Magnification relations of quad lenses and applications on Einstein crosses

Zhang, Chu; Li, G. L.; Lin, Weipeng; Pan, H. X.

doi:10.1093/mnras/stw1614

Cited by 7 publications

(8 citation statements)

References 90 publications

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“…Nevertheless, there have been attempts to model extended lenses, including quadrupole and general shear distortions of the lensing potential [2,[11][12][13] as well as to describe binaries [14]. It was recognized that such deviations from spherical symmetry lead to the formation of caustics, which complicates image formation [15][16][17][18]. Most of these investigations were conducted using the geometric optics approximation, which is known to be of limited utility when it comes to describing light amplification, especially in the presence of caustics [19,20], where such results have singularities.…”

Section: Introductionmentioning

confidence: 99%

Gravitational lensing by an extended mass distribution

Turyshev,

Toth

2021

Preprint

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We continue our investigations of the optical properties of the solar gravitational lens (SGL). We treat the Sun as an extended axisymmetric body and model its gravitational field using zonal harmonics. We consider a point source that is positioned at a large but finite distance from the Sun and, using our new angular eikonal method, we established the electro-magnetic (EM) field on the image plane in the focal region behind the SGL and derive the SGL's impulse response in the form of its point-spread function (PSF). The expression that we derive describes the extended Sun in all regions of interest, including the regions of strong and weak interference and the region of geometric optics. The result is in the form of a single integral with respect to the azimuthal angle of the impact parameter, covering all lensing regimes of the SGL. The same expression can be used to describe gravitational lensing by a compact axisymmetric mass distribution, characterized by small deviations from spherical symmetry. It is valid in all lensing regimes. We also derive results that describe the intensity of light observed by an imaging telescope in the focal region. We present results of numerical simulations showing the view by a telescope that moves in the image plane toward the optical axis. We consider imaging of both point and extended sources. We show that while point sources yield a number of distinct images consistent with the caustics due to zonal harmonics of a particular order (e.g., Einstein cross), extended sources always result in forming an Einstein ring. These results represent the most comprehensive wave-theoretical treatment of gravitational lensing in the weak gravitational field of a compact axisymmetric gravitational lens.

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Section: Introductionmentioning

confidence: 99%

Gravitational lensing by an extended mass distribution

Turyshev,

Toth

2021

Preprint

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“…For even if coarse geometric optics effects are undetectable, the above action still predicts accumulative modifications for the way electromagnetic field energy is transported [12]. These result in a potentially measurable modification of Etherington's distance duality relation [33] already in a weak gravitational field that admits birefringence [19], and which may also address otherwise inexplicable magnification anomalies [34].…”

Section: Discussionmentioning

confidence: 99%

“…In our below derivation of the gravitational closure equations -which take a test matter action satisfying the three matter conditions as input and yields the underlying gravitational dynamics as output -the key information contained in the matter dynamics trickles down to the gravitational side exclusively through the Legendre maps x , whence (34) presents the most important result of this review section from a practical point of view.…”

Section: Massive Dispersion Relation and Local Observer Framesmentioning

confidence: 99%

Gravitational closure of matter field equations

et al. 2018

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The requirement that both the matter and the geometry of a spacetime canonically evolve together, starting and ending on shared Cauchy surfaces and independently of the intermediate foliation, leaves one with little choice for diffeomorphism-invariant gravitational dynamics that can provide consistent evolution equations to the coefficients of a given system of matter field equations. Concretely, we show how starting from any linear local matter field equations whose principal polynomial satisfies three physicality conditions, one may calculate coefficient functions which then enter an otherwise immutable set of countably many linear homogeneous partial differential equations.Any solution of these so-called gravitational closure equations then provides a Lagrangian density for any type of tensorial geometry that features ultralocally in the initially specified matter Lagrangian density. Thus the given system of matter field equations is indeed closed by the so obtained gravitational equations. In contrast to previous work, we build the theory on a suitable associated bundle encoding the canonical configuration degrees of freedom, which allows to include necessary constraints on the geometry in practically tractable fashion. By virtue of the presented mechanism, one thus can practically calculate, rather than having to postulate, the gravitational theory that is required by specific matter field dynamics. For the special case of standard model matter one obtains general relativity. a Corresponding author. Electronic address fps@aei.mpg.de 1 arXiv:1611.08878v3 [gr-qc]

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“…Thereby, it is also difficult to derive the magnifications of the three images. In this work, we use of a precise numerical ray-tracing method, developed by Chu et al (2016), to calculate the positions and corresponding magnifications of different images for a given source. The results can be found in section 3.…”

Section: Circular Lens Modelsmentioning

confidence: 99%

“…With the purpose of calculating the accurate position of the image and its corresponding magnification for a given source, we utilize the analytical ray-tracing method in different image regions to numerically evaluate magnification for each image. This precise numerical method has been introduced in Chu et al (2016) to study the magnification relations of quad lenses, which is shortly described as follows.…”

Section: The Test Of Magnification Summationmentioning

confidence: 99%

The magnification invariant of circularly-symmetric lens models

Chi

Zhang

Shu

2018

Res. Astron. Astrophys.

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In the context of strong gravitational lensing, the magnification of image is of crucial importance to constrain various lens models. For several commonly used quadruple lens models, the magnification invariants, defined as the sum of the signed magnifications of images, have been analytically derived when the image multiplicity is a maximum. In this paper, we further study the magnification of several disk lens models, including (a) exponential disk lens, (b) Gaussian disk lens, (c) modified Hubble profile lens, and another two of the popular three-dimensional symmetrical lens model, (d) NFW lens and (e) Einasto lens. We find that magnification invariant does also exist for each lens model. Moreover, our results show that magnification invariants can be significantly changed by the characteristic surface mass density κ c .

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Magnification relations of quad lenses and applications on Einstein crosses

Cited by 7 publications

References 90 publications

Gravitational lensing by an extended mass distribution

Gravitational lensing by an extended mass distribution

Gravitational closure of matter field equations

The magnification invariant of circularly-symmetric lens models

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