What are Variable Stars?

What if I told you that the “two” stars you see here are actually one and the same?

This star, known as L Carinae after its location in the southern constellation Carina, is actually what we call a variable star. It is fairly bright, and its brightness varies significantly. And it’s not alone.

You might be familiar with a few variable stars. Betelgeuse, the bright giant in Orion’s shoulder, was all the rage among astronomers not too long ago. Polaris, the North Star, is also a variable. So is Algol in Perseus.

We’ve actually talked about one type of variable stars before. A variable star is any star whose brightness varies significantly and repeatedly. That means that eclipsing binaries fall within the definition. Algol is this type of variable star.

Now, though, we’re interested specifically in intrinsic variables, stars whose brightness changes because of something going on internally—not because another object passes in front of them and dims their light similarly to casting a shadow, as is the case with eclipsing binaries.

But…why would a star change in brightness like that?

First, let’s take a closer look at the nature of the stars we’re talking about.

Meet Delta Cephei, the topmost star in this imageand one of the first intrinsic variables discovered. Delta Cephei was noticed as a variable star in 1784 by the deaf and mute English astronomer John Goodrich, who was only 19 years old at the time.

Since then, hundreds of similar stars have been found and classified as Cepheid variable stars.

So…when we say that these stars vary in brightness, what exactly do we mean?

Well, here’s Delta Cephei’s light curve for your viewing pleasure.

On the horizontal axis, we have time, and on the vertical axis, we have the visual magnitude—that is, the star’s brightness. So the star is varying in brightness from about +3.5 to +4.5 over the course of a…”phase.”

Meaning what, exactly?

Well, here’s the magnitude scale to help us out a bit.

So this means…Delta Cephei is a naked-eye star a little dimmer than Polaris, the North Star. It varies by about one unit on the apparent magnitude scale. And as far as phases go, one phase is roughly 4 days for this star. So it varies by one unit of brightness every four days.

But…there’s still one very important question. What kinds of stars are these? Young stars? Old stars? Main sequence? Cool or hot? Dwarfs or giants?

It turns out that Cepheid variable stars are supergiants or bright giants of spectral type F or G…

Which means what, exactly?

Well, let’s return to our old friend, the H-R diagram.

The H-R diagram graphs stars according to their temperature and luminosity, and tells you everything you could possibly want to know about a star. Seriously. Everything you want to know has mathematical relationships that can be plotted here…which is a bit beyond the scope of this post.

See the groups labeled supergiants, giants, main sequence, and white dwarfs?

We’re looking at supergiant stars, which are big and bright, and the bright end of the scale as far as plain-ol’ giants are concerned. And if you look down at the temperature axis, you can see that those stars line right up with the spectral classes F and G.

There are also variable stars that are a bit fainter than Cepheids. These are the RR Lyrae variables.

While we’re looking at the H-R diagram, let’s take a look at where exactly these variable stars are located.

Meet the instability strip.

Keep in mind that the H-R diagram does not refer to a star’s location in space. The instability strip refers to a relationship between surface temperature and luminosity that indicates instability within a star—leading to variability.

So…what makes a star pulsate, anyway?

Stars in the instability strip have a special layer of their atmospheres at just the right depth. This is a layer of partially ionized helium. Let’s follow what happens to the layer and how it works in the star.

So, we have a layer of singly ionized helium. It’s transparent to radiation, so energy produced in the star’s core just passes right on through. But not all of the helium in the layer is ionized. The neutral helium absorbs some of the energy and heats up.

As the layer heats up, the ionized helium loses a second electron, becoming doubly ionized—and that means it’s opaque to radiation. Now the energy produced in the core can’t get through. It pushes outward against the ionization layer. The layer is forced to expand.

But as it expands, its pressure decreases, and so does its temperature. The doubly ionized helium gradually gets its electrons back, becoming singly ionized again and therefore transparent to radiation once again. Now that radiation buildup can get through…like water breaking through a dam.

Now there’s no radiation pressure building up below, so the ionization layer contracts under the star’s gravity…until it collapses enough to heat up again and begin the cycle anew.

In this way, the ionization zone acts like a spring, bouncing the star’s outer layers in and out. And it’s important to note that this only happens in the outer layers. The inner layers are way too dense to participate.

But why does this only happen for stars in the instability strip?

Notice that the instability strip corresponds to a specific range of stellar temperatures? Stars hotter than the F spectral class will fall outside of it, and so will stars cooler than the G spectral class. And I’ll show you why that matters…

This chart shows the distance between the ionization layer and the surface of a star in stars of three different temperatures. The star in the middle, with a temperature of 6500 Kelvins, falls right smack dab in the middle of the instability strip. The 5500 K star is too cool and the 7500 K star is too hot.

Notice the blue region labeled He+. That’s the ionization layer we’ve been talking about. See how it’s super low in the coolest star’s atmosphere, much higher in the middle star’s atmosphere, and just a smidge too high in the hottest star’s atmosphere?

That’s the key. All stars have a region of partially ionized helium, but if it’s too deep within a star’s atmosphere, it can’t expand and pulsate under the weight of the layers above. And if it’s too near the surface, there won’t be enough weight above it to compress it. Either way, it won’t work like a spring.

Now here’s something cool about these stars’ pulsation rhythm.

Smaller Cepheid variables have much shorter periods—that is, time between oscillations—than larger Cepheids, just as large bells go “bong” and small bells go “ding.” Smaller things vibrate at a higher frequency than larger things. And we can see this pattern in their luminosities, as well.

Essentially, the H-R diagram correctly predicts that more massive stars are also more luminous. Why? They generally have more surface area, and surface area is the main determinant of luminosity.

The result? The brighter Cepheids have the slowest pulsations, and the fainter Cepheids have the fastest pulsations.

For the past several posts, I’ve described how stars evolve. They’re not unchanging points of light in our night sky. They’re roiling balls of plasma that are surprisingly peaceful due to the hydrostatic equilibrium they maintain, essentially their version of homeostasis. They are born, age over millions and billions of years, and die.

Cepheids are definitive evidence that stars do evolve. If they didn’t, we wouldn’t observe the slight changes in pulsation periods that we do. But the question is…what happens next? How do stars meet their ends?

We’ll begin covering how and why stars die in my next post…and soon enough, we’ll dive into neutron stars, pulsars, and black holes.

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