Gravitational Lensing for Measuring Astrophysical Quantities

2005 ◽  
Vol 277-279 ◽  
pp. 783-788
Author(s):  
K. Chang
Keyword(s):  
Time Delay ◽  
Gravitational Lensing ◽  
Critical Curve ◽  
Gravitational Lens ◽  
Density Parameter ◽  
Cosmological Distance Scale ◽  
Compact Source ◽  
Cosmological Distance ◽  
Structure Density ◽  
Source Structure

Gravitational lensing (GL) provides the sudden changes in flux densities, when a compact source crosses a critical curve. Due to lensing, the image of the lensed object is split into at least two images, and merged together upon the source crossing the critical curve. Light paths of the images differ from one another’s, so results time delay to the observer. Asymmetric light curves and the time delay in lensing contain astrophysical information on the GL system: e.g. source structure, density distribution, and cosmological distance scale. The disalignment of GL system, b, is an important parameter in the GL analysis. We derive b as a function of density parameter of gravitational lens mass. We present an analytical formulation to determine cosmological distance scales, hence the Hubble parameter, and other properties of GL system. We also discuss degeneracies in the GL mapping.

scholarly journals Strong gravitational lensing: relativity in action

2009 ◽  
Vol 5 (S261) ◽  
pp. 249-259
Author(s):  
Joachim Wambsganss
Keyword(s):  
Gravitational Lensing ◽  
Extrasolar Planets ◽  
Hubble Constant ◽  
Stellar Atmospheres ◽  
Gravitational Lens ◽  
Cosmological Distance Scale ◽  
Galaxy Halos ◽  
Guided Tour ◽  
Observational Science

AbstractDeflection of light by gravity was predicted by Einstein's Theory of General Relativity and observationally confirmed in 1919. In the following decades, various aspects of the gravitational lens effect were explored theoretically, among them measuring the Hubble constant from multiple images of a background source, making use of the magnifying effect as a gravitational telescope, or the possibility of a “relativistic eclipse” as a perfect test of GR. Only in 1979, gravitational lensing became an observational science when the first doubly imaged quasar was discovered. Today lensing is a booming part of astrophysics and cosmology. A whole suite of strong lensing phenomena have been investigated: multiple quasars, giant luminous arcs, Einstein rings, quasar microlensing, and galactic microlensing. The most recent lensing application is the detection of extrasolar planets. Lensing has contributed significant new results in areas as different as the cosmological distance scale, mass determination of galaxy clusters, physics of quasars, searches for dark matter in galaxy halos, structure of the Milky Way, stellar atmospheres and exoplanets. A guided tour through some of these applications will illustrate how gravitational lensing has established itself as a very useful universal astrophysical tool.

scholarly journals Generalized multi-plane gravitational lensing: time delays, recursive lens equation, and the mass-sheet transformation

2019 ◽  
Vol 624 ◽  
pp. A54 ◽  
Author(s):  
Peter Schneider
Keyword(s):  
Time Delay ◽  
Gravitational Lensing ◽  
Large Scale ◽  
Light Propagation ◽  
Simple Expression ◽  
Gravitational Lens ◽  
Alternative Form ◽  
Delay Function ◽  
Distance Matrices ◽  
The Impact

We consider several aspects of the generalized multi-plane gravitational lens theory, in which light rays from a distant source are affected by several main deflectors, and in addition by the tidal gravitational field of the large-scale matter distribution in the Universe when propagating between the main deflectors. Specifically, we derive a simple expression for the time-delay function in this case, making use of the general formalism for treating light propagation in inhomogeneous spacetimes which leads to the characterization of distance matrices between main lens planes. Applying Fermat’s principle, an alternative form of the corresponding lens equation is derived, which connects the impact vectors in three consecutive main lens planes, and we show that this form of the lens equation is equivalent to the more standard one. For this, some general relations for cosmological distance matrices are derived. The generalized multi-plane lens situation admits a generalized mass-sheet transformation, which corresponds to uniform isotropic scaling in each lens plane, a corresponding scaling of the deflection angle, and the addition of a tidal matrix (mass sheet plus external shear) to each main lens. The scaling factor in the lens planes exhibits a curious alternating behavior for odd and even numbered planes. We show that the time delay for sources in all lens planes scale with the same factor under this generalized mass-sheet transformation, thus precluding the use of time-delay ratios to break the mass-sheet transformation.

scholarly journals Gravitational lens time-delay as a probe of a possible time variation of the fine-structure constant

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
L. R. Colaço ◽  
J. E. Gonzalez ◽  
R. F. L. Holanda
Keyword(s):  
Fine Structure ◽  
Time Delay ◽  
Gravitational Lensing ◽  
Large Scale ◽  
Temporal Evolution ◽  
Structure Constant ◽  
Gravitational Lens ◽  
Fine Structure Constant ◽  
Type Ia ◽  
Ia Supernovae

AbstractA new method based on large scale structure observations is proposed to probe a possible temporal variation of the fine-structure constant ($$\alpha $$ α ). Our analyses are based on time-delay of Strong Gravitational Lensing and Type Ia Supernovae observations. By considering the runaway dilaton scenario, where the cosmological temporal evolution of the fine-structure constant is given by $$\frac{\Delta \alpha }{\alpha } \approx -\gamma \ln {(1+z)}$$ Δ α α ≈ - γ ln ( 1 + z ) , we obtain limits on the physical properties parameter of the model ($$\gamma $$ γ ) at the level $$10^{-2}$$ 10 - 2 ($$1\sigma $$ 1 σ ). Although our limits are less restrictive than those obtained by quasar spectroscopy, the approach presented here provides new bounds on the possibility of $$\frac{\Delta \alpha }{\alpha } \ne 0$$ Δ α α ≠ 0 at a different range of redshifts.

scholarly journals Gravitational lensing by exotic objects

2017 ◽  
Vol 32 (34) ◽  
pp. 1730031 ◽  
Author(s):  
Hideki Asada
Keyword(s):  
Time Delay ◽  
Equation Of State ◽  
Gravitational Lensing ◽  
Modified Gravity ◽  
Standard Form ◽  
Phenomenological Approach ◽  
Gravity Theory ◽  
Gravitational Lens ◽  
Lens Model ◽  
Modified Gravity Theory

This paper reviews a phenomenological approach to the gravitational lensing by exotic objects such as the Ellis wormhole lens, where the exotic lens objects may follow a non-standard form of the equation of state or may obey a modified gravity theory. A gravitational lens model is proposed in the inverse powers of the distance, such that the Schwarzschild lens and exotic lenses can be described in a unified manner as a one parameter family. As observational implications, the magnification, shear, photo-centroid motion and time delay in this lens model are discussed.

scholarly journals Imprints of Gravitational Millilensing on the Light Curve of Gamma-Ray Bursts

2021 ◽  
Vol 922 (1) ◽  
pp. 77
Author(s):  
Zeinab Kalantari ◽  
Alaa Ibrahim ◽  
Mohammad Reza Rahimi Tabar ◽  
Sohrab Rahvar
Keyword(s):  
Black Holes ◽  
Time Delay ◽  
Light Curve ◽  
Gamma Ray ◽  
Detection Method ◽  
Mass Range ◽  
Gamma Ray Bursts ◽  
Point Mass ◽  
Gravitational Lens ◽  
Density Parameter

Abstract In this work, we search for signatures of gravitational millilensing in gamma-ray bursts (GRBs) in which the source−lens−observer geometry produces two images that manifest in the GRB light curve as superimposed peaks with identical temporal variability (or echoes), separated by the time delay between the two images. According to the sensitivity of our detection method, we consider millilensing events due to point-mass lenses in the range of 105 − 107 M ⊙ at lens redshift about half that of the GRB, with a time delay on the order of 10 s. Current GRB observatories are capable of resolving and constraining this lensing scenario if the above conditions are met. We investigated the Fermi/GBM GRB archive from the year 2008 to 2020 using the autocorrelation technique and found one millilensed GRB candidate out of 2137 GRBs searched, which we use to estimate the optical depth of millilensed GRBs by performing a Monte Carlo simulation to find the efficiency of our detection method. Considering a point-mass model for the gravitational lens, where the lens is a supermassive black hole, we show that the density parameter of black holes (ΩBH) with mass ≈ 106 M ⊙ is about 0.007 ± 0.004. Our result is one order of magnitude larger compared to previous work in the lower mass range of 102 − 103 M ⊙, which gave a density parameter ΩBH ≈ 5 × 10−4, and recent work in the mass range of 102 − 107 M ⊙, which reported ΩBH ≈ 4.6 × 10−4. The mass fraction of black holes in this mass range to the total mass of the universe would be f = ΩBH/Ω M ≈ 0.027 ± 0.016.

scholarly journals Quantifying the structure of strong gravitational lens potentials with uncertainty-aware deep neural networks

2020 ◽  
Vol 499 (4) ◽  
pp. 5641-5652
Author(s):  
Georgios Vernardos ◽  
Grigorios Tsagkatakis ◽  
Yannis Pantazis
Keyword(s):  
Confidence Intervals ◽  
Galaxy Evolution ◽  
Gravitational Lensing ◽  
Probability Distributions ◽  
Mass Density ◽  
Ground Truth ◽  
Gaussian Random Fields ◽  
Training Data ◽  
Gravitational Lens ◽  
Data Set

ABSTRACT Gravitational lensing is a powerful tool for constraining substructure in the mass distribution of galaxies, be it from the presence of dark matter sub-haloes or due to physical mechanisms affecting the baryons throughout galaxy evolution. Such substructure is hard to model and is either ignored by traditional, smooth modelling, approaches, or treated as well-localized massive perturbers. In this work, we propose a deep learning approach to quantify the statistical properties of such perturbations directly from images, where only the extended lensed source features within a mask are considered, without the need of any lens modelling. Our training data consist of mock lensed images assuming perturbing Gaussian Random Fields permeating the smooth overall lens potential, and, for the first time, using images of real galaxies as the lensed source. We employ a novel deep neural network that can handle arbitrary uncertainty intervals associated with the training data set labels as input, provides probability distributions as output, and adopts a composite loss function. The method succeeds not only in accurately estimating the actual parameter values, but also reduces the predicted confidence intervals by 10 per cent in an unsupervised manner, i.e. without having access to the actual ground truth values. Our results are invariant to the inherent degeneracy between mass perturbations in the lens and complex brightness profiles for the source. Hence, we can quantitatively and robustly quantify the smoothness of the mass density of thousands of lenses, including confidence intervals, and provide a consistent ranking for follow-up science.

Strong Gravitational Lensing Time Delay Statistics and the Density Profile of Dark Halos

2002 ◽  
Vol 568 (2) ◽  
pp. 488-499 ◽  
Author(s):  
Masamune Oguri ◽  
Atsushi Taruya ◽  
Yasushi Suto ◽  
Edwin L. Turner
Keyword(s):  
Time Delay ◽  
Density Profile ◽  
Gravitational Lensing ◽  
Strong Gravitational Lensing

scholarly journals When Darwin Met Einstein: Gravitational Lens Inversion with Genetic Algorithms

2005 ◽  
Vol 22 (2) ◽  
pp. 128-135 ◽  
Author(s):  
Brendon J. Brewer ◽  
Geraint F. Lewis
Keyword(s):  
Genetic Algorithms ◽  
Gravitational Lensing ◽  
Surface Brightness ◽  
Initial Study ◽  
Brightness Distribution ◽  
Gravitational Lens ◽  
Atmospheric Effects ◽  
Lens Model ◽  
New Approach ◽  
Genetic Algorithm Approach

AbstractGravitational lensing can magnify a distant source, revealing structural detail which is normally unresolvable. Recovering this detail through an inversion of the influence of gravitational lensing, however, requires optimisation of not only lens parameters, but also of the surface brightness distribution of the source. This paper outlines a new approach to this inversion, utilising genetic algorithms to reconstruct the source profile. In this initial study, the effects of image degradation due to instrumental and atmospheric effects are neglected and it is assumed that the lens model is accurately known, but the genetic algorithm approach can be incorporated into more general optimisation techniques, allowing the optimisation of both the parameters for a lensing model and the surface brightness of the source.

scholarly journals Ambiguities in gravitational lens models: impact on time delays of the source position transformation

2018 ◽  
Vol 617 ◽  
pp. A140 ◽  
Author(s):  
Olivier Wertz ◽  
Bastian Orthen ◽  
Peter Schneider
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Hubble Constant ◽  
Companion Paper ◽  
Gravitational Lens ◽  
Source Position ◽  
Double Image ◽  
Validity Criterion ◽  
Mass Profile ◽  
Image Pairs

The central ambition of the modern time delay cosmography consists in determining the Hubble constant H0 with a competitive precision. However, the tension with H0 obtained from the Planck satellite for a spatially flat ΛCDM cosmology suggests that systematic errors may have been underestimated. The most critical of these errors probably comes from the degeneracy existing between lens models that was first formalized by the well-known mass-sheet transformation (MST). In this paper, we assess to what extent the source position transformation (SPT), a more general invariance transformation which contains the MST as a special case, may affect the time delays predicted by a model. To this aim, we have used pySPT, a new open-source python package fully dedicated to the SPT that we present in a companion paper. For axisymmetric lenses, we find that the time delay ratios between a model and its SPT-modified counterpart simply scale like the corresponding source position ratios, Δtˆ/Δt ≈ βˆ/β, regardless of the mass profile and the isotropic SPT. Similar behavior (almost) holds for nonaxisymmetric lenses in the double image regime and for opposite image pairs in the quadruple image regime. In the latter regime, we also confirm that the time delay ratios are not conserved. In addition to the MST effects, the SPT-modified time delays deviate in general no more than a few percent for particular image pairs, suggesting that its impact on time delay cosmography seems not be as crucial as initially suspected. We also reflected upon the relevance of the SPT validity criterion and present arguments suggesting that it should be reconsidered. Even though a new validity criterion would affect the time delays in a different way, we expect from numerical simulations that our conclusions will remain unchanged.

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