How Massive is the Milky Way?

Over centuries of philosophy and research, through the times of the classical astronomers to Galileo’s observations of the Milky Way, humanity’s understanding of our universe has evolved from a simple model of the sun and planets to a vast wheel of stars we now know as our galaxy.

And since the “discovery” of our Milky Way–or, more accurately, the discovery of what that hazy band of stars in the sky is–we’ve come to realize just how massive our home in the cosmos really is.

That scientific journey started with the Herschels’ mapping of what was then called the “star system.” Later astronomers began to realize just how far out from the sun the stars of our galaxy really reached. Determining distances across our galaxy was the first step to discovering its size.

Later, we began to understand its structure–mapping the extraordinarily thin disk, the chaotic central bulge, and the visible part of the halo, a sphere of stars that extends beyond the plane of the galaxy.

And since then, we’ve begun to master the next critical part of understanding our galaxy: its mass.

So, how massive is our galaxy?

In order to answer that question, we first need an understanding of what mass is.

First things first: it is not the same as weight.

You can think of mass as the amount of “stuff” in an object. That is, the physical material it’s made of. The anvil in the image above isn’t just empty space, right? It’s made of something. And there is a certain amount of that something.

Mass is a property of an object that never changes. The anvil will have the same mass regardless of whether it’s on the Earth, in space, or on the moon. Weight, however, is a force–defined in the most basic physics as “a push or pull.” It’s the force that, in this case, holds the anvil on the surface of a planet or moon.

In other words, you’re always going to have the same mass, but you’ll weigh less on the moon than you do on Earth–that’s why astronauts have to learn to space-walk. And in space, obviously, you’ll feel “weightless.”

(You’re not entirely weightless, though, because without some force of gravity on you, you’d drift off into space forever and space programs would never allow that! Erm…theoretically. 😉 )

But the Milky Way Galaxy is not a solid object. When we talk about finding the mass of our galaxy, we mean finding the combined mass of all the stuff that makes up the galaxy–the stars, gas, dust clouds, planets, etc.

Yeah…that’s a lot of mass. And I think I misplaced my kitchen scale…

On second thought, I don’t think a kitchen scale is going to be big enough. So how the heck do we tackle this problem?

We ran into the same problem seemingly eons ago when we explored the masses of stars. And we’re going to turn to the same solution now: gravity.

In the diagram above, you see two stars that orbit one another in the same star system–which is, you might remember from old posts of mine, the norm rather than the exception in the universe. This is called a binary star system.

I’m not the only one who doesn’t have a big enough scale to measure mass in space. Professional astronomers don’t either, which means they need to rely on the effects of mass. And as I’ve described before, gravity is a result of mass.

In the case of binary stars, we map the stars’ orbital motion. Kepler’s laws of motion relate mass to orbital motion. So, if we can discover the average distance between binary stars and the period of their orbits, we can measure the unknown variable in Kepler’s third law: mass.

But how do we translate that to measuring the mass of a whole galaxy?

It’s actually not as complicated as you’d think.

The first fundamental fact we need to establish is that the galaxy rotates, just like the Earth, the other planets, the sun, and likely every other solid object in the universe.

Imagine spinning a frisbee. In fact, the galaxy’s movement is very similar to that of a frisbee: it travels forward through space, too, as it spins. (But, relative to a human reference frame, it doesn’t move nearly as fast as a frisbee.)

Alright, now that we’ve got that down, let’s check out the diagram above. There’s the sun, shown in its orbit around the galaxy.

That’s a second fundamental fact: our sun orbits the center of our galaxy, just as the planets of the solar system orbit the sun.

In fact–everything in the galaxy orbits the center of the galaxy. And here’s the crux: that literally is the rotation of the galaxy.

Let’s say that again. The rotation of the galaxy is the motion of the galaxy’s stars around its center.

That makes sense, right? Technically, you could describe the rotation of a frisbee as the motion of its outer material around its center.

Okay, so there’s our orbital motion. Literally all the objects in the galaxy are orbiting objects that we can stick into Kepler’s equations for orbital motion.

So, let’s start with something familiar: our own sun.

The diagram above gives us everything we need to determine the mass enclosed by the sun’s orbit.

Wait…the mass enclosed by the sun’s orbit? What the heck is that supposed to mean?

Well, consider that when we’re using orbital motion to find the masses of binary stars, we are, in fact, finding the mass enclosed by their orbits–it’s just that the mass is concentrated in the location of each star.

And when we use planetary motion to find the mass of the sun, we’re finding the mass enclosed by the orbit of the specific planet we input, too–but the sun comprises 99% of the mass of the solar system, so we’re still mostly estimating the sun’s mass alone.

Kepler’s third law of motion, specific to galaxies, requires two pieces of information: the distance between the center of the galaxy and the star we’re using, and the period of the star’s orbit.

We’ve got all that right up above. The distance to the center of the galaxy is 26,100 ly (light-years), or about 8.5 kpc (kiloparsecs). That distance, multiplied by 2π and divided by the sun’s estimated orbital velocity of 240 km/s, gives us an orbital period of about 225 million years.

Now all we have to do is stick all that into Kepler’s third law of motion. The total mass we get is 100 billion M (solar masses).

Of course, there’s one problem: this only describes the mass enclosed by the sun’s orbit, and the sun is not at the edge of the galaxy. So this is a very rough estimate. There’s more mass orbiting outside of the sun’s orbit. Astronomers calculate the total mass of the galaxy to be at least 400 billion M.

400 billion times the mass of our sun! Isn’t that crazy?

But there’s something even crazier going on with the rotation (orbital motion) of our galaxy…

There is something very strange going on here. Do you see it?

I’ll give you some needed information…

The red line is a graph plotting the observed orbital velocity of stars in our galaxy in relation to their distance from the center. We call this a rotation curve for the galaxy. It shows that, very close to the center of the galaxy, stars are moving at around 250 km/s.

At around 5 kpc from the center, average orbital velocities dip to 200 km/s. Until around 12 kpc out, the average orbital velocity of all the stars oscillates within this range. Beyond 15 kpc, the average orbital velocity begins to flatten–and then gradually increases beyond 250 km/s.

The dashed line, on the other hand, is predicted data–not the actual data. This is the kind of orbital motion we see in our own solar system. Essentially, orbital velocity closer to the sun is faster, and farther out, orbital velocity decreases. This is called Keplerian motion, based off of Kepler’s laws of planetary motion.

Kepler’s third law can calculate the mass of the galaxy from observed orbital speeds. But those orbital speeds aren’t what we would expect, based on Kepler’s predictions.

So what’s going on here?

Let’s break this down.

The rotation curve for the Milky Way shows that objects orbiting at the edge of the galaxy–over 30 kpc from the center–are orbiting faster than objects much closer to the center.

According to Kepler’s laws, those larger orbits must enclose more mass. But what does that mean?

If the galaxy were like the solar system, estimating its mass using the sun’s orbit wouldn’t be a problem. Most of the mass would be concentrated at the very center, well within the sun’s orbit.

But if orbits of objects at the edges of the galaxy enclose even more mass than the sun’s orbit does, then a great deal of mass must be spread evenly throughout the galaxy–including out at the edges!

And here’s the kicker.

Currently, an astronomer’s most important tool is the electromagnetic spectrum: the spectrum of all electromagnetic radiation in the universe, from the ultra-high-energy gamma rays to the extremely low-frequency radio waves.

All kinds of different telescopes have been designed to intercept and study specific portions of the electromagnetic spectrum, from radio telescopes, to the average amateur’s visible light telescope, to gamma-ray observatories.

Everything we can see and study depends on observations from these telescopes. If we can’t see it with electromagnetic light, it gets much harder to study. Black holes, for example, are invisible by definition–and our best chance at studying them lies with the effects of their gravity on visible objects.

Now, back to the mass of the Milky Way.

We know how much mass should be there–from the orbital motion of the outermost stars. But we can’t see it.

Wait–rewind that.

There’s mass in the outer reaches of our galaxy that we can’t see.

Could it be stars that are too faint to see from Earth? Maybe interstellar dust that doesn’t produce its own light?

Neither are massive enough to account for the galaxy’s rotation curve.

The astronomy and cosmology buffs among you might know exactly where I’m headed with this: dark matter.

Yes, dark matter.

We’re finally there.

There’s a whole world of theoretical science surrounding dark matter. But now you know the origins of the idea: galaxies, including the Milky Way, rotate way too fast at the edges to make sense for the mass we can actually see.

That’s why astronomers have dubbed this mysterious form of matter “dark” matter.

We’ll be coming back to dark matter soon–but first, we’ll explore a bit more of our home galaxy.

Questions? Or just want to talk?

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