The theory of transparent gravitational lenses

Bourassa, R.R.; Kantowski, R.

doi:10.1086/153300

Cited by 117 publications

(85 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This substitution can be performed on the projected mass distribution, κ(x) → κ(x ε ), leading to elliptical mass distributions (Bourassa et al 1973;Bourassa & Kantowski 1975;Bray 1984). An alternative is to construct pseudo-elliptical models, by making the substitution in the lensing potential, ϕ(x) → ϕ(x ε ), which leads to simple analytic expressions for the lensing functions (GK02; Kassiola & Kovner 1993;Oguri 2002;Jullo et al 2007).…”

Section: Pseudo-elliptical Modelsmentioning

confidence: 99%

Domain of validity for pseudo-elliptical NFW lens models

Dúmet-Montoya

Caminha

Makler

2012

A&A

View full text Add to dashboard Cite

Context. Owing to their computational simplicity, models with elliptical potentials (pseudo-elliptical) are often used in gravitational lensing applications, in particular for mass modeling using arcs and for arc statistics. However, these models generally lead to negative mass distributions in some regions and to dumbbell-shaped surface density contours for high ellipticities. Aims. We revisit the physical limitations of the pseudo-elliptical Navarro-Frenk-White (PNFW) model, focusing on the behavior of the mass distribution close to the tangential critical curve, where tangential arcs are expected to be formed. We investigate the shape of the mass distribution on this region and the presence of negative convergence. We obtain a mapping from the PNFW to the NFW model with elliptical mass distribution (ENFW). We compare the arc cross section for both models, aiming to determine a domain of validity for the PNFW model in terms of its mass distribution and for the cross section. Methods. We defined a figure of merit to i) measure the deviation of the iso-convergence contours of the PNFW model to an elliptical shape, ii) assigned an ellipticity ε Σ to these contours, iii) defined a corresponding iso-convergence contour for the ENFW model. We computed the arc cross section using the "infinitesimal circular source approximation". Results. We extend previous work by investigating the shape of the mass distribution of the PNFW model for a broad range of the potential ellipticity parameter ε and characteristic convergence κ ϕ s . We show that the maximum value of ε to avoid dumbbellshaped mass distributions is explicitly dependent on κ ϕ s , with higher ellipticities (ε 0.5, i.e., ε Σ 0.65) allowed for small κ ϕ s . We determine a relation between the ellipticity of the mass distribution ε Σ and ε valid for any ellipticity. We also derive the relation of characteristic convergences, obtaining a complete mapping from PNFW to ENFW models, and provide fitting formulae for connecting the parameters of both models. Using this mapping, the cross sections for both models are compared, setting additional constraints on the parameter space of the PNFW model such that it reproduces the ENFW results. We also find that the negative convergence regions occur far from the arc formation region and should therefore not be a problem for studies with gravitational arcs. Conclusions. We conclude that the PNFW model is well-suited to model an elliptical mass distribution on a larger ε-κ ϕ s parameter space than previously expected. However, if we require the PNFW model to reproduce the arc cross section of the ENFW well, the ellipticity is more restricted, particularly for low κ ϕ s . The determination of a domain of validity for the PNFW model and the mapping to ENFW models could have implications for the use of PNFW models for the inverse modeling of lenses and for fast arc simulations, for example.

show abstract

Section: Pseudo-elliptical Modelsmentioning

confidence: 99%

Domain of validity for pseudo-elliptical NFW lens models

Dúmet-Montoya

Caminha

Makler

2012

A&A

View full text Add to dashboard Cite

show abstract

“…The phenomena resulting from the deflection of electromagnetic radiation in a gravitational field are referred to as gravitational lensing (GL) and an object causing a detectable deflection is known as a gravitational lens. The basic theory of GL was developed by Liebes [1], Refsdal [2] and Bourassa, Kantowski [3]. Detailed discussions on limit (SDL)), has received wide attention in the recent past.…”

Section: Introductionmentioning

confidence: 99%

Kerr-Sen dilaton-axion black hole lensing in the strong deflection limit

Gyulchev

Yazadjiev

2007

Phys. Rev. D

View full text Add to dashboard Cite

In the present work we study numerically quasi-equatorial lensing by the charged, stationary, axially-symmetric Kerr-Sen dilaton-axion black hole in the strong deflection limit. In this approximation we compute the magnification and the positions of the relativistic images. The most outstanding effect is that the Kerr-Sen black hole caustics drift away from the optical axis and shift in clockwise direction with respect to the Kerr caustics. The intersections of the critical curves on the equatorial plane as a function of the black hole angular momentum are found, and it is shown that they decrease with the increase of the parameter Q 2 /M . All of the lensing quantities are compared to particular cases as Schwarzschild, Kerr and Gibbons-Maeda black holes. I. INTRODUCTIONOne of the consequences of Einstein's General Theory of Relativity is that light rays are deflected by gravity. Although this discovery was made in the last century, the possibility that there could be such a deflection had been suspected much earlier, by Newton and Laplace, for the first time. The phenomena resulting from the deflection of electromagnetic radiation in a gravitational field are referred to as gravitational lensing (GL) and an object causing a detectable deflection is known as a gravitational lens. Nowadays, gravitational lensing is a rapidly developing area of research, and it has found applications ranging from the search of extrasolar planets and compact dark matter to the estimation of the values of the cosmological parameters [10]. In most of these cases it is possible to assume that the gravitational field is weak, hence the angle of deflection of the light in the field of a spherically symmetric body with mass M can be approximated by: that the present lens model could be able to distinguish observationally a black hole from naked singularity.The study of the gravitational lensing when light passes very close to a massive body, such as a black hole (a process also known as gravitational lensing in the strong deflection

show abstract

“…When v ∞ → c, this result can be compared to the (GR) result [4,5]. Notwithstanding the (ubiquitous) factor of 2 between classical mechanics and (GR), eq.…”

Section: Conclusion On the Transparent Deflectormentioning

confidence: 79%

“…For (b > R), the deviation is exactly given by equation (3), the weak gravity approximation corresponding to equation (4).…”

Section: The Transparent Deflectormentioning

confidence: 99%

A Newtonian pre-introduction to gravitational lenses

Garel¹

2004

Eur. J. Phys.

View full text Add to dashboard Cite

Understanding the deflection of light by a massive deflector, as well as the associated gravitational lens phenomena, require the use of the theory of General Relativity. I consider here a classical analogy, based on Newton's equation of motion for massive particles. These particles are emitted by a distant source and deflected by the gravitational field of a (opaque) star or of a (transparent) galaxy. The dependence of the deviation angle D on the impact parameter b, and the -Euclidean -geometry of the (source, deflector, earth) triplet, imply that different particle trajectories may reach an earth based observer. Since D(b) does not depend on the mass of the particles, a (Newtonian) flavor of gravitational lenses phenomena is naively obtained by setting the particles' velocity equal to the speed of light. Orders of magnitude are obtained through this classical approach, and are compared to the General Relativity results.Saclay T03/171

show abstract

The theory of transparent gravitational lenses

Cited by 117 publications

References 0 publications

Domain of validity for pseudo-elliptical NFW lens models

Domain of validity for pseudo-elliptical NFW lens models

Kerr-Sen dilaton-axion black hole lensing in the strong deflection limit

A Newtonian pre-introduction to gravitational lenses

Contact Info

Product

Resources

About