gravitational redshift; ‘modern’ tests have to do with, inter alia, relativistic time delay, equivalence principle tests, gravitational lensing, strong field gravity, and gravitational waves. The orthodoxy is that both classic and modern tests of GR afford experimental confirmation of that theory in particular. In this article, we question this orthodoxy, by showing there are classes of both relativistic theories (with spatiotemporal geometrical properties different from those of GR) and non-relativistic theories (in which the lightcones of a relativistic spacetime are ‘widened’) which would also pass such tests. Thus, (a) issues of underdetermination in the context of GR loom much larger than one might have thought, and (b) given this, one has to think more carefully about what exactly such tests in fact are testing.