# Dark Matter, Part 1: How we know it exists

Cosmic Web of Dark Matter
Credit: Millennium Simulation Project

Introduction

We live in a 13.8-billion-year-old Universe that’s vast beyond comprehension. 13.8 billion years—that means the Universe is 13.8 billion light-years in radius, right? Well, no, because our Universe is as weird as it is vast. One of the weird things about it is that there’s this strange stuff called dark energy that’s stretching the Universe, causing it to expand faster and faster as time passes. As a result, the observable Universe today has a radius of about 46 billion light-years (and this is just the observable Universe; the Universe is far, far larger than that, perhaps even infinite. See my previous article to get an idea of what “observable Universe” means, here). And that weird stuff makes up about 70 percent of the Universe’s contents.

So, what’s the rest? Well, it’s stuff, or matter. But because the Universe never fails at being fascinatingly weird, only some of this matter is stuff that we’re used to, stuff that interacts with light, like you, me, the stars, your dog, the device you’re using right now to read this. And when I say some, I mean like a really small amount: 5%. Just 5% of the Universe is normal matter. The remaining 25%? Dark matter, stuff that doesn’t interact with light at all, revealing itself only through its gravitational interactions. Theorized by Fritz Zwicky in the 30s to explain why galaxy clusters weren’t flying apart, and discovered via its gravitational interactions in galaxy rotation curves by Vera Rubin in the 70s, dark matter comprises a huge chunk of the Universe’s contents, and yet, remains a mystery.

The Solar System: Our Gravitational Lab

Because dark matter doesn’t interact with light, it makes it really hard to study. But there is something we can use to study it: its interactions with gravity. We understand gravity pretty well, and have obtained really precise measurements of it using our own little lab in space: the solar system. The Sun, being the heaviest mass in the solar system, is the main source of gravity for the planets. Because the planets are located at different distances from the Sun, the Sun’s gravitational pull is different on each, decreasing by the square of the distance—that is, it gets weaker the farther out you go, so planets farther from the Sun will experience a weaker gravitational pull, and in turn, have lower orbital velocities1 than those closer in.

1This comes from the fact that when we set the force due to gravity, $F_{g}=\frac{GMm}{r^2}$ equal to the centripetal force, $F_{c}=\frac{mv^2}{r}$, when we solve for the velocity, we get $v^2=\frac{GM}{r}$. That means that the velocity is proportional to the inverse square roor of the distance, $v\propto \frac{1}{\sqrt{r}}$, hence it decreases as we move further out from the central mass.

Galaxy Rotation Curves

Now, let’s zoom out and look at a galaxy. Stars in galaxies orbit about the galactic core, much like planets orbit their host star. If you were to plot a velocity curve of the stars, from the core out to the edge of the disk, you’d expect it to look something like the velocity curve of our solar system, with velocities decreasing at further distances as ~$\frac{1}{\sqrt{r}}$. The kicker: when you actually plot one, velocities tend to remain relatively constant, or sometimes, even slightly increase, with distance. When you account for all the normal matter in a galaxy, it cannot explain how velocities are constant with distance–there’s just not enough gravity from the stuff we can see.

Example of the rotation curve you’d expect (the red Keplerian curve) compared to the rotation curve we actually get (green curve) for a galaxy. Credit: Astronomy 162.

There’s also stuff we can’t see, like black holes and brown dwarfs, and things that simply aren’t luminous enough to detect (these are called Massive Astrophysical Compact Halo Objects, or MACHOs1). Still, accounting for these along with the visible matter doesn’t explain the rotation curves! This tells us there must be stuff we can’t see contributing to the force of gravity acting on these stars way out at the edge, giving them higher velocities—dark matter. This is how Vera Rubin, along with her colleague Kent Ford, discovered the existence of dark matter in the Andromeda galaxy in the 70s.

A rotation curve for the Andromeda galaxy. The open circle data points are from data taken by Rubin and Ford, and the solid dots are from data taken by Roberts and Whitehurst. Figure from Barbara Ryden’s Introduction to Cosmology.

1MACHOs are a form of dark matter. However, there isn’t enough of it in the Universe to explain the anomalies we observe.

Gravitational Lensing

Another way we know it’s there is through a phenomenon called “gravitational lensing” which happens with giant clusters of galaxies. Gravitational lensing is an effect of Albert Einstein’s Theory of General Relativity, which says masses curve spacetime1: because clusters are massive, they bend spacetime, and bending spacetime causes the path of photons leaving objects behind the cluster to bend, too. The bent trajectory of these photons originating from the object behind the cluster creates images of the object that are warped into the form of arcs and rings around the cluster. The amount the object behind the cluster is warped, or lensed, tells us how much mass is in the cluster doing the lensing. We find that these clusters are warping the image of the object way too much for the visible matter to account for, which means there must be tons of dark matter in these systems.

Galaxy cluster RCS2 032727-132623, a cluster about 5 billion light-years away, gravitationally lensing a galaxy that’s even more distant at 10 billion light-years away.
Credit: NASAESA, J. Rigby (NASA Goddard Space Flight Center), K. Sharon (Kavli Institute for Cosmological Physics, University of Chicago), and M. Gladders and E. Wuyts (University of Chicago)

The Cosmic Microwave Background

Another thing that tells us dark matter is exists comes from a whisper of the Big Bang: the Cosmic Microwave Background (CMB). The CMB is a snapshot of our baby Universe, just 380,000 years old. It’s also the farthest we can see back into our Universe’s history1 because before that, the Universe was opaque—it was a subatomic particle soup! At that time, photons just kept bouncing off of other particles, so they weren’t free to travel through space like they are today. When photons finally decoupled from matter, they traveled freely through space, no longer bumping into matter, and left us a nice little photograph of a time in the Universe’s distant past.

The CMB shows us a time in the Universe’s history when the density of this soup was relatively uniform—except for little quantum mechanical fluctuations that caused the density to vary. Now, here’s the cool part: these density fluctuations caused matter to want to bunch up under gravity, but because regular matter interacts with light, photon pressure pushed the matter out and prevented it from collapsing under gravity2. But dark matter doesn’t interact with photons, so the radiation pressure didn’t affect it, and it collapsed into dense clumps. Then, photons decoupled from the soup and started traveling through the Universe freely, some from deeper gravitational potential wells than others due to the fluctuations, resulting in a slight variation in the energies the photons left the soup with. So they arrive here today at slightly different temperatures, resulting in the mottled photograph of the CMB we have. These little anisotropies allowed for dark matter to collapse and form the seeds for matter to form bigger stuff later in the Universe’s history, like stars, galaxies, and clusters of galaxies. In fact, without dark matter, the anisotropies are far too small for just matter alone to have formed structure because matter interacts with light and was affected by the radiation pressure, and enough time hasn’t passed for matter alone to form the structure we see today. Hence, dark matter is necessary for structure formation.

The Cosmic Microwave Background, as seen by the Planck Satellite.
Credit: ESA and the Planck Collaboration.

Keep in mind, although there are little anisotropies, the CMB is extremely homogeneous on large scales—homogeneous to 1 part in 100,000, in fact. The homogeneity is likely a result of inflation in the early Universe (you can read all about it in a post I wrote on it, here). But the small fluctuations stuck, and grew as the Universe did, where dark matter accumulated and provided the seeds for formation of the structure we see today.

1The CMB also very closely coincides with what we call our particle horizon (the particle horizon is a bit farther back in time) which is as far back as we can possibly see into the Universe even if the CMB wasn’t opaque; read my previous post on inflation to learn more about this, here.

2This may not have always been the case: if primordial black holes, a hypothetical form of dark matter, exist, then they would’ve formed during this time. If the radiation pressure wasn’t sufficient to push back the matter that was grouping into the density fluctuations, then the matter could collapse and form black holes. We’ve not found any of these yet.

Concluding thoughts

So now we know some of the ways dark matter reveals itself to us. Another thing we do now is use simulations to help us figure out stuff about the Universe, putting in all the relevant physics so that we can watch the Universe unfold at far quicker timescales (because we’re humans, and we simply don’t have 13.8 billion years to watch the Universe grow). When we simulate galaxies, and galaxy clusters, with just normal matter (including stars, gas, even MACHOs and all the tables and chairs and textbooks that a cluster can possibly contain), we find that these galaxies and galaxy clusters just fly apart. However, when we throw in dark matter, the galaxies and clusters of galaxies hold together and come out in one piece. So dark matter is required to ensure structure formation holds. …unless our understanding of gravity is fundamentally wrong

To be continued: Learn about some viable possibilities for dark matter, with a focus on the type I’m researching called Self-Interacting Dark Matter, in an upcoming post!

## 8 thoughts on “Dark Matter, Part 1: How we know it exists”

1. A really clear introduction to dark matter. Question: what’s the closest dark matter that’s ever been observed?

Like

1. Sophia Nasr says:

Thanks! If you are asking if we’ve detected it really close, say, in the solar system, the answer is that we have not. Although there *is* dark matter in the solar system, it’s too small an amount for us to detect its effects on the planets.

Like

1. No worries. What about other planetary systems? I guess because we can’t “see” it directly, it’d be hard to tell if we were detecting it’s effects.

Like

2. Sophia Nasr says:

Other planetary systems would be impossible if we can’t in our own. We have trouble detecting wobbles from their main mass (their host star) as it is!

Like

3. Fair enough. I didn’t think it would be possible.

Like

4. Sophia Nasr says:

It was a very good question! It also stands to show just how difficulty thus search is.

Like

2. I’m curious about something. The universe appears to be expanding at an accelerating rate. This doesn’t make much sense to me. After the Big Bang, I’d expect galaxies to expand, but at a constant rate, or perhaps even slowing down due to any gravity from any mass remaining at the center. So, has anyone suggested that perhaps the universe is not actually expanding, but is being stretched, as it is being pulled back into the center black hole? I’ve heard that as things fall into a black hole they stretch.

I imagine that the universe gets recollected by the black holes at the center of each galaxy, and that these may converge into a super-duper black hole until some tipping point is reached, and we get another Big Bang. Sort of like a yo-yo.

Or, given infinity, there might be room for lots of universes collapsing and exploding again in their own Big Bangs, all the time, like popping corn. Perhaps even exchanging material at their edges.

Like

1. Sophia Nasr says:

There are lots of ideas and hypotheses on what’s going on with dark energy! While the Universe is expanding at an accelerating rate, it shouldn’t *really* be thought of as stretching in that sense; that type of stretching would warp spacetime and its contents, but all the expansion does is move objects farther apart from each other.

The other things you’re talking about are basically cyclic Universes that expand and recollapse over and over. To the best of our knowledge, the shape of the Universe and its dark energy content prevent it from collapsing in on itself.

I can tell you that if I had a definitive answer to the question “what is dark energy”, I’d probably be up for a Nobel Prize next year =)

Like