Gravitational Lensing with Three-Dimensional Ray Tracing

One of the cool things about the universe is that light rays don't travel in straight lines. As they pass through the cosmos, lumps of mass (stars, galaxies, clusters, black holes etc) tug on the path of light rays and so they follow a wiggly path.

It looks something like this

The colours here represent density in the universe, where yellow is high density, purple middling and black low density, and you can see the cosmic web of mass which has come from a computer simulation of structure formation.

The green line is a light path travelling through the universe, and as you can see, it wiggles.

Here's another version of the picture
The result is that view of the distant universe is distorted, and a considerable focus of future telescopes is to measure the amount of distortion that we see. This will allow us to measure a couple of key things, namely the distribution of matter (which is good, because a lot of it is that pesky dark matter that we can't see), and also the underlying cosmology (and so will be a probe of dark energy).

But to understand all of this, we need some theoretical models to compare to the observations. How do we do this? Well, it's not easy to follow light rays and typically people use what's known as the multi-plane approximation. It's easy to visualize - you take your continuous mass distribution and chop it into chunks, and then squash the chunks onto flat planes. Light rays then travel in straight lines between the planes, but as they pass through a plane, they feel the mass in the plane and get deflected.

This looks something like this
which I took from the paper by Hilbert et al.

But the question is, is this a good approximation. People generally shrug and go "I think so".

I'm please to announce that my ex-student, Madhura Killedar, who got her PhD earlier this year and is now a postdoc in Trieste, has just had one of her thesis papers accepted where she tests this, by comparing the multiplane method with a more "correct approach", actually integrating the geodesic equation through the simulations.

The task should not be underestimated, as it took three years of her PhD to do this. There are lots of technical issues which I will not go into here, but involved big simulations, Fourier transforms, multi-dimensional integrals, resolution scales etc etc, So this paper is the first of a series presenting her thesis work. This one got a pretty sweet referees report too :)

I encourage you to have a look. Well done Mud!!

Gravitational Lensing with Three-Dimensional Ray Tracing

High redshift sources suffer from magnification or demagnification due to weak gravitational lensing by large scale structure. One consequence of this is that the distance-redshift relation, in wide use for cosmological tests, suffers lensing-induced scatter which can be quantified by the magnification probability distribution. Predicting this distribution generally requires a method for ray-tracing through cosmological N-body simulations. However, standard methods tend to apply the multiple thin-lens approximation. In an effort to quantify the accuracy of these methods, we develop an innovative code that performs ray-tracing without the use of this approximation. The efficiency and accuracy of this computationally challenging approach can be improved by careful choices of numerical parameters; therefore, the results are analysed for the behaviour of the ray-tracing code in the vicinity of Schwarzschild and Navarro-Frenk-White lenses. Preliminary comparisons are drawn with the multiple lens-plane ray-bundle method in the context of cosmological mass distributions for a source redshift of $z_{s}=0.5$.


  1. Age, I think. I've been using for donkeys and it's automatic.


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