January 20, 2003
Dark matter caustics have specific density profiles and, therefore, precisely calculable gravitational lensing properties. We present a formalism which simplifies the relevant calculations, and apply it to four specific cases. In the first three, the line of sight is tangent to a smooth caustic surface. The curvature of the surface at the tangent point is positive, negative or zero. In the fourth case the line of sight passes near a cusp. For each we derive the map between the image and source planes. In some cases, a point source has multiple images and experiences infinite magnification when the images merge. Unfortunately, for the dark matter caustics expected in realistic galactic halo models, the angular resolution required to resolve the multiple images is not presently achievable. A more promising approach aims to observe the distortions caused by dark matter caustics in the images of extended sources such as radio jets.
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January 9, 2004
There are compelling reasons to believe that the dark matter of the universe is constituted, in large part, by non-baryonic collisionless particles with very small primordial velocity dispersion. Such particles are called cold dark matter (CDM). The leading candidates are axions and weakly interacting massive particles (WIMPs). The word ``collisionless'' indicates that the particles are so weakly interacting that they move purely under the influence of gravity. Galaxies are s...
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I elaborate on my prediction that an indirect detection of cold dark matter (CDM) may be possible by observing the gravitational lensing effects of the CDM cusp caustics at cosmological distances. Cusps in the distribution of CDM are plentiful once density perturbations enter the nonlinear regime of structure formation. Caustic ring model of galactic halo formation provides a well defined density profile and geometry near the cusps of the caustic rings. I calculate the gravit...
October 13, 2005
Gravitational lensing by the dual cusp catastrophes of the cold dark matter (CDM) caustic rings at cosmological distances may provide the tantalizing opportunity to detect CDM indirectly, and discriminate between axions and weakly interacting massive particles (WIMPs). Caustics are places where the CDM particles are naturally focussed. Our focus is upon the caustic rings which are closed tubes whose cross-section is an elliptic umbilic catastrophe with three dual cusps. A cau...
August 6, 2002
Very little attention has been paid to the properties of optical wavefronts and caustic surfaces due to gravitational lensing. Yet the wavefront-based point of view is natural and provides insights into the nature of the caustic surfaces on a gravitationally lensed lightcone. We derive analytically the basic equations governing the wavefronts, lightcones, caustics on wavefronts, and caustic surfaces on lightcones in the context of weak-field, thin-screen gravitational lensing...
June 11, 2002
We present a rigorous, detailed study of the generic, quantitative properties of gravitational microlensing near cusp catastrophes. We derive explicit formulas for the total magnification and centroid of the images created for sources outside, on, and inside the cusped caustic. We obtain results on how the image magnifications scale with respect to separation from the cusped caustic for arbitrary source positions. Along the axis of symmetry of the cusp, the total magnificatio...
May 25, 2023
One of the most challenging open questions in physics today is discovering the nature of dark matter. In this work we study the imaging formation in dark matter (DM) halos due to an external light source using some DM profiles for comparison with astronomical observations. Approaching these models on a small scale, we analyze the images generated on the lens plane by obtaining the analytical scaled surface mass densities $\Sigma_{*}(x)$ and their corresponding deflection angl...
October 19, 2005
Caustics are formally singular structures, with infinite density, that form in collisionless media. The non-negligible velocity dispersion of dark matter particles renders their density finite. We evaluate the maximum density of the caustics within the framework of secondary infall model of formation of dark matter haloes. The result is then used to demonstrate that caustics can be probed by properly stacking the weak-lensing signal of about 600 haloes. CFHTLS accompanied by ...
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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 position...
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Caustics are high-density structures that form frequently in collisionless media. Under self-gravity, cold dark matter flows focus onto caustics which are yet to be resolved in numerical simulations and or observed in the real world. If detected, caustics would provide a strong evidence for dark matter and would rule out alternative models such as those with modified dynamics. Here, we demonstrate how they might be observed in the weak lensing data. We evaluate the shear dist...
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We study the problem of gravitational lensing by an isothermal elliptical density galaxy in the presence of a tidal perturbation. When the perturbation is fairly strong and oriented near the galaxy's minor axis, the lens can produce image configurations with six or even eight highly magnified images lying approximately on a circle. We classify the caustic structures in the model and identify the range of models that can produce such lenses. Sextuple and octuple lenses are lik...