How Gravitational Lensing Shows Us Dark Matter!

“You may hate gravity, but gravity doesn’t care.” –Clayton Christensen

What’s the deal with gravity, dark matter, and this whole “lensing” business anyway? You’ve probably heard that energy — most commonly mass — bends light. And perhaps you’ve seen an image or two like this one to illustrate that.

Image credit: ESA, NASA, J.-P. Kneib and Richard Ellis.

Above is the great galaxy cluster Abell Cluster 2218. But those giant, stretched arcs you see? Those are actually background galaxies that get distorted and magnified by the giant cluster.

As the light leaves its source, the mighty gravity of the massive cluster bends that light, creating the multiple, swooping images you see above.

This is called strong gravitational lensing, and it’s one of the most spectacular sights in the Universe. But, unfortunately, it’s ultra-rare that we get such a fortuitous alignment between a foreground mass and a background galaxy. How, then, are we supposed to measure where the matter is (and how much matter there is) if we get a galaxy cluster without those strong features.

Like, say, this guy.

Image credit: NASA/STScI; Magellan/U.Arizona/D.Clowe et al.

It turns out that almost every cluster has no arcs, multiple images, or Einstein rings to help us out. So how do we map the dark matter?

We turn to the much less visually spectacular (but much more cosmically powerful) weak gravitational lensing.

What the hell is that? Let’s dive on in.

Image credit: ESA's Euclid.

Above is what part of the Universe might look like. There might be some regions with lots of mass in it, where the matter has started to cluster together on large scales. There are others with dearths of matter, where we have great voids in the Universe. As a result, when light from objects behind these masses makes its way towards us, it doesn’t get bent in a spectacular fashion, but it gets sheared.

What does that mean? Let’s show you. Take a look at what some circular light sources would look like if there were no mass in between us — looking out — and those light sources.

Image credit: Smoot lensing subgroup, as is the image below.

But now, what if we took those same light sources, and in between us and them, we put some typical-to-the-Universe sources of mass? Now remember, we’re not allowing any strong effects: no magnification, no multiple images, no rings, no great distorted arcs. What would it look like now?

Why, these light sources get distorted: stretched into elliptical shapes, due to the masses in between us and them!

“Great,” you must be thinking, “all we have to do is measure how elliptical galaxies are, and we can figure out the masses in between us and them!”

Not so fast. The problem is, real galaxies come in different shapes. As we astrophysicists are creative name-givers, we call this effect “shape noise.” (No, seriously, we name things like kindergarteners.) So when we look out at the Universe, what we see is a combination of this shape noise and the weak gravitational lensing effects of the intervening mass.

Image credit: TallJimbo.

So what can we do? Well, we have to measure many background galaxies, to average out the effect of shape noise. How do we do this? Let’s take a look at a cropped (but un-edited) version of one of the most famous pictures of the Universe: the Hubble Deep Field!

Image credit: R. Williams (STScI), the Hubble Deep Field Team and NASA.

As you can well imagine, the largest galaxies in that picture are, by-and-large, the closest galaxies to us. So, if we understand dark matter (and we think we do), the blue lines show us how we expect the background galaxies to be distorted.

Image credit: Mike Hudson. mhvm.uwaterloo.ca is his research page.

That’s the effect of weak lensing: a shear in how the background galaxies appear.

Well, we can work the other way, too! Observe the distortion of the background galaxies, account for the shape noise, and re-create a map of the total matter — both luminous and dark — based on what we know about weak lensing. So what do we get, looking at that arc-free cluster back up top? (The third image in this article.)

Image credit: Douglas Clowe et al.

Well, we can recreate the distribution of matter, most of which is not accounted for by atoms! In fact, if we show those results from weak lensing in blue, and overlay the Chandra X-Ray observatory data in pink, you may recognize this as one of the most famous images ever…

Image credit: X-ray: NASA/CXC/CfA/M.Markevitch et al.; Lensing Map: NASA/STScI; ESO WFI; Magellan/U.Arizona/ D.Clowe et al.; Optical: NASA/STScI; Magellan/U.Arizona/D.Clowe et al.

The Bullet Cluster! You can not only measure the amount of total matter, with weak lensing, but you can compare it with where the hot gas is in the X-ray. This combination is a big part of how we know dark matter doesn’t collide with either itself or with normal, atomic matter.

So if you want to know how much mass is in a cluster, and where that mass is, all you need to do is measure all the background sources of light coming from behind that cluster, and as long as you’ve got enough of them, weak gravitational lensing takes care of the rest!

And that’s how weak gravitational lensing shows us where dark matter is!