Gravitational Lensing Properties Research Articles

Non-commutative Schwarzschild black hole surrounded by Perfect fluid dark matter: Plasma lensing and thermodynamics analysis

The focus of this paper is to examine the properties of thermodynamics and weak gravitational lensing about the geometry of black holes within the context of a non-commutative Schwarzschild black hole surrounded by Perfect fluid dark matter. We examine the geometric mass and thermal temperature in this context to discuss the stability of the black hole solution. We examine the phase transition and stability while calculating the specific heat. We also research the black hole's energy emission process. We deduce that our researched black hole solution is thermally stable based on its thermodynamic features. Furthermore, we analyze uniform and non-uniform plasma by calculating the deflection angle, and we examine gravitational lensing in the weak plasma field. It is observed that in uniform plasma, the deflection angle is larger than in non-uniform plasma. We also looked at the image magnification caused by source brightness and found that the source image is enlarged more in uniform plasma than in non-uniform plasma.

Strong gravitational lensing by Bardeen black holes in 4D EGB gravity: Constraints from supermassive black holes

Observation indicates that many nearby galaxies host supermassive central black holes. We use the Bardeen black holes in four-dimensional Einstein–Gauss–Bonnet (4D EGB) gravity, with additional parameters-the coupling constant α̃ and charge q, as central black holes in various galaxies to investigate gravitational lensing properties in strong field regime. Taking the supermassive black holes Sgr A* and M87* as the lens, we compare observable signatures of 4D EGB Bardeen black holes with those of the Schwarzschild black holes. In the case of 4D EGB Bardeen black holes we observed that he angular position θ∞ for Sgr A* ∈ (23.19, 25.56) μ as, whereas for M87* it is ∈ ( 17.94,19.78) μ as. Further, the angular separation s, which is an increasing function of α̃ and q for Sgr A* and M87* differs significantly, respectively, in (0.032, 0.15) μ as and (0.025, 0.115) μ as. The deviations of the lensing observables Δθ∞ and Δs for 4D EGB Bardeen black hole (α̃=0.9,q=0.09) from the Schwarzschild black hole, respectively, can reach up to 2.38μ as and 0.12μ as for Sgr A* , 1.84μ as and 0.09μ as for M87*. On the other hand, the relative magnification ∈ (4.66,6.82). Considering twenty-one massive central black holes as lens, we also estimate the time delay ΔT2,1s between the first and second relativistic image to find that, e.g., the time delay for Sgr A* and M87*, respectively, can reach ∼9.86 min and ∼16023.93 min. We also show that the existing shadow size measurements place strong constraints on the parameters considered Bardeen model. This combination of gravitational lensing and EHT results may complement comprehensive restrictions on modifications of the general relativity.

CHEX-MATE: CLUster Multi-Probes in Three Dimensions (CLUMP-3D). I. Gas analysis method using X-ray and Sunyaev–Zel’dovich effect data

Galaxy clusters are the products of structure formation through myriad physical processes that affect their growth and evolution throughout cosmic history. As a result, the matter distribution within galaxy clusters, or their shape, is influenced by cosmology and astrophysical processes, in particular the accretion of new material due to gravity. We introduce an analysis method for investigating the three-dimensional triaxial shapes of galaxy clusters from the Cluster HEritage project with -- Mass Assembly and Thermodynamics at the Endpoint of structure formation (CHEX-MATE). In this paper, the first in a CHEX-MATE triaxial analysis series, we focus on utilizing X-ray data from and Sunyaev-Zel'dovich (SZ) effect maps from and the Atacama Cosmology Telescope to obtain a three-dimensional triaxial description of the intracluster medium (ICM) gas. We present the forward modeling formalism of our technique, which projects a triaxial ellipsoidal model for the gas density and pressure, to be compared directly with the observed two-dimensional distributions in X-rays and the SZ effect. A Markov chain Monte Carlo is used to estimate the posterior distributions of the model parameters. Using mock X-ray and SZ observations of a smooth model, we demonstrate that the method can reliably recover the true parameter values. In addition, we applied the analysis to reconstruct the gas shape from the observed data of one CHEX-MATE galaxy cluster, PSZ2 G313.33+61.13 (Abell 1689), to illustrate the technique. The inferred parameters are in agreement with previous analyses for the cluster, and our results indicate that the geometrical properties, including the axial ratios of the ICM distribution, are constrained to within a few percent. With a much better precision than previous studies, we thus further establish that Abell 1689 is significantly elongated along the line of sight, resulting in its exceptional gravitational lensing properties.

Weak gravitational lensing by an ESTGB black hole in the presence of a plasma

This paper is devoted to studying the weak-field gravitational lensing properties of a 4D ESTGB black hole, which is surrounded by the plasma medium. The effects of the magnetic charges and the three plasma distribution models in the deflection of light around a 4D ESTGB black hole are investigated in detail. We find that the uniform plasma leads to a larger deflection of light rays in comparison with the singular isothermal sphere (SIS), the non-singular isothermal sphere (NSIS) models. Moreover, the deflection angle increases slightly as the absolute value of the magnetic charge decreases. Finally, we analyze the total magnification of image due to weak gravitational lensing around the black hole. The result shows that the presence of a uniform plasma medium remarkably enhances the total magnification whereas the non-uniform plasma reduces the total magnification.

The Application of Gravitational Lensing on Observation of Dark Matter Candidates

Basic properties of gravitational lensing could help scientists in detecting the structure of the universe. For instance, the non-luminous dark matter, cannot detected by normal astronomical telescope. The large population low-mass halo which is the cosmological mode of cold dark matter, CDM, locating along the line-of-sight will perturb the strong lensing. In that way, alternation of dark matter from CDM to WDM will be detected by analysis the halo perturbed image. The main proposes of this review is to introduce the history of gravitational lensing, describe the principle of gravitational lensing and state the application of gravitational lensing in modern astrophysics.

Galaxies in the central regions of simulated galaxy clusters

Context. Recent observations found that observed cluster member galaxies are more compact than their counterparts in ΛCDM hydrodynamic simulations, as indicated by the difference in their strong gravitational lensing properties, and they reported that measured and simulated galaxy–galaxy strong lensing events on small scales are discrepant by one order of magnitude. Among the possible explanations for this discrepancy, some studies suggest that simulations with better resolution and implementing different schemes for galaxy formation could produce simulations that are in better agreement with the observations. Aims. In this work, we aim to assess the impact of numerical resolution and of the implementation of energy input from AGN feedback models on the inner structure of cluster sub-haloes in hydrodynamic simulations. Methods. We compared several zoom-in re-simulations of a sub-sample of cluster-sized haloes obtained by varying mass resolution and softening the length and AGN energy feedback scheme. We studied the impact of these different setups on the sub-halo (SH) abundances, their radial distribution, their density and mass profiles, and the relation between the maximum circular velocity, which is a proxy for SH compactness Results. Regardless of the adopted numerical resolution and feedback model, SHs with masses of MSH ≲ 1011 h−1 M⊙, the most relevant mass range for galaxy–galaxy strong lensing, have maximum circular velocities ∼30% smaller than those measured from strong lensing observations. We also find that simulations with less effective AGN energy feedback produce massive SHs (MSH ≳ 1011 h−1 M⊙) with higher maximum circular velocity and that their Vmax − MSH relation approaches the observed one. However, the stellar-mass number count of these objects exceeds the one found in observations, and we find that the compactness of these simulated SHs is the result of an extremely over-efficient star formation in their cores, also leading to larger than observed SH stellar mass. Conclusions. Regardless of the resolution and galaxy formation model adopted, simulations are unable to simultaneously reproduce the observed stellar masses and compactness (or maximum circular velocities) of cluster galaxies. Thus, the discrepancy between theory and observations that emerged previous works. It remains an open question as to whether such a discrepancy reflects limitations of the current implementation of galaxy formation models or the ΛCDM paradigm.

The Dependence of The Gravitational Lensing Properties on The Lens And Source Redshifts

This work aims to investigate the dependence of gravitational lensing properties on the lens redshift and source redshift.
 The angular diameter distance hereafter referred to as ADD has been determined using two different numerical integral methods, Simpson's rule, and definite integral methods. Both of those two methods gave identical results. In addition, observational data of gravitational Lensing systems have been used to find the most probable value of lens redshift and source redshift. The result showed that the lens redshift and source redshift are more likely to occur in the ranges of zL=0.2-0.6 and zS=1-3, respectively.
 Einstein radius and the critical surface mass density have been studied for those ranges of lens and source redshift. The result clearly showed that the redshifts and distances affect the lensing properties. This indicates that observations of gravitational lensing can be efficiently used to probe the distances and redshifts.

Gravitational Lensing by a Massive Object in a Dark Matter Halo. I. Critical Curves and Caustics

Abstract We study the gravitational lensing properties of a massive object in a dark matter halo, concentrating on the critical curves and caustics of the combined lens. We model the system in the simplest approximation by a point mass embedded in a spherical Navarro–Frenk–White density profile. The low number of parameters of such a model permits a systematic exploration of its parameter space. We present galleries of critical curves and caustics for different masses and positions of the point in the halo. We demonstrate the existence of a critical mass, above which the gravitational influence of the centrally positioned point is strong enough to eliminate the radial critical curve and caustic of the halo. In the point-mass parameter space we identify the boundaries at which critical-curve transitions and corresponding caustic metamorphoses occur. The number of transitions as a function of the position of the point is surprisingly high, ranging from three for higher masses to as many as eight for lower masses. On the caustics we identify the occurrence of six different types of caustic metamorphoses. We illustrate the peculiar properties of the single radial critical curve and caustic appearing in an additional unusual nonlocal metamorphosis for a critical mass positioned at the halo center. Although we construct the model primarily to study the lensing influence of individual galaxies in a galaxy cluster, it can also be used to study the lensing by dwarf satellite galaxies in the halo of a host galaxy, as well as (super)massive black holes at a general position in a galactic halo.

Fast Calculation of Gravitational Lensing Properties of Elliptical Navarro–Frenk–White and Hernquist Density Profiles

We present a new approach for fast calculation of gravitational lensing properties, including the lens potential, deflection angles, convergence, and shear, of elliptical Navarro–Frenk–White (NFW) and Hernquist density profiles, by approximating them by superpositions of elliptical density profiles for which simple analytic expressions of gravitational lensing properties are available. This model achieves high fractional accuracy better than 10−4 in the range of the radius normalized by the scale radius of 10−4–103. These new approximations are ∼300 times faster in solving the lens equation for a point source compared with the traditional approach resorting to expensive numerical integrations, and are implemented in glafic software.

Weak gravitational lensing Schwarzschild-MOG black hole in plasma

This paper is devoted to study weak gravitational lensing properties around black hole surrounded plasma medium in modified gravity (MOG). We have investigated the effects of the MOG-parametr and plasma medium on the deflection angle and total magnification of the images. we have presented the comparisons of the effects of the uniform plasma, singular isothermal sphere and non-singular isothermal sphere. We have also shown that the uniform plasma effects significantly stronger than the other models of plasma medium.Through the studies of the total magnifications of images of a remote source we have shown that the effects of the MOG parameter and plasma medium are similar and the increase of the MOG parameter and plasma frequency cause to increase the total magnification. Moreover, we have explored and analyzed how the MOG effects can reflect the plasma medium providing the same values of the total magnification of images.

The Dekel-Zhao profile: a mass-dependent dark-matter density profile with flexible inner slope and analytic potential, velocity dispersion, and lensing properties

ABSTRACTWe explore a function with two shape parameters for the dark-matter halo density profile subject to baryonic effects, which is a special case of the general Zhao family of models applied to simulated dark-matter haloes by Dekel et al. This profile has variable inner slope and concentration parameter, and analytic expressions for the gravitational potential, velocity dispersion, and lensing properties. Using the Numerical Investigation of a Hundred Astrophysical Objects cosmological simulations, we find that it provides better fits than the Einasto profile and the generalized NFW profile with variable inner slope, in particular towards the halo centres. We show that the profile parameters are correlated with the stellar-to-halo mass ratio Mstar/Mvir. This defines a mass-dependent density profile describing the average dark-matter profiles in all galaxies, which can be directly applied to observed rotation curves of galaxies, gravitational lenses, and semi-analytic models of galaxy formation or satellite–galaxy evolution. The effect of baryons manifests itself by a significant flattening of the inner density slope and a 20 per cent decrease of the concentration parameter for Mstar/Mvir = 10−3.5–10−2, corresponding to $M_{\rm star} \!\sim \! 10^{7-10}\, \mathrm{ M}_\odot$. The accuracy by which this profile fits simulated galaxies is similar to certain multiparameter mass-dependent profiles, but its fewer parameters and analytic nature make it most desirable for many purposes.

Model-independent and model-based local lensing properties of CL0024+1654 from multiply imaged galaxies

Context. Local gravitational lensing properties, such as convergence and shear, determined at the positions of multiply imaged background objects, yield valuable information on the smaller-scale lensing matter distribution in the central part of galaxy clusters. Highly distorted multiple images with resolved brightness features like the ones observed in CL0024 allow us to study these local lensing properties and to tighten the constraints on the properties of dark matter on sub-cluster scale. Aim. We investigate to what precision local magnification ratios, $\mathcal{J}$, ratios of convergences, f, and reduced shears, g = (g1, g2), can be determined independently of a lens model for the five resolved multiple images of the source at zs = 1.675 in CL0024. We also determine if a comparison to the respective results obtained by the parametric modelling tool Lenstool and by the non-parametric modelling tool Grale can detect biases in the models. For these lens models, we analyse the influence of the number and location of the constraints from multiple images on the lens properties at the positions of the five multiple images of the source at zs = 1.675. Methods. Our model-independent approach uses a linear mapping between the five resolved multiple images to determine the magnification ratios, ratios of convergences, and reduced shears at their positions. With constraints from up to six multiple image systems, we generate Lenstool and Grale models using the same image positions, cosmological parameters, and number of generated convergence and shear maps to determine the local values of $\mathcal{J}$, f, and g at the same positions across all methods. Results. All approaches show strong agreement on the local values of $\mathcal{J}$, f, and g. We find that Lenstool obtains the tightest confidence bounds even for convergences around one using constraints from six multiple-image systems, while the best Grale model is generated only using constraints from all multiple images with resolved brightness features and adding limited small-scale mass corrections. Yet, confidence bounds as large as the values themselves can occur for convergences close to one in all approaches. Conclusions. Our results agree with previous findings, support the light-traces-mass assumption, and the merger hypothesis for CL0024. Comparing the different approaches can detect model biases. The model-independent approach determines the local lens properties to a comparable precision in less than one second.

Wormholes with fluid sources: A no-go theorem and new examples

For static, spherically symmetric space-times in general relativity (GR), a no-go theorem is proved: it excludes the existence of wormholes with flat and/or AdS asymptotic regions on both sides of the throat if the source matter is isotropic, i.e., the radial and tangential pressures coincide. It explains why in all previous attempts to build such solutions it was necessary to introduce boundaries with thin shells that manifestly violate the isotropy of matter. Under a simple assumption on the behavior of the spherical radius $r(x)$, we obtain a number of examples of wormholes with isotropic matter and one or both de Sitter asymptotic regions, allowed by the no-go theorem. We also obtain twice asymptotically flat wormholes with anisotropic matter, both symmetric and asymmetric with respect to the throat, under the assumption that the scalar curvature is zero. These solutions may be on equal grounds interpreted as those of GR with a traceless stress-energy tensor and as vacuum solutions in a brane world. For such wormholes, the traversability conditions and gravitational lensing properties are briefly discussed. As a by-product, we obtain twice asymptotically flat regular black hole solutions with up to four Killing horizons. As another by-product, we point out intersection points in families of integral curves for the function $A(x) = g_{tt}$, parametrized by its values on the throat.

A test for skewed distributions of dark matter, and a possible detection in galaxy cluster Abell 3827

Simulations of self-interacting dark matter (SIDM) predict that dark matter should lag behind galaxies during a collision. If the interaction is mediated by a high-mass force carrier, the distribution of dark matter can also develop asymmetric dark matter tails. To search for this asymmetry, we compute the gravitational lensing properties of a mass distribution with a free {\em skewness} parameter. We apply this to the dark matter around the four central galaxies in cluster Abell~3827. In the galaxy whose dark matter peak has previously been found to be offset, we tentatively measure a skewness $s=0.23^{+0.05}_{-0.22}$ in the same direction as the peak offset. Our method may be useful in future gravitational lensing analyses of colliding galaxy clusters and merging galaxies.

Strong lensing by fermionic dark matter in galaxies

It has been shown that a self-gravitating system of massive keV fermions in thermodynamic equilibrium correctly describes the dark matter (DM) distribution in galactic halos and predicts a denser quantum core towards the center of the configuration. Such a quantum core, for a fermion mass in the range of $50$ keV $\lesssim m c^2 \lesssim 345$ keV, can be an alternative interpretation of the central compact object in Sgr A*. We present in this work the gravitational lensing properties of this novel DM model in Milky Way-like spiral galaxies. We describe the lensing effects of the pure DM component both on halo scales, where we compare them to the effects of the Navarro-Frenk-White and the Non-Singular Isothermal Sphere DM models, and near the galaxy center, where we compare them with the effects of a Schwarzschild BH. For the particle mass leading to the most compact DM core, $m c^2\approx 10^{2}$ keV, we draw the following conclusions. At distances $r\gtrsim 20$ pc from the center of the lens the effect of the central object on the lensing properties is negligible. However, we show that measurements of the deflection angle produced by the DM distribution in the outer region at a few kpc, together with rotation curve data, could help to discriminate between different DM models. We show that at distances $\sim 10^{-4}$ pc strong lensing effects, such as multiple images and Einstein rings, may occur. Large differences in the deflection angle produced by a DM central core and a central BH appear at distances $r\lesssim 10^{-6}$ pc; in this regime the weak-field formalism is no longer applicable and the exact general-relativistic formula has to be used. We find that quantum DM cores do not show a photon sphere what implies that they do not cast a shadow. Similar conclusions apply to the other DM distributions for other fermion masses in the above specified range and for other galaxy types.

Strong gravitational lensing by a Konoplya-Zhidenko rotating non-Kerr compact object

Konoplya and Zhidenko have proposed recently a rotating non-Kerr black hole metric beyond General Relativity and make an estimate for the possible deviations from the Kerr solution with the data of GW 150914. We here study the strong gravitational lensing in such a rotating non-Kerr spacetime with an extra deformation parameter. We find that the condition of existence of horizons is not inconsistent with that of the marginally circular photon orbit. Moreover, the deflection angle of the light ray near the weakly naked singularity covered by the marginally circular orbit diverges logarithmically in the strong-field limit. In the case of the completely naked singularity, the deflection angle near the singularity tends to a certain finite value, whose sign depends on the rotation parameter and the deformation parameter. These properties of strong gravitational lensing are different from those in the Johannsen-Psaltis rotating non-Kerr spacetime and in the Janis-Newman-Winicour spacetime. Modeling the supermassive central object of the Milk Way Galaxy as a Konoplya-Zhidenko rotating non-Kerr compact object, we estimated the numerical values of observables for the strong gravitational lensing including the time delay between two relativistic images.

Strong lensing constraints on bimetric massive gravity

We derive dynamical and gravitational lensing properties of local sources in the Hassan-Rosen bimetric gravity theory. Observations of elliptical galaxies rule out values of the effective length-scale of the theory, in units of the Hubble radius, in the interval 10^-6 < lambda_g/r_H < 10^-3, unless the proportionality constant between the metrics at the background level is far from unity, in which case general relativity is effectively restored for local sources. In order to have background solutions resembling the concordance cosmological model, without fine-tuning of the parameters of the model, we are restricted to the upper interval, or lambda_g/r_H ~ 1. Except for a limited range of parameter values, the Hassan-Rosen theory is thus consistent with the observed lensing and dynamical properties of elliptical galaxies.

The effect of particle noise in N-body simulations of gravitational lensing

High resolution dark matter only simulations provide a realistic and fully general means to study the theoretical predictions of cosmological structure formation models for gravitational lensing. Due to the finite number of particles, the density field only becomes smooth on scales beyond a few times the local mean interparticle separation. This introduces noise on the gravitational lensing properties such as the surface mass density, the deflection angles and the magnification. At some small-scale mass limit, the noise due to the discreteness of the N-body simulation becomes comparable to the effects of physical substructures. We present analytic expressions to quantify the Poisson noise and study its scaling with the particle number of the simulation and the Lagrangian smoothing size. We use the Phoenix set of simulations, currently the largest available dark matter simulations of clusters to study the effect of limited numerical resolution and the gravitational strong lensing effects of substructure. We quantify the smallest resolved substructure, in the sense that the effect of the substructure on any strong lensing property is significant compared to the noise, and we find that the result is roughly independent of the strong lensing property. A simple scaling relates the smallest resolved substructures in a simulation with the resolution of the N-body simulation.

OPTIMAL MASS CONFIGURATIONS FOR LENSING HIGH-REDSHIFT GALAXIES

We investigate the gravitational lensing properties of lines of sight containing multiple cluster-scale halos, motivated by their ability to lens very high-redshift (z ~ 10) sources into detectability. We control for the total mass along the line of sight, isolating the effects of distributing the mass among multiple halos and of varying the physical properties of the halos. Our results show that multiple-halo lines of sight can increase the magnified source-plane region compared to the single cluster lenses typically targeted for lensing studies, and thus are generally better fields for detecting very high-redshift sources. The configurations that result in optimal lensing cross sections benefit from interactions between the lens potentials of the halos when they overlap somewhat on the sky, creating regions of high magnification in the source plane not present when the halos are considered individually. The effect of these interactions on the lensing cross section can even be comparable to changing the total mass of the lens from 10^15 M_sun to 3x10^15 M_sun. The gain in lensing cross section increases as the mass is split into more halos, provided that the lens potentials are projected close enough to interact with each other. A nonzero projected halo angular separation, equal halo mass ratio, and high projected halo concentration are the best mass configurations, whereas projected halo ellipticity, halo triaxiality, and the relative orientations of the halos are less important. Such high mass, multiple-halo lines of sight exist in the SDSS.

THE CLUSTER LENSING AND SUPERNOVA SURVEY WITH HUBBLE: AN OVERVIEW

The Cluster Lensing And Supernova survey with Hubble (CLASH) is a 524-orbit multi-cycle treasury program to use the gravitational lensing properties of 25 galaxy clusters to accurately constrain their mass distributions. The survey, described in detail in this paper, will definitively establish the degree of concentration of dark matter in the cluster cores, a key prediction of CDM. The CLASH cluster sample is larger and less biased than current samples of space-based imaging studies of clusters to similar depth, as we have minimized lensing-based selection that favors systems with overly dense cores. Specifically, twenty CLASH clusters are solely X-ray selected. The X-ray selected clusters are massive (kT > 5 keV; 5 - 30 x 10^14 M_solar) and, in most cases, dynamically relaxed. Five additional clusters are included for their lensing strength (Einstein radii > 35 arcsec at z_source = 2) to further quantify the lensing bias on concentration, to yield high resolution dark matter maps, and to optimize the likelihood of finding highly magnified high-redshift (z > 7) galaxies. The high magnification, in some cases, provides angular resolutions unobtainable with any current UVOIR facility and can yield z > 7 candidates bright enough for spectroscopic follow-up. A total of 16 broadband filters, spanning the near-UV to near-IR, are employed for each 20-orbit campaign on each cluster. These data are used to measure precise (sigma_phz < 0.02(1+z)) photometric redshifts for dozens of newly discovered multiply-lensed images per cluster. Observations of each cluster are spread over 8 epochs to enable a search, primarily in the parallel fields, for Type Ia supernovae at z > 1 to improve constraints on the time dependence of the dark energy equation of state and the evolution of such supernovae in an epoch when the universe is matter dominated.