How big is our galaxy, anyway?

And more than that–how do we know?

Consider that we can’t really take a photo like this of our galaxy. We’re inside it, and space travel has not advanced to the point where we can leave it just yet. There’s no way we can get a camera out to take a picture from this perspective.

Most things in the universe–like stars, planets, and even other galaxies–can be measured using their angular diameters. That is, we use trigonometry to find their actual sizes based on how large they appear to us in the sky.

But that doesn’t work for an object that we’re inside of.

In order measure the size of our own galaxy, early astronomers had to get a bit creative–with variable stars.

We first discussed variable stars–specifically Cepheid variables–seemingly an eternity ago while we covered stellar evolution. Recently, I published a post explaining the stages of stellar evolution in a nutshell, but I left Cepheids out for length.

So what is a Cepheid variable star?

In a nutshell, Cepheids are aging stars that “cross” through the instability strip on the H-R diagram.

The H-R diagram–also known as the Hertzsprung-Russell diagram for its creators–graphs stars according to surface temperature and luminosity. But because all characteristics of stars are interrelated, we can plot a star on the H-R diagram by just about any characteristic–temperature, spectral class, luminosity, absolute magnitude, apparent magnitude, radius, and even mass.

So, when we say that a star “moves” on the H-R diagram or “crosses” certain features (usually the main sequence or the instability strip), we’re really describing changes in the star’s structure that move its data point on the diagram.

As I’ve described before, the “main sequence”–the main strip of stars you see above, including the sun–diagrams the relationship between surface temperature and luminosity that’s found in stable, hydrogen-fusing stars. As stars evolve off the main sequence, they undergo periods of expansion and contraction that move their data point in zigzags across the H-R diagram.

Expanding, giant stars zigzag through the instability strip several times. This region of the H-R diagram represents a specific relationship between surface temperature and luminosity that indicates a star is rhythmically fluctuating in brightness.

But…why would a star fluctuate like that?

The first Cepheid variable discovered was Delta Cephei. It wasn’t considered a “Cepheid variable” yet. “Delta Cephei” was simply the name of the star, following stellar naming conventions. “Cephei” was the possessive form of the constellation Cepheus, and “Delta” indicated that this was the fourth brightest star in Cepheus.

In 1784, the young astronomer John Goodricke discovered that Delta Cephei’s brightness was not, in fact, fixed. It remained constant enough to stay the fourth brightest star in Cepheus, but it fluctuated rhythmically.

Soon, other stars that underwent similar fluctuations were discovered–and they were named for the first of their kind, “Cepheid” variables.

I discussed the reason Cepheids fluctuate in brightness way back when I was posting on stellar evolution. What’s important to know for this post is that there is a relationship between a Cepheid’s average luminosity and its period of pulsation.

Think of it like a bell. Smaller bells have a higher-pitched ding; larger bells have a much lower pitched gong. Similarly, smaller giant stars have a higher “pitch” to their pulsation (that is, they pulsate rapidly). Larger giant stars have a much lower “pitch” and pulsate more slowly.

We also know that for all stars, there is a relationship between luminosity and surface area (that is, radius or size). So, a Cepheid variable star that pulsates slowly must be large and therefore luminous, and a Cepheid that pulsates rapidly must be smaller and therefore less luminous.

So why does all of that matter?

If you can measure a Cepheid’s period, you can determine its luminosity. From its luminosity, you can use the H-R diagram to determine its absolute magnitude (how bright its visible light actually is) and its apparent magnitude (how bright it appears from Earth).

And all you need to discover a star’s actual distance from Earth is the difference between its absolute and apparent magnitudes.

That makes Cepheid variables an extremely important tool for measuring distances in astronomy. And in around 1920, astronomer Harlow Shapley was able to use them to measure the size of our galaxy.

Dang, we’re in the modern day now! I’ve written about countless classical and early modern astronomers from Thales of Miletus to William Herschel, and that’s the first proper photograph I’ve included. Everyone else has had portraits, and the closest thing Thales had to a portrait was an armless, stone bust.

Anyway. Just before the turn of Shapley’s century, William and Caroline Herschel had concluded that there was a broader system of stars beyond our solar system that they called the “star system,” and that the sun was at the center.

Shapley continued their work, discovering that the sun was not in fact at the center–and that this “star system” was quite a bit larger than previously thought.

Shapley’s work focused on globular clusters, a type of star cluster. These are very old clusters that appear as dense spheres of stars. They’re different from open clusters–younger, more diffuse clusters whose stars drift away from the cluster over time.

Globular clusters are some of my favorite objects–one of my star party favorites being M13, the Hercules Cluster. (M13 is in the constellation Hercules.)

They are also very mysterious objects, subjects of ongoing research. There’s one hypothesis that they are the remains of smaller galaxies that have been torn apart by larger galaxies (like our own large Milky Way). Either way, one thing is clear: they are some of the oldest objects in the universe, likely some of the first groups of stars to form.

Shapley noticed that over half of globular clusters (or, at least, the ones known in the 1920s) were found in the constellation Sagittarius. He correctly assumed that their orbital motion was controlled by the gravitation at the core of the “star system,” and that the center of the star system must therefore be in the direction of that constellation, not near our sun.

If Shapley could determine the distribution of those globular clusters through space, he could discover the center of their distribution–the gravitational center of the star system.

But the question was, how far away were those clusters?

This is where Cepheid variables come in.

For reasons that astronomers don’t quite understand yet, globular clusters contain a broad distribution of both old and young stars. And that includes Cepheids.

By using the period-luminosity relation, Shapley was able to calculate the distance to globular clusters that contained observable Cepheids. For the more distant ones where the Cepheids were too faint to observe, he relied upon angular diameter, calculating the linear diameter and therefore the distance based on the known values of nearer clusters.

The graph above shows Shapley’s globular clusters, plotted according to distance from Earth. The Earth itself is at the origin. Shapley estimated the center of gravity influencing the clusters to be at the red X.

It blows my mind a little just how much larger Shapley’s estimates were than the Herschels’ map of the star system.

Here, you see the Herschels’ map represented as an approximate black shape dotted with white stars. The Herschels estimated the sun to be considerably closer to the center than it’s shown here, but the point is the broad distribution of globular clusters that completely dwarfs the Herschels’ model.

Shapley’s globular cluster distribution was, in fact, too large.

The Cepheids he used to calibrate the distances to the nearer clusters lay mostly in the plane of our galaxy, largely hidden behind interstellar dust clouds. They appeared much fainter than they actually were. Their distance calibration relies upon the period-luminosity relation–luminosity being the operative word.

With an inaccurate measurement that early on in the calculation, the calibration was way off.

Also, the more distant globular clusters that Shapley observed were not obscured by interstellar dust–that’s why he was able to see such faraway objects in the first place. With different variables affecting the different clusters, Shapley’s estimates couldn’t be accurate.

Not to mention, Shapley didn’t even know there were multiple types of variable stars (even among Cepheids), which also affected his distance calibration.

As a result, Shapley estimated the distance to the galactic center to be as many as 30 kiloparsecs (98,000 light-years)–more than three times the modern estimate of 8.5 kiloparsecs (28,000 light-years).

But the important thing is that Shapley was able to show that the sun is not at the center of our star system.

It wasn’t long before other astronomers built on Shapley’s work, discovering that it is not merely a “star system,” but just one of many galaxies previously known only as unremarkable smudges of light.

Very soon, we’ll explore that vast universe of galaxies. But first, we’ll turn our attention to the structure of our own Milky Way.