Gravitational Lensing by Dark Matter Caustics

We study the observational signatures of the lensing signal produced by dark matter halos with embedded misaligned disks. This issue is of particular interest at the present time since most of the observed multiple lens systems have magnification ratios and image geometries that are not well-fit by standard mass models. The presence of substructure exterior to the lens has been invoked by several authors in the context of Cold Dark Matter (CDM) models in order to explain the ...

When the gravitational lensing potential can be approximated by that of circularly symmetric system affected by weak perturbations, it is found that the shape of the resulting (tangential) caustics is entirely specified by the local azimuthal behaviour of the affecting perturbations. This provides a common mathematical groundwork for understanding problems such as the close-wide (d <-> 1/d) separation degeneracy of binary lens microlensing lightcurves and the shear-ellipticit...

We consider compensated spherical lens models and the caustic surfaces they create in the past light cone. Examination of cusp and crossover angles associated with particular source and lens redshifts gives explicit lensing models that confirm previous claims that area distances can differ by substantial factors from angular diameter distances even when averaged over large angular scales. `Shrinking' in apparent sizes occurs, typically by a factor of 3 for a single spherical ...

We interpret the recent gravitational lensing observations of Jee et al. \cite{Jee} as first evidence for a {\it caustic} ring of dark matter in a galaxy cluster. A caustic ring unavoidably forms when a cold collisionless flow falls with net overall rotation in and out of a gravitational potential well. Evidence for caustic rings of dark matter was previously found in the Milky Way and other isolated spiral galaxies. We argue that galaxy clusters have at least one and possibl...

The primary optical caustic surface behind a Kerr black hole is a four-cusped tube displaced from the line of sight. We derive the caustic surface in the nearly asymptotic region far from the black hole through a Taylor expansion of the lightlike geodesics up to and including fourth-order terms in m/b and a/b, where $m$ is the black hole mass, a the spin and b the impact parameter. The corresponding critical locus in the observer's sky is elliptical and a point-like source in...

Recent observations of lensed galaxies at cosmological distances have detected individual stars that are extremely magnified when crossing the caustics of lensing clusters. In idealized cluster lenses with smooth mass distributions, two images of a star of radius $R$ approaching a caustic brighten as $t^{-1/2}$ and reach a peak magnification $\sim 10^{6}\, (10\, R_{\odot}/R)^{1/2}$ before merging on the critical curve. We show that a mass fraction ($\kappa_\star \gtrsim \, 10...

I investigate the caustics produced by the fall of collisionless dark matter in and out of a galaxy in the limit of negligible velocity dispersion. The outer caustics are spherical shells enveloping the galaxy. The inner caustics are rings. These are located near where the particles with the most angular momentum are at their distance of closest approach to the galactic center. The surface of a caustic ring is a closed tube whose cross-section is a $D_{-4}$ catastrophe. It ha...

Gravitational lensing provides a unique and powerful probe of the mass distributions of distant galaxies. Four-image lens systems with fold and cusp configurations have two or three bright images near a critical point. Within the framework of singularity theory, we derive analytic relations that are satisfied for a light source that lies a small but finite distance from the astroid caustic of a four-image lens. Using a perturbative expansion of the image positions, we show th...

We describe a series of new applications of gravitational lenses as astrophysical and cosmological tools. Such applications are becoming possible thanks to advances in the quality and quantity of observations. CASTLES (CfA-Arizona-Space-Telescope-LEns-Survey) {cfa-www.harvard.edu/castles} is an ongoing project that exploits the sensitivity and resolution of the Hubble Space Telescope (HST) at optical and infrared wavelengths to study the sample of over 50 known gravitational ...

The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature. It includes the basic equations and the relevant techniques for calculating the position, the shape, and the brightness of images in an arbitrary general-relativistic spacetime. It also...