A Cusp—Counting Formula for Caustics due to Multiplane Gravitational Lensing

A Cusp—Counting Formula For Caustics Due To Multiplane Gravitational Lensing

Symposium - International Astronomical Union ◽

10.1017/s0074180900231550 ◽

1996 ◽

Vol 173 ◽

pp. 281-282

Author(s):

A. O. Petters

Keyword(s):

Light Source ◽

Gravitational Lensing ◽

Deflection Angle ◽

Gravitational Lens ◽

Source Plane ◽

Lens System ◽

Light Rays ◽

Counting Formula

Consider a gravitational lens system with K planes. If light rays are traced back from the observer to the light source plane, then the points on the first lens plane where a light ray either terminates, or, passes through and terminates before reaching the light source plane, are “obstruction points.” More precisely, tracing rays back to the source plane induces a K-plane lensing map η : U ⊆ R2 → R2 of the form η(x1) = x1 −∑i=1k αi(xi(xi)). We then define an obstruction point of η to be a point a of U where limx1→a |αi(xi(x1))| = ∞ for some “deflection angle” αi.

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Astrophysical Applications of Gravitational Lensing

10.1017/cbo9781139940306 ◽

2016 ◽

Cited By ~ 3

Keyword(s):

Gravitational Lensing

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Nonlocal Gravity

10.1093/oso/9780198803805.001.0001 ◽

2017 ◽

Cited By ~ 5

Author(s):

Bahram Mashhoon

Keyword(s):

Gravitational Field ◽

Gravitational Lensing ◽

Past History ◽

Lorentz Invariance ◽

Minkowski Spacetime ◽

Field Measurements ◽

Local Principle ◽

History Of ◽

Expansion Of The Universe ◽

Nearby Galaxies

A postulate of locality permeates through the special and general theories of relativity. First, Lorentz invariance is extended in a pointwise manner to actual, namely, accelerated observers in Minkowski spacetime. This hypothesis of locality is then employed crucially in Einstein’s local principle of equivalence to render observers pointwise inertial in a gravitational field. Field measurements are intrinsically nonlocal, however. To go beyond the locality postulate in Minkowski spacetime, the past history of the accelerated observer must be taken into account in accordance with the Bohr-Rosenfeld principle. The observer in general carries the memory of its past acceleration. The deep connection between inertia and gravitation suggests that gravity could be nonlocal as well and in nonlocal gravity the fading gravitational memory of past events must then be taken into account. Along this line of thought, a classical nonlocal generalization of Einstein’s theory of gravitation has recently been developed. In this nonlocal gravity (NLG) theory, the gravitational field is local, but satisfies a partial integro-differential field equation. A significant observational consequence of this theory is that the nonlocal aspect of gravity appears to simulate dark matter. The implications of NLG are explored in this book for gravitational lensing, gravitational radiation, the gravitational physics of the Solar System and the internal dynamics of nearby galaxies as well as clusters of galaxies. This approach is extended to nonlocal Newtonian cosmology, where the attraction of gravity fades with the expansion of the universe. Thus far only some of the consequences of NLG have been compared with observation.

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Inclination Effects in Spiral Galaxy Gravitational Lensing

The Astrophysical Journal ◽

10.1086/304558 ◽

1997 ◽

Vol 486 (2) ◽

pp. 681-686 ◽

Cited By ~ 29

Author(s):

Ariyeh H. Maller ◽

Ricardo A. Flores ◽

Joel R. Primack

Keyword(s):

Spiral Galaxy ◽

Gravitational Lensing

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New Limits on a Cosmological Constant from Statistics of Gravitational Lensing

The Astrophysical Journal ◽

10.1086/306575 ◽

1999 ◽

Vol 510 (1) ◽

pp. 42-53 ◽

Cited By ~ 74

Author(s):

Masashi Chiba ◽

Yuzuru Yoshii

Keyword(s):

Cosmological Constant ◽

Gravitational Lensing

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Scale dependence of galaxy biasing investigated by weak gravitational lensing: An assessment using semi-analytic galaxies and simulated lensing data

Astronomy and Astrophysics ◽

10.1051/0004-6361/201732248 ◽

2018 ◽

Vol 613 ◽

pp. A15 ◽

Cited By ~ 13

Author(s):

Patrick Simon ◽

Stefan Hilbert

Keyword(s):

Gravitational Lensing ◽

Spatial Scales ◽

Scale Dependence ◽

Reconstruction Technique ◽

Weak Gravitational Lensing ◽

Physical Scale ◽

The Galaxy ◽

Galaxy Bias ◽

The Impact ◽

Lens Galaxies

Galaxies are biased tracers of the matter density on cosmological scales. For future tests of galaxy models, we refine and assess a method to measure galaxy biasing as a function of physical scalekwith weak gravitational lensing. This method enables us to reconstruct the galaxy bias factorb(k) as well as the galaxy-matter correlationr(k) on spatial scales between 0.01hMpc−1≲k≲ 10hMpc−1for redshift-binned lens galaxies below redshiftz≲ 0.6. In the refinement, we account for an intrinsic alignment of source ellipticities, and we correct for the magnification bias of the lens galaxies, relevant for the galaxy-galaxy lensing signal, to improve the accuracy of the reconstructedr(k). For simulated data, the reconstructions achieve an accuracy of 3–7% (68% confidence level) over the abovek-range for a survey area and a typical depth of contemporary ground-based surveys. Realistically the accuracy is, however, probably reduced to about 10–15%, mainly by systematic uncertainties in the assumed intrinsic source alignment, the fiducial cosmology, and the redshift distributions of lens and source galaxies (in that order). Furthermore, our reconstruction technique employs physical templates forb(k) andr(k) that elucidate the impact of central galaxies and the halo-occupation statistics of satellite galaxies on the scale-dependence of galaxy bias, which we discuss in the paper. In a first demonstration, we apply this method to previous measurements in the Garching-Bonn Deep Survey and give a physical interpretation of the lens population.

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