Dark Matter, Gravity, and Wine Glasses

Dark Matter is a mystery substance that virtually all physicists believe to exist, even though we don't know what it is.  Our best guess is that it is some form of yet-unknown fundamental particle, which interacts through gravity but neither emits nor absorbs light.  Since direct searches for the mystery Dark Matter particle have been making news lately, I thought I'd start this blog by reviewing some of the best indirect evidence we have that Dark Matter exists.  There are, by now, lots of independent lines of evidence that point to the presence of large amounts of invisible ("dark") matter in the universe, but this post will concentrate on my favorite:  gravitational lenses.

Introducing Galaxy Cluster Abell 1689

When astrophysicists look at an image like this one from the Hubble Space Telescope, they interpret the image using what they know about physics:  the nature of matter, the behavior of light, and the mathematical equations describing the force of gravity.  In this image, the fuzzy yellowish blobs are all galaxies, in a grouping known as a "galaxy cluster".  Each galaxy is, like our Milky Way, composed of around one-hundred billion stars (!!!).   Even though these galaxies are remote, the stuff they are made of is no different from what makes up our own galaxy.  The glowing stars in each galaxy are mostly made of the ordinary chemical elements hydrogen and helium, with a few other chemical elements mixed in.

All of the chemical elements we find around us (or in distant stars and galaxies) are what we might call "ordinary matter".  Ordinary matter is ultimately made up of just a few basic fundamental particles:  protons, neutrons, and electrons.   Two properties of "ordinary matter" are important for this discussion.  First of all, all ordinary matter has mass, which also means that it exerts a gravitational pull on other stuff that has mass.  The earth, for example, is made up of ordinary matter with enough mass that its gravity keeps us firmly anchored on the ground. Second, all ordinary matter is capable of emitting and absorbing light (electromagnetic radiation).   Even though some forms of ordinary matter (like the gasses that make up the air) appear to be invisible to our eyes, they all still absorb or emit some form of electromagnetic radiation, perhaps just not in the frequencies that our eyes can detect.  Telescopes that are sensitive to other forms of electromagnetic radiation like x-rays, radio waves, or infrared light can be used in addition to those sensitive to visible light, in order to study the ordinary matter that exists in the universe.  Using the Hubble picture above, we can measure how much light is emitted by the ordinary matter in the galaxy cluster Abell 1689.  We can then apply what we know about the physics of stars and dust and gas to make some rough estimates of how much mass there is in the glowing yellow galaxies. This means we can calculate the strength of the gravitational field that we expect to be associated with this collection of objects.

Gravity and the Warping of Space-Time

According to Einstein's theory of General Relativity, the attractive force of gravity is actually caused by the fact that massive objects warp space and time.  In areas where there are very large objects, space itself is literally bent out of shape.  This causes objects to "fall in" to areas where there is a lot of mass, appearing to be attracted through the force we call gravity.  The usual visual metaphor for this is the picture of a bowling ball on a trampoline:  marbles placed on the trampoline will fall toward the bowling ball because of how it has warped the surface.

(Image taken from a blog posting from Discovery Magazine, by Clifford Johnson, in 2005)

The one trick in applying this metaphor, though, is that you have to remember that a trampoline surface is essentially a two-dimensional sheet.  When we talk about gravity, what's happening is that matter is warping three-dimensional space (plus time, too), which is not as easy to picture in your head.

A "Gravitational Lens"

Let's go back to that Hubble image, and zoom in on a particularly interesting feature:
 

(Image credit:   NASA, N. Benitez (JHU), T. Broadhurst (The Hebrew University), H. Ford (JHU), M. Clampin(STScI), G. Hartig (STScI), G. Illingworth (UCO/Lick Observatory), the ACS Science Team and ESA.  Downloaded from HubbleSite.)

What exactly are those "arcs" that stream through the picture?  They are a very cool side effect of the warping of space-time in Einstein's picture of gravity.  Essentially, in areas where there is a lot of mass, the path taken by light follows the curvature of space.  It's as if the light is being "bent" around an object that is extremely massive. The arcs we see here are images of even more distant galaxies (far behind the cluster of yellowish galaxies that make up most of the picture).  The intense gravitational field of the galaxy cluster in the foreground has bent the light and created bizarre arc-like patterns out of the light from the distant galaxies.

The bending of light around areas where gravity is very strong has been observed many times, and it's one of the main ways that Einstein's theory was experimentally demonstrated to be correct.   This bending of light is not entirely unlike how light gets bent when it goes through common lenses like the ones in your eyeglasses or in your camera.  Hence, this phenomenon is known as "gravitational lensing".  In fact, a common glass lens that imitates the gravitational lensing seen by Hubble is the bottom of an ordinary wine glass:

Here, you can see some coffee beans being "lensed" by the bottom of a wine glass from my cabinet.   Notice how the glass bends the light in such a way to create arc-like images of the coffee beans, much like the arc-like images of distant galaxies in the Hubble picture.  Here, the glass in the wine glass is bending the light, but there it's the warping of space by a very large amount of mass.  And that brings us back to the idea of Dark Matter.

Evidence for Dark Matter from Gravitational Lensing

The phenomenon of gravitational lensing by itself is just cool and weird. It's also informative.  The patterns created by a strong gravitational lens like this galaxy cluster can be used to calculate to what degree the space in the vicinity of the cluster is warped, which is the same thing as figuring out how much mass is there.  The more mass there is, the greater the warping of space, and the more the light will be bent by the "gravitational lens".   When we do this calculation, we find that the particular cluster Abell 1689 is really whoppingly amazingly massive:  something on the scale of 1,000,000,000,000,000 times the mass of our Sun (as first reported here)!  However, there is no way that the visible "ordinary matter" in this cluster of galaxies could possibly have that much mass.  There's just not enough stuff there to account for it.

This is just one of the lines of argumentation that leads to the idea of Dark Matter.  In galaxy clusters that act like gravitational lenses, we know for certain that much more mass is present than the amount of visible, ordinary matter would lead us to believe.  The way that we explain this is by postulating that there is some kind of "dark" (invisible) matter present surrounding all of the galaxies in the cluster.  It is massive and warps space the way ordinary matter does, but it doesn't absorb or emit light.  We can't see it, but we know it's there because of its gravitational effect.  Most of the cosmological lines of evidence for the existence of Dark Matter involve observing its gravitational effects.  This just happens to be my personal favorite line of evidence.

The next time you're sipping a glass of wine, play around a little bit with the lensing effects you can create.  It's fun to compare this simple demonstration with the other-worldly images of gravitational lenses collected by Hubble Space Telescope.  Individual galaxies with a lot of mass (also mostly believed to be in the form of Dark Matter) also act as lenses, and some cool pictures can be found here and here. 

For more on the topic of gravitational lensing, check out local physicist Evalyn Gates' new book, Einstein's Telescope, which is in bookstores now.