If you needed to measure the mass of, say, a brick–or some other Earthly object–you could just set it on a scale. (Yes, scales measure mass, not weight.)

With galaxies, it’s not so easy! I don’t think anyone’s invented a scale big enough yet…

But if we can measure the mass of a galaxy, it brings us that much closer to understanding its origin. And that brings us closer to learning the story of the universe.

So…how do you measure a galaxy’s mass? And just how massive are they?

Well, if we can’t measure the mass directly with a laboratory scale, we need to turn to measuring its effects. That is, gravity.

It’s not the first time we’ve used gravity to measure mass. We also did that back when we were studying stars. I introduced the notion in my post on binary stars.

Why binary stars, rather than single stars?

Because binary stars orbit one another–around their center of mass.

See? There’s mass for ya.

Galaxies may not be binary stars, but they are systems of stars–and gas and dust–orbiting a center of mass. For a galaxy, that center of mass is the galactic core…or, more specifically, the central supermassive black hole.

When we observe distant galaxies, we often can’t make out individual stars. What we can observe is the galaxy’s overall rotation. This is the same as observing the orbits of all the stars together–because that’s why we say that galaxies “rotate.”

Okay, okay, I know…when we look at any one galaxy through a telescope, it always appears the same. We don’t actually live long enough to see galaxies rotate.

But what we can do, is measure the galaxy’s Doppler shift.

Not sure what I’m talking about? I recommend checking out my post on the Doppler effect. The long story short: light from objects that are moving toward the observer is shifted toward shorter (bluer) wavelengths, and light from objects that are moving away from the observer is shifted toward longer (redder) wavelengths.

(Still not sure what the heck I’m talking about? You might want to check out my posts explaining the electromagnetic spectrum, the basics of atoms, and how they interact with light, all of which are the keys to understanding stellar spectra–one of astronomers’ most fundamental tools. Eventually, I’ll write a post with an overview of all of that…)

…Anyway.

By measuring the blueshift of the approaching side and the redshift of the receding side, we can observe the galaxy’s rotation curve.

This is the rotation curve for the Andromeda Galaxy, or Messier 31–our nearest galactic neighbor.

Alright, let me break down what we’re looking at here.

First off–the axes. The horizontal axis is just showing distance from the galactic center. The radial velocity is just…well, the velocity. “Radial” just means we’re talking about motion in a circle rather than a straight line.

As for the data points–what we’re seeing is how fast objects in the galaxy are orbiting, depending on how far away they are from the center.

Just by measuring the Doppler shift, we can calculate how fast parts of the galaxy are rotating at any given distance from the center.

Okay, so…how do we get mass from that?

If you know the orbital velocity at any given distance from the center, you can calculate the period of that orbit. Kepler’s third law can then give you the mass.

This method is called, quite creatively, the rotation curve method. It’s the most accurate method of measuring a galaxy’s mass. But there’s a couple problems.

One problem comes in the form of Kepler’s third law itself.

It’s great for measuring mass in planetary systems. In fact, that’s exactly what the classical astronomer Johannes Kepler meant for it to calculate. But galaxies have a pesky little thing called dark matter, and it loves to get in the way of rotation curves.

What you see above is “half” of a rotation curve–that is, the curve for just one side of the galaxy. And the observed velocity of rotation is a heck of a lot faster than expected, given the luminosity of the stars we can actually see.

To explain this, astronomers have hypothesized “dark matter”: an invisible type of matter that emits no light (and doesn’t even get silhouetted by distant starlight), but sure as heck has a ton of mass. (We’ll explore dark matter soon!)

That, of course, will change the overall mass of any one galaxy. The mass you calculate from the rotation curve method will actually be too low a number.

What’s the other problem, you ask?

This, right here.

This is what happens when astronomers point a large telescope at a tiny, black, utterly nondescript bit of night sky and take a ridiculously long camera exposure. Turns out that tiny bit of sky wasn’t so “nondescript” after all!

There are only a few single stars in this image, identifiable by their four-point diffraction spikes. These are foreground stars, located within our own Milky Way Galaxy. The rest are whole galaxies beyond ours.

I know, right? Coulda fooled me!

But my point is…how are we supposed to observe the rotation of those faint, distant galaxies that look kinda like little dots? We just can’t observe enough detail to plot a rotation curve.

What we can do instead, is ask ourselves this…

How do orbits work?

The simple answer is gravity. No matter if a cannonball is orbiting the Earth–like the image above–or if stars are orbiting the core of a galaxy, the gravitational force of the system must be strong enough to keep its parts bound together.

Wait a second…that comes down to mass again!

For any one galaxy, the mass must be great enough to keep all its stars, dust, and gas gravitationally bound. Otherwise, the fastest-moving objects will reach escape velocity and fly off into intergalactic space.

And from there, we get the velocity dispersion method.

This graphic depicts a star, not a galaxy–but the concept is the same. We’re using the Doppler effect to measure an object’s rotation. Imagine here that we’re tracking one atom in the star’s atmosphere.

Here’s the key: because we are measuring motion using the Doppler effect, we can only detect motion directly toward or away from us.

Look at the third (middle) frame. There is no Doppler shift visible because the atom we’re tracking is not moving toward or away from us. But it is not motionless. Relative to our line of sight, it is moving sideways.

If we’re observing a relatively nearby object, we’ll be able to resolve enough detail to see each “slide” of this process. But a more distant object will be much more difficult to resolve.

Its spectral lines will appear “smeared”–as if we’re seeing all the above slides at once, in one image. This is called spectral-line broadening.

When observing distant galaxies, astronomers can’t resolve enough detail to plot a rotation curve, but they can measure the spectral broadening. That can tell them the “maximum” velocity in the galaxy–that of the fastest object.

From there, it’s a question of how massive the galaxy must be so that its escape velocity is greater than its fastest-moving object.

Which brings me to the final (and least accurate) method of measuring a galaxy’s mass…

The cluster method depends on–you guessed it–galaxy clusters.

Most galaxies actually don’t stand alone. They’re found within larger clusters of galaxies. Since that’s so common, it’s pretty safe to assume that galaxy clusters are stable structures–that is, that they aren’t generally on the verge of flying apart.

If we assume that all the galaxies within a galaxy cluster are, in fact, gravitationally bound, we can ask ourselves this:

How massive must the cluster be to have an escape velocity greater than its fastest-moving galaxy?

This is basically a different version of the velocity dispersion method. This time, instead of using broad spectral lines to determine the highest orbital velocity within one galaxy, we measure the velocities of entire galaxies.

That gives us the mass of the whole cluster. Then we divide that number by the number of galaxies to find, well…the average mass of the individual galaxies.

But then we run into a bit of a problem.

This table shows the general properties of the main types of galaxies.

As you can see…the masses vary quite a bit. So, finding the average mass in a cluster means we really don’t know the individual mass of each galaxy.

But the masses we’ve measured do tell us something important…

Notice that each type of galaxy–spiral, irregular, dwarf elliptical, and giant elliptical–has a different range of masses?

That will definitely become important as we explore galactic evolution.

And finally, we can answer the question we asked at the very beginning of this post: how massive are galaxies?

It depends on the type of galaxy. The least massive are dwarf ellipticals, which range in mass from “only” 10⁵ to 10⁷ times the mass of our sun. Irregular galaxies sit smack dab in the center of that range, at 10⁶ solar masses.

Spiral galaxies like our own, however, are much more massive–on the order of 10¹¹ times the mass of our sun. And giant ellipticals, at 10¹³ solar masses, are even massive-r.

Is “massiver” even a word? On the galactic scale, I feel like it should be!