Notes on Gravitational Lensing
LSST Stuff
The first LSST page has movies showing the evolution of background galaxies being lensed by a foreground cluster. The second is how the movies were made. Of particular note is how the galaxies were handled. They stacked a series of images planes behind the cluster, 6 out to redshift 3, plus some fainter ones beyond that.
Books & Papers
- Sean M. Carroll, Spacetime and Geometry: An Introduction to General Relativity
- Section 7.3 - Newtonian Fields and Photon Trajectories
- Narayan & Bartelmann 1997
- Lectures on Gravitational Lensing
These lectures give an introduction to Gravitational Lensing. We discuss lensing by point masses, lensing by galaxies, and lensing by clusters and larger-scale structures in the Universe. The relevant theory is developed and applications to astrophysical problems are discussed.
Methods (Papers)
Desperately need to keep track of what methods are currently being used, and to do the classic estimates of scaling, performance, and accuracy.
Mass Reconstruction
- Khiabanianand, Dell’Antonio 2008
- A Multiresolution Weak-Lensing Mass Reconstruction Method
Motivated by the limitations encountered with the commonly used direct reconstruction techniques of producing mass maps, we have developed a multiresolution maximum likelihood reconstruction method for producing two-dimensional mass maps using weak gravitational lensing data. To utilize all the shear information, we employ an iterative inverse method with a properly selected regularization coefficient which fits the deflection potential at the position of each galaxy. By producing mass maps with multiple resolutions in the different parts of the observed field, we can achieve a comparable level of signal to noise by increasing the resolution in regions of higher distortions or regions with an overdensity of background galaxies. In addition, we are able to better study the substructure of the massive clusters at a resolution which is not attainable in the rest of the observed field. We apply our method to the simulated data and to a 4 deg2 field obtained by the Deep Lens Survey.
Multiple Lens Plane
- Premadi, Martel, Matzner 1998
- Light Propagation in Inhomogeneous Universes I: Methodology and Preliminary Results
We describe a numerical algorithm which simulates the propagation of light in inhomogeneous universes, using the multiple lens-plane method. The deformation and deflection of light beams as they interact with each lens plane are computed using the filled-beam approximation.
- Premadi, Martel, Matzner 2001
- Light Propagation in Inhomogeneous Universes II. Cosmological Parameter Survey
Using a multiple-lens plane algorithm, we study light propagation in inhomogeneous universes, for 43 different COBE-normalized Cold Dark Matter models, with various values of the density parameter Omega_0, cosmological constant lambda_0, Hubble constant H_0, and rms density fluctuation sigma_8...
Ray Casting
- Pyne, Birkinshaw 1995
- Beyond the Thin Lens Approximation
We obtain analytic formulae for the null geodesics of FLRW spacetimes with scalar perturbations in the longitudinal gauge. From these we provide a rigorous derivation of the cosmological lens equation, and obtain an expression for the magnification of a bundle of light rays without restriction to static or thin lens scenarios. We show how the usual magnification matrix naturally emerges in the appropriate limits.
- Carbone, Springel, Baccigalupi, Bartelmann, Matarrese 2007
- We use the large cosmological Millennium Simulation (MS) to construct the first all-sky maps of the lensing potential and the deflection angle, aiming at gravitational lensing of the CMB. Exploiting the Born approximation, we implement a map-making procedure based on direct ray-tracing through the gravitational potential of the MS. We stack the simulation box in redshift shells up to $z\sim 11$...
Multiple
- Tomita, Premadi, Nakamura 1999
- Various Approaches to Cosmological Gravitational Lensing in Inhomogeneous Models
...In this review paper we compare the following three main approaches: (a) the approach in the multi-lens-plane theory; (b) the approach due to the direct integration method; and (c) the perturbational approach...
- Kling, Newman, Perez 2000
- Comparative Studies of Lensing Methods
Predictions of the standard thin lens approximation and a new iterative approach to gravitational lensing are compared with an exact approach in simple test cases involving one or two lenses. We show that the thin lens and iterative approaches are remarkably accurate in predicting time delays, source positions and image magnifications for a single monopole lens and combinations of two monopole lenses...
- Bartelmann 2003
- Numerical Methods in Gravitational Lensing
Most problems in gravitational lensing require numerical solutions. The most frequent types of problems are (1) finding multiple images of a single source and classifying the images according to their properties like magnification or distortion; (2) propagating light rays through large cosmological simulations; and (3) reconstructing mass distributions from their tidal field...
Software
- GRAVLENS
- Reference paper: Computational Methods for Gravitational Lensing. Looks like closed source, only provides binaries.
- GLAMROC: Gravitational Lens Adaptive Mesh Raytracing of Catastrophes
- The GLAMROC code is a semi-analytic raytracing code for studying gravitational lens systems.
Looks like it does über-multi-lens plane calculations. The manual has some good info on the lens equation.
- HEALPix
- Spherical surface decomposition, used in Carbone, et al. Need to figure out how to get the pixel centers from it.
CMB
- Lieu & Mittaz 2004
- On the absence of gravitational lensing of the cosmic microwave background
The magnification of distant sources by mass clumps at lower ($z \leq 1$) redshifts is calculated analytically. The clumps are initially assumed to be galaxy group isothermal spheres with properties inferred from an extensive survey. The average effect, which includes strong lensing, is exactly counteracted by the beam divergence in between clumps...
