An Introduction to Weak Lensing

Weak lensing is a subset of gravitational lensing, along with strong lensing, micro lensing, and galaxy-galaxy lensing. In fact weak lensing has several sub-fields which are separated mainly in terms of scale. A study of weak lensing by the large scale structure of the Universe is a form of cosmology and was the focus of my master's work.

Large scale structure is a term to describe how matter arranges itself on the largest scales in the Universe, scales large enough that the Universe is actually similar everywhere, or, as cosmologists say, the Universe is homogeneous! A homogeneous Universe is quite a departure from our everyday experiences, it's quite different from our Solar System, or our Galaxy, or the local group of galaxies. All of these scales are extraordinarily dense compared to the average density of the Universe. You must go to truly astronomical scales before one part of the Universe is similar to any other part.

Gravitational lensing is a result of general relativity, a consequence of the bending of light trajectories by mass. Anything with mass bends space-time and causes photons to travel on curved paths. This is similar to standing on a trampoline and attempting to roll a ball across the warped surface. The ball will not travel on a straight path, instead it will be deflected towards the depression in the surface. Mass is the depression in space-time, causing it to curve.

In gravitational lensing we are interested in how mass causes galaxies to look elliptical when in fact they are spherical. Light coming from a spherical galaxy may encounter mass as it travels towards us, this mass will bend the light and the galaxy will be sheared (it will look elliptical). The orientation of the ellipse (equivalently the direction of the shear), and the ellipticity (how elliptical does the galaxy look), depends on the mass distribution and its properties.

If all galaxies were inherently round, then measuring the ellipticity would be a direct measure of the shear and in turn this would be a direct measure of the amount of mass between us and the lensed galaxy (the lensed galaxy is the one that has its shape distorted). One of the most useful, and unique, properties of lensing is that it is sensitive to the total mass, luminous or dark matter will bend light in the same way. This is extremely important since the vast majority of matter in the Universe is dark, having a means of directly probing this component of the Universe is very valuable.

Of course not all galaxies are inherently round, this nasty little problem is easy to circumvent in theory, but is one of the reasons it took so long to turn weak lensing theory into observations. What is most certainly true is that there is no preferred direction for galaxies to be orientated, so if I were to average many galaxy ellipticities I would expect to find zero, that is on average the galaxies are round. Any deviation from this average roundness is attributed to lensing. The first measurements of a weak lensing signal were made in 2000 by several groups (one of which was lead by my supervisor). This makes observational weak lensing a relatively new field of study, which I find very exciting.

At the end of the day weak lensing is a tool to probe the total mass, this is done by asking a profoundly simple question: "How round are galaxies?" The simplicity of the question is by no means a measure of how simple the needed measurement is to perform. Weak lensing (by large scale structure) was not measurable for over a decade because it is very difficult to determine the shape of a galaxy to the required accuracy. The complications of measuring this signal will not be addressed here, it remains a large area of research in the community, and we are still far from our goal of making sub-percent level measurements.

 
 

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