Weak Lensing

All of the (physics) research I did as an undergrad related in some way to gravitational lensing. As papers with long author lists often take a while to go through the do-the-work-then-do-more-work-then-someone-writes-it-up-then-argue-over-what-got-written-up-then-try-to-publish-it process, it's no big surprise that a paper on "high precision weak lensing analyses" based in part on work I haven't touched in two years now showed up on astro-ph this week.

Gravitational lensing refers to the bending of the path of light due to gravity. If there is mass between us and some faraway source (which for something sufficiently far away, there always is) then that mass will act as a lens and distort how the source appears to us. If the source is very close to directly behind the lens, the source's image can be so distorted that a single galaxy is stretched out into an arc, or even have multiple images. This is known as strong lensing. In weak lensing, the background image is only slightly distorted; for instance, a perfect circle might be sheared to appear slightly elliptical. The neat—and useful—thing about gravitational lensing is that it is only susceptible to where the mass is—and that's it. Even if we can't "see" the mass. The other incredibly alluring aspect to graviational lensing is its (albeit, somewhat superficial) simplicity: all we need is a working theory of gravity. That's it. One theory. No chemistry, no convection modelling, no particle physics, no theory of galaxy evolution or anything else of the like.

We define the "ellipticity" of an object to be (1 - b/a), where b/a is the axis ratio. (If it's a circle, for instance, then the long axis and the short axis are the same length (the diameter), so a circle has zero ellipticity. A straight line, on the other hand, has an ellipticity of 1.) The effects of weak lensing are very very small—only on the order of a few percent—and since a typical galaxy has an ellipticity of tens of percent, it's impossible to measure distortions due to weak lensing for a single galaxy.

This doesn't stop us, however, from measuring the effects of weak lensing on lots of galaxies. Specifically, lensing doesn't happen haphazardly; the direction along which a galaxy is sheared tells us about where the mass is that is doing the lensing. The idea is that if you have some field of un-lensed galaxies, then they should be randomly oriented, and have an average shear of zero. On the other hand, say we have some lensing mass (like a cluster of galaxies) then the average shear of the background galaxies is not zero, and we can figure out how the mass is distributed in the cluster.

Now, this sounds all fine and dandy, but there are two very difficult steps. The obvious one is that "measuring the shear" of a galaxy isn't exactly the most straightforward procedure. Sure, you can just measure the axis ratio, but unfortunately, it's not nearly that simple. Galaxies are very complicated creatures, and deconvolving the galaxy's inherent properties from the changes due to lensing is... tricky. Is it better to directly measure the shape moments of the galaxy, or do you take an idealized model of a galaxy and stretch and squish it until it looks like the one in question? We don't really know.

The much more subtle problem is that of the PSF, or point spread function. See, data have this unfortunate feature of not being ideal. The PSF is one of the descriptions of how data can be annoying; it describes how a single point of light is spread out into a blob. When you see spikes on images, for instance, they are due to the PSF. The irritating part is that the PSF often has an ellipticity on the order of a few percent (just like the shear signal we want to measure!), varies with time (so not all of your images have the same PSF), and can vary across the detector itself (so that the PSF on the left-hand side of the image is different from on the right-hand side). The PSF must be accounted for before the shear can be measured, and a mis-estimation in the PSF's properties can lead to a mis-measurement of the shear signal. And then, assuming the PSF is perfectly modelled (unlikely), is it better to just subtract the PSF's ellipticity from that of the galaxies, or should we attempt to deconvolve the galaxy and the PSF? Again, there are arguments both ways, but no clear answer.

This recent work is part of a courageous attempt to try to determine which measurement methods work, which don't, and, more importantly, why. This is perhaps more effective than the scientific equivalent of lots of people saying, "mine's better than yours because I like mine and I don't like yours." What we have done is to make a set of simulated images, with realistic PSFs, realistic galaxies, and realistic noise, like what one would get from data taken at a large ground-based telescope. Most importantly, a shear was applied to each image which could then be measured. (My contribution to this work, by the way, was in making the simulated images.) Different people threw their weak lensing analysis pipelines at the images just like they would real data, and from their results, we can now quantitatively talk about why a certain method is more effective at correcting for the PSF than another method, or in what situations certain methods are more or less effective at measuring the shear. Other factors potentially affecting shear measurment, such as how galaxy evolution and—get this—pixel size, are also becoming clearer. The cautionary bit is that anyone doing or planning on doing a weak lensing survey should strongly test their measurements methods on simulated data. The good news, though, is that "high precision" weak lensing is in fact possible.