Gravitational Lensing Observations Research Articles

Gravitational lensing of spherically symmetric black holes in dark matter halos

The gravitational lensing of supermassive black holes surrounded by dark matter halo has attracted a great number of interests in recent years. However, many studies employed simplified dark matter density models, which makes it very hard to give a precise prediction on the dark matter effects in real astrophysical galaxies. In this work, to more accurately describe the distribution of dark matter in real astrophysical galaxies, we study the gravitational lensing of black holes in astrophysical dark matter halo models (Beta, Burkert, Brownstein, and Moore). The deflection angle is obtained using a generalized Gibbons-Werner approach. The visual angular positions and the Einstein rings are also calculated by adopting the gravitational lens equation. Specifically, we choose the supermassive black holes in Milky Way Galaxy, Andromeda galaxy (M31), Virgo galaxy (M87), and ESO138-G014 galaxy as examples, including the corresponding fitted value of dark matter halos. The results suggest that the dark matter halo described by the Beta model has non-negligible influences on the gravitational deflection angle and gravitational lensing observations. However, the Burkert, Brownstein, and Moore models have relatively small influences on angular position of images and the Einstein ring.

The SLACS strong lens sample, debiased

Strong gravitational lensing observations can provide extremely valuable information on the structure of galaxies, but their interpretation is made difficult by selection effects, which, if not accounted for, introduce a bias between the properties of strong lens galaxies and those of the general population. A rigorous treatment of the strong lensing bias requires, in principle, to fully forward model the lens selection process. However, doing so for existing lens surveys is prohibitively difficult. With this work we propose a practical solution to the problem: using an empirical model to capture the most complex aspects of the lens finding process, and constraining it directly from the data together with the properties of the lens population. We applied this method to real data from the SLACS sample of strong lenses. Assuming a power-law density profile, we recovered the mass distribution of the parent population of galaxies from which the SLACS lenses were drawn. We found that early-type galaxies with a stellar mass of log M*/M⊙ = 11.3 and average size have a median projected mass enclosed within a 5 kpc aperture of log M5/M⊙ = 11.332 ± 0.013, and an average logarithmic density slope of γ = 1.99 ± 0.03. These values are respectively 0.02 dex and 0.1 lower than inferred when ignoring selection effects. According to our model, most of the bias is due to the prioritisation of SLACS follow-up observations based on the measured velocity dispersion. As a result, the strong lensing bias in γ reduces to ∼0.01 when controlling for stellar velocity dispersion.

Investigating the shadows and strong gravitational lensing of modified Bardeen black holes

This study is dedicated to exploring the distinctive observational features affected by the modified Bardeen black hole through meticulous analysis of its shadow and strong gravitational lensing observations. We thoroughly investigated the impact of the black hole’s parameters q, g and μ on its shadow radius through numerical simulations and graphical representations. Utilizing the Event Horizon Telescope (EHT) data, we constrained the modified Bardeen black hole parameter μ of the modified Bardeen black hole within specific ranges: 0.24 ≤ μ ≤ 1.16 for M87*; and 0.036 ≤ μ ≤ 0.51 for Sgr A *, while maintaining the fixed values g = 0.2 and q = 0.3. This restriction of the modified Bardeen black hole parameter μ by the EHT findings illustrates the viability of modified Bardeen black holes as astrophysical candidates. Additionally, we study strong gravitational lensing and its various observables for the modified Bardeen black hole, comparing its behavior to other astrophysical black holes such as the Schwarzschild (μ = 0 = q) and Bardeen (μ = 0) black holes. By examining the astrophysical ramifications through strong gravitational lensing, considering supermassive black holes at the center of nearby galaxies, we uncovered that the modified Bardeen black hole exhibits distinct characteristics, offering a quantitative distinction from other black holes such as the Schwarzschild and Bardeen black holes. These findings in astrophysical consequences provide a promising pathway to differentiate the modified black hole from its counterparts in the realm of general relativity.

Complex angular structure of three elliptical galaxies from high-resolution ALMA observations of strong gravitational lenses

The large-scale mass distributions of galaxy-scale strong lenses have long been assumed to be well described by a singular ellipsoidal power-law density profile with external shear. However, the inflexibility of this model could lead to systematic errors in astrophysical parameters inferred with gravitational lensing observables. Here, we present observations with the Atacama Large (sub-)Millimetre Array (ALMA) of three strongly lensed dusty star-forming galaxies at $ mas angular resolution and investigate the sensitivity of these data to angular structure in the lensing galaxies. We jointly infer the lensing mass distribution and the full surface brightness of the lensed sources with multipole expansions of the power-law density profile up to the fourth order using a technique developed for interferometric data. All three datasets strongly favour third and fourth-order multipole amplitudes of $ percent of the convergence. While the infrared stellar isophotes and isodensity shapes agree for one lens system, for the other two the isophotes disagree to varying extents, suggesting contributions to the angular structure from dark matter intrinsic or extrinsic to the lensing galaxy.

Neural style transfer of weak lensing mass maps

We propose a new generative model of projected cosmic mass density maps inferred from weak gravitational lensing observations of distant galaxies (weak lensing mass maps). We construct the model based on a neural style transfer so that it can transform Gaussian weak lensing mass maps into deeply non-Gaussian counterparts as predicted in ray-tracing lensing simulations. We develop an unpaired image-to-image translation method with Cycle-Consistent Generative Adversarial Networks (Cycle GAN), which learn efficient mapping from an input domain to a target domain. Our model is designed to enjoy important advantages; it is trainable with no need for paired simulation data, flexible to make the input domain visually meaningful, and expandable to rapidly-produce a map with a larger sky coverage than training data without additional learning. Using 10,000 lensing simulations, we find that appropriate labeling of training data based on field variance allows the model to reproduce a correct scatter in summary statistics for weak lensing mass maps. Compared with a popular log-normal model, our model improves in predicting the statistical natures of three-point correlations and local properties of rare high-density regions. We also demonstrate that our model enables us to produce a continuous map with a sky coverage of ∼166deg2 but similar non-Gaussian features to training data covering ∼12deg2 in a GPU minute. Hence, our model can be beneficial to massive productions of synthetic weak lensing mass maps, which is of great importance in future precise real-world analyses.

Fast emulation of two-point angular statistics for photometric galaxy surveys

ABSTRACT We develop a set of machine-learning-based cosmological emulators, to obtain fast model predictions for the C(ℓ) angular power spectrum coefficients, characterizing tomographic observations of galaxy clustering and weak gravitational lensing from multiband photometric surveys (and their cross-correlation). A set of neural networks are trained to map cosmological parameters into the coefficients, achieving, with respect to standard Boltzmann solvers, a speed-up of $\mathcal {O}(10^3)$ in computing the required statistics for a given set of cosmological parameters, with an accuracy better than 0.175 per cent (<0.1 per cent for the weak lensing case). This corresponds to $\lesssim 2~{{\ \rm per\ cent}}$ of the statistical error bars expected from a typical Stage IV photometric surveys. Such overall improvement in speed and accuracy is obtained through (i) a specific pre-processing optimization, ahead of the training phase, and (ii) an effective neural network architecture. Compared to previous implementations in the literature, we achieve an improvement of a factor of 5 in terms of accuracy, while training a considerably lower amount of neural networks. This results in a cheaper training procedure and a higher computational performance. Finally, we show that our emulators can recover unbiased posteriors when analysing synthetic Stage-IV galaxy survey data sets.

The cold interstellar medium of a normal sub-L⋆ galaxy at the end of reionization

We present the results of a ∼60-h multiband observational campaign with the Atacama Large Millimeter Array targeting a spectroscopically confirmed and lensed sub-L⋆ galaxy at z = 6.07, first identified during the ALMA Lensing Cluster Survey (ALCS). We sampled the dust continuum emission from rest frame 90–370 μm at six different frequencies and set constraining upper limits on the molecular gas line emission and content by targeting the CO (7 − 6) and [C I](3P2−3P1) transitions in two lensed images with μ ≳ 20. Complementing these submillimeter observations with deep optical and near-IR photometry and spectroscopy with JWST, we find this galaxy to form stars at a rate of SFR ∼ 7 M⊙ yr−1, ∼50 − 70% of which is obscured by dust. This is consistent with what one would predict for a M⋆ ∼ 7.5 × 108 M⊙ object by extrapolating the relation between the fraction of the obscured star formation rate and stellar mass at z < 2.5 and with observations of IR-detected objects at 5 < z < 7. The light-weighted dust temperature of Tdust ∼ 50 K is similar to that of more massive galaxies at similar redshifts, although with large uncertainties and with possible negative gradients. We measure a dust mass of Mdust ∼ 1.5 × 106 M⊙ and, by combining [C I], [C II], and a dynamical estimate, a gas mass of Mgas ∼ 2 × 109 M⊙. Their ratio (δDGR) is in good agreement with predictions from models and empirical relations in the literature. The dust-to-stellar mass fraction of fdust ∼ 0.002 and the young stellar age (100 − 200 Myr) are consistent with efficient dust production via supernovae, as predicted by existing models and simulations of dust evolution. Also, the expected number density of galaxies with Mdust ∼ 106 M⊙ at z = 6 from a subset of these models is in agreement with the observational estimate that we set from the parent ALCS survey. The combination of gravitational lensing and deep multiwavelength observations allowed us to probe luminosity and mass regimes up to two orders of magnitude lower than what has been explored so far for field galaxies at similar redshifts. Our results serve as a benchmark for future observational endeavors of the high-redshift and faint sub-L⋆ galaxy population that might have driven the reionization of the Universe.

Assessing mass-loss and stellar-to-halo mass ratio of satellite galaxies: a galaxy–galaxy lensing approach utilizing DECaLS DR8 data

ABSTRACT The galaxy–galaxy lensing technique allows us to measure the subhalo mass of satellite galaxies, studying their mass-loss and evolution within galaxy clusters and providing direct observational validation for theories of galaxy formation. In this study, we use the weak gravitational lensing observations from Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys DR8, in combination with the redMaPPer galaxy cluster catalogue from Sloan Digital Sky Survey (SDSS) DR8 to accurately measure the dark matter halo mass of satellite galaxies. We confirm a significant increase in the stellar-to-halo mass ratio of satellite galaxies with their halo-centric radius, indicating clear evidence of mass-loss due to tidal stripping. Additionally, we find that this mass-loss is strongly dependent on the mass of the satellite galaxies, with satellite galaxies above $10^{11}~{{\rm M}_{\odot }}\, h^{-1}$ experiencing more pronounced mass-loss compared to lower mass satellites, reaching 86 per cent at projected halo-centric radius 0.5R200c. The average mass-loss rate, when not considering halo-centric radius, displays a U-shaped variation with stellar mass, with galaxies of approximately $4\times 10^{10}~{{\rm M}_{\odot }}\, h^{-1}$ exhibiting the least mass-loss, around 60 per cent. We compare our results with state-of-the-art hydrodynamical numerical simulations and find that the satellite galaxy stellar-to-halo mass ratio in the outskirts of galaxy clusters is higher compared to the predictions of the Illustris-TNG project about factor 5. Furthermore, the Illustris-TNG project’s numerical simulations did not predict the observed dependence of satellite galaxy mass-loss rate on satellite galaxy mass.

Gravitational lensing of Schwarzschild and charged black holes immersed in perfect fluid dark matter halo

Dark matter and dark energy dominate the behavior of our universe. The dark matter usually forms halo structures in large number of galaxies. Properties of dark matter halo can be revealed and understood from the gravitational lensing observations. In this work, a comprehensive study on the gravitational lensing of black holes immersed in dark matter halos is presented. To effectively model the supermassive black hole in a galaxy center (which is surrounded by dark matter halo) in a simple way, we investigate the Schwarzschild black hole and charged Reissner-Nordström black hole immersed in a perfect fluid dark matter halo. In the present work, several basic quantities in gravitational lensing (the gravitational deflection angle of light, photon sphere, black hole shadow radius, gravitational lens equation and Einstein ring) are calculated and analyzed analytically and numerically. A second order analytical expansion of gravitational deflection angle is obtained in the weak deflection limit, and the full gravitational deflection angle (including all order perturbation contributions applicable to both weak and strong deflection limits) is also calculated numerically as comparisons. It enables us to analyze the perfect fluid dark matter influences on gravitational deflection angle and gravitational lensing beyond the leading order, which were not sufficiently studied in previous works. Assuming M ∼ λDM ∼ Q, our results show that dark matter can greatly influence the gravitational lensing of central black holes.

Dynamics of the galactic component of Abell S1063 and MACS J1206.2−0847

Context. The galactic component in clusters is commonly thought to be generally nonrotating and in a dynamical state different from that of a collisionally relaxed system. In practice, a test for such conditions is often not available. Aims. We consider the member galaxies of the two clusters Abell S1063 and MACS J1206.2−0847 and study the possible presence of mean rotation and some properties of their distribution in phase space. We look for empirical evidence of factors normally found in collisionally relaxed systems and other characteristics of violently relaxed collisionless systems. Methods. Starting from the CLASH-VLT data, we obtained positions, stellar masses, and individual line-of-sight velocities for a large number of galaxies (NAS1063 ≈ 1200 and NM1206 ≈ 650) extending out to ≈1.6 (Abell) and ≈2.5 (MACS) times the radius r200. We studied the spatial distribution of the galaxy velocities and the properties of the available galaxy sets when divided into stellar mass bins. To test the presence of velocity dispersion anisotropy, we compared the results based on the Jeans equations with those obtained by assuming a specific form of the galaxy distribution function incorporating the picture of violent relaxation, where the total gravitational potential is imposed as set by the available gravitational lensing observations. Results. We find evidence of systematic rotation in both clusters, with significant rotation in each core (within 0.5′ from the center) and no signatures of rotation at large radii. While no signs of energy equipartition were found, there is a clear indication of (stellar) mass segregation. Velocity dispersion anisotropy is present and qualitatively similar to what has been found in violently relaxed collisionless systems. This last conclusion is strengthened by the overall success in matching the observations with the predictions of the physically justified distribution function.

Test of conformal theory of gravity as an alternative paradigm to dark matter hypothesis from gravitationallensing studies

Weyl's conformal gravity theory, which is considered as a compelling alternative to general relativity theory, has been claimed to describe the observed flat rotation curve feature of spiral galaxies without the need of invoking dark matter. However, it is important to examine whether the Weyl theory can also explain the relevant gravitational lensing observations correctly without considering any dark matter. In this regard, the gravitational bending angle in static spherically space-time (Mannheim-Kazanas metric) in Weyl theory has been calculated by several authors over the last two decades, but the results are found largely divergent. In this work, we have revisited the problem and obtain the correct and consistent expression of the deflection angle in conformal gravity. Subsequently we perform the gravitational lensing analysis. We compare the prediction of Weyl gravity with the gravitational lensing observations of the rich galaxy clusters Abell 370 and Abell 2390 and is found that Weyl theory cannot describe the stated lensing observations without considering dark matter.

Constraining interacting dark energy models with the halo concentration–mass relation

ABSTRACT The interacting dark energy (IDE) model is a promising alternative cosmological model that has the potential to solve the fine-tuning and coincidence problems by considering the interaction between dark matter and dark energy. Previous studies have shown that the energy exchange between the dark sector components in this model can significantly affect the dark matter halo properties. In this study, by utilizing a large set of cosmological N-body simulations, we analyse the redshift evolution of the halo concentration–mass (c–M) relation in the IDE model, and show that the c–M relation is a sensitive proxy of the interaction strength parameter ξ2, especially at lower redshifts. Furthermore, we construct parametrized formulae to quantify the dependence of the c–M relation on ξ2 at redshifts ranging from z = 0 to z = 0.6. Our parametrized formulae provide a useful theoretical tool in constraining ξ2 with the observational c–M relation. As a first attempt, we use the data from X-ray, gravitational lensing, and galaxy rotational curve observations and obtain a tight constraint on ξ2, i.e. ξ2 = 0.071 ± 0.034. Our work demonstrates that the halo c–M relation, which reflects the halo assembly history, is a powerful probe to constrain the IDE model.

The gravitational bending of acoustic Schwarzschild black hole

Acoustic black hole is becoming an attractive topic in recent years, for it open-up new direction for experimental/observational explorations of black holes. In this work, the gravitational bending of acoustic Schwarzschild black hole is investigated. The gravitational deflection angle of particles traveling along null geodesics, weak gravitational lensing and Einstein ring for acoustic Schwarzschild black hole are carefully studied and analyzed. Particularly, in the calculation of gravitational deflection angle, we resort to two approaches—the Gauss–Bonnet theorem and the geodesic method. The results show that the gravitational bending effect in acoustic Schwarzschild black hole is enhanced, compared with conventional Schwarzschild black hole. This result indicates that the acoustic black holes may be more easily detectable in gravitational bending effects and weak gravitational lensing observations.

Strong Deflection Gravitational Lensing for the Photons Coupled to the Weyl Tensor in a Conformal Gravity Black Hole

In the present paper, strong deflection gravitational lensing is studied in a conformal gravity black hole. With the help of geometric optics limits, we have formulated the light cone conditions for the photons coupled to the Weyl tensor in a conformal gravity black hole. It is explicitly found that strong deflection gravitational lensing depends on the coupling with the Weyl tensor, the polarization directions, and the black hole configuration parameters. We have applied the results of the strong deflection gravitational lensing to the supermassive black holes SgrA* and M87* and studied the possibility of encountering quantum improvement. It is not practicable to recognize similar black holes through the strong deflection gravitational lensing observables in the near future, except for the possible size of the black hole’s shadow. We also notice that by directly adopting the constraint of the measured shadow of M87*, the quantum effect demands immense care.

Statistical inference for strong gravitational lensing observations in the presence of dark matter

AbstractWe study the properties of strong lenses generated by dark matter galaxy halos in the Universe and the statistical inference process to understand the density profile of the lens. For that, we used mock data of strong gravitational lenses using the publicly available software paltas, which is a pipeline based on the well‐known package lenstronomy and written in Python. The deflectors are modeled according to the so‐called elliptical power law lens profile, and the background cosmology is assumed to be that of the standard cosmological model ΛCDM. The generated lensing observations include the contribution of dark matter substructure in the form of either subhalos or halos along the line of sight. In both cases, the underlying profile is the Navarro‐Frenk‐White one, which corresponds to the cold dark matter model. Performing a statistical inference process on these mock observations, our final objective is to identify the influence of the substructure on the inferred parameters that describe the lens profile.

Direct Tests of General Relativity under Screening Effect with Galaxy-scale Strong Lensing Systems

Observations of galaxy-scale strong gravitational lensing (SGL) systems have enabled unique tests of nonlinear departures from general relativity (GR) on the galactic and supergalactic scales. One of the most important cases of such tests are constraints on the gravitational slip between two scalar gravitational potentials. In this paper, we use a newly compiled sample of strong gravitational lenses to test the validity of GR, focusing on the screening effects on the apparent positions of lensed sources relative to the GR predictions. This is the first simultaneous measurement of the post-Newtonian parameter (γ PN) and the screening radius (Λ) without any assumptions about the contents of the universe. Our results suggest that the measured parameterized post-Newtonian is marginally consistent with GR (γ PN = 1) with increasing screening radius (Λ = 10–300 kpc), although the choice of lens models may have a significant influence on the final measurements. Based on a well-defined sample of 5000 simulated strong lenses from the forthcoming LSST, our methodology will provide a strong extragalactic test of GR with an accuracy of 0.5%, assessed up to scales of Λ ∼ 300 kpc. For the current and future observations of available SGL systems, there is no noticeable evidence indicating some specific cutoff scale on kiloparsec-megaparsec scales, beyond which new gravitational degrees of freedom are expressed.

Strong gravitational lensing and shadow constraint from M87* of slowly rotating Kerr-like black hole

Motivated by (i) more and more interest in strong gravitational lensing by supermassive black holes due to the achievement of EHT observations, (ii) the ongoing popular topic on the possibility of Lorentz symmetry being broken in gravitation and its consequences, we will apply the Einstein bumblebee gravity with Lorentz violation (LV) to the study of strong gravitational lensing effect and the black hole shadow of slowly rotating Kerr-like black hole. In the strong gravitational lensing sector, we first calculate the deflection angle; then treating the slowly rotating Kerr-like black hole as supermassive M87* black hole, we evaluate the gravitational lensing observables (position, separation and magnification) and the time delays between the relativistic images. In the black hole shadow sector, we show the effect of LV parameter on the luminosity of the black hole shadow and photon sphere using the infalling spherical accretion. Moreover, we explore the dependence of various shadow observables on the LV parameter, and then give the possible constraint on the LV parameter by M87* black hole of EHT observations. We find that the LV parameter shows significant effect on the strong gravitational lensing effect, the black hole shadow and photon sphere luminosity by accretion material. Our results point out that the future generations of EHT observation may help to distinguish the Einstein bumblebee gravity from GR, and also give a possible constrain on the LV parameter.

Constraining a modified gravity theory in strong gravitational lensing and black hole shadow observations

We study the strong gravitational lensing effect around rotating black holes in different gravity theories. By calculating the deflection angle of strong gravitational lensing, we evaluate the lensing observables including the image position, separation, magnification, and the time delays between the relativistic images of different rotating black holes. We argue that the differences in image positions, separations between the rotating black hole in modified gravity (MOG) theory and the Kerr black hole in general relativity (GR) are more significant in SgrA* than those in M87*; however the differences in time delays between rotating black holes in MOG and GR are shorter in SgrA* than that in M87*. Our evaluations on lensing observables in the strong gravity regime can help to distinguish the MOG from GR. Furthermore, we investigate the shadow observables of different rotating black holes. Employing the Event Horizon Telescope observations on the angular shadow radius for supermassive M87* and SgrA* black holes, respectively, we estimate the ranges of MOG parameter and obtain its upper limit constraint $0.350\ensuremath{\lesssim}{\ensuremath{\alpha}}_{\mathrm{up}}\ensuremath{\lesssim}0.485$ and $0.162\ensuremath{\lesssim}{\ensuremath{\alpha}}_{\mathrm{up}}\ensuremath{\lesssim}0.285$ correspondingly, relating to black hole spins. This is the first constraint on the MOG parameter for rotating supermassive black holes from Event Horizon Telescope observations on the angular shadow radius. Our constraint on the MOG parameter is much tighter compared with the result obtained from the orbital precession of the S2 star.

Constraining a possible time-variation of the speed of light along with the fine-structure constant using strong gravitational lensing and Type Ia supernovae observations

The possible time variation of the fundamental constants of nature has been an active subject of research since the large-number hypothesis was proposed by Dirac. In this paper, we propose a new method to investigate a possible time variation of the speed of light (c) along with the fine-structure constant (α) using Strong Gravitational Lensing (SGL) and Type Ia Supernovae (SNe Ia) observations. We assume a general approach to describe the mass distribution of lens-type galaxies, the one in favor of the power-law index model (PLAW). We also consider the runaway dilaton model to describe a possible time-variation of α. In order to explore the results deeply, we split the SGL sample into five sub-samples according to the lens stellar velocity dispersion and three sub-samples according to lens redshift. The results suggest that it is reasonable to treat the systems separately, but no strong indication of varying c was found.

Field-level inference of galaxy intrinsic alignment from the SDSS-III BOSS survey

As a large-scale overdensity collapses, it affects the orientation and shape of galaxies that form, by exerting tidal shear along their axes. Therefore, the shapes of elliptical galaxies align with the tidal field of cosmic structures. This intrinsic alignment provides insights into galaxy formation and the primordial universe, complements late-time cosmological probes and constitutes a significant systematic effect for weak gravitational lensing observations. In the present study, we provide constraints on the linear alignment model using a fully Bayesian field-level approach, using galaxy shape measurements from the SDSS-III BOSS LOWZ sample and three-dimensional tidal fields constrained with the LOWZ and CMASS galaxy samples of the SDSS-III BOSS survey. We find 4σ evidence of intrinsic alignment, with an amplitude of AI = 2.9 ± 0.7 at 20 Mpch.