Cepheid Variable Stars

Background
Absolute magnitude is the intrinsic brightness of a star rather than its observed brightness from Earth. The absolute magnitude of a star is the magnitude it would appear from a standard distance of 10 parsecs (32.5 light-years). What’s a parsec? It’s a unit of distance based on parallax measurements: a parsec is the distance at which a star would exhibit one arc-second of parallax. One arc-second is 1/60 of an arc-minute which is in turn 1/60 degree.

We can measure apparent brightness of a star and still not know how far away the star is. Remember that the farther away a star is, the dimmer it looks. If we had a set of “standard 100 watt light bulbs” scattered around the Universe, we could tell how far away they were by seeing how dim they appeared. The dimmest would be farthest away.

But how do we know if a star is bright because it is close, or bright because it really is a “200 watt star?” Of course stars, like the Sun, are much brighter than 100 watt light bulbs.

Some stars are inherently brighter than others. The inherent brightness of a star is called its absolute brightness (or absolute magnitude). The absolute brightness of a star is what its brightness would be if it was viewed at a standard distance.

Background
Absolute magnitude of a star is the magnitude it would appear from a standard distance of 10 parsecs (32.5 light-years). What’s a parsec? It’s a unit of distance based on parallax measurements: a parsec is the distance at which a star would exhibit one arc-second of parallax. One arc-second is 1/60 of an arc-minute which is in turn 1/60 degree.

In an odd twist of fate, the absolute magnitude of some stars can be known because of how they pulsate in brightness over time. They are called variable stars. 

DIGITAL EFFECT: Constellation Cepheus
Crossfade the scene to be landed back on Earth at 2012/10/01, midnight, when Cepheus is high in the sky. Also turn on a green outline of Cepheus to indicate its location. You may need to adjust the exact date and time if Cepheus is out of view.
For unidirectional theaters, you may rotate the dome 180° to put North in the “front”, and restore the dome to put South in the front.

Crossfade the Cepheus outline with the Cepheus stick figure so as to not hide the stars in Cepheus.

Note:  For unidirectional theaters, optional effects may be used to rotate the dome from South to North to put Cepheus at dome front, and to restore the dome back to its previous setup.

In the early part of this century, astronomer Henrietta Swan Leavitt discovered a characteristic of a very special kind of variable star that has become a crucial “yardstick” for measuring distances to very distant stars. The type of variable star whose behavior she studied is called a Cepheid variable star, because the first one was found in the constellation Cepheus. It is a kind of star that tells us how many watts it puts out.

Point out Cepheus.

Let’s look at two Cepheid variable stars to see how they are special. As an exercise, to make things simpler, let’s say that these two Cepheid variable stars are very nearby, and exactly the same distance away from us. 

DIGITAL EFFECT: Variable A/B On
Show Cepheid variable A and Cepheid variable B, preferably going side by side at Delta Cephei and at Alpha Cephei. Cepheid A should peak at magnitude 1, about the brightness of Vega. A should appear at least twice as bright as B.

Pulse the two variable stars, A & B. A should appear at least twice as slow as B. For example, you may use A = 6 pulses/30 sec (every 5 sec); B=12 pulses/30 sec (every 2.5 sec).

What is the difference between these two Cepheid variable stars?  

[Call the brighter one Cepheid variable A and the dimmer one Cepheid variable B.
The dimmer one is pulsing faster than the other.]

Optional: for Older Students
DIGITAL EFFECT: Variable A Pulse
Pulse Variable A alone. Useful for the audience to get a count of the pulse rate.

Quantitative Measurements of Cepheid Variables
Let’s measure the pulsing rate of Cepheid variable A. Its period is how long it takes to go from maximum brightness to maximum brightness. We are observing the variable star in accelerated time: each second in our planetarium is about 1 day of real time.

Please count silently how many pulses occur while I time 30 days of real time. Ready? Set. Count. Wait until the sixth flash. Stop! How many pulses were there? [6.] If there were six pulses in 30 days, how long did each pulse last?  [5 days.] 

So the period of this Cepheid variable star is 5 days.

Now let’s look at Cepheid variable star B.

Please count how many pulses occur while I again time 30 days of real time. Ready? Set. Count.

DIGITAL EFFECT: Variable B Pulse
Pulse Variable B alone. Useful for the audience to get a count of the pulse rate.

Wait until the twelfth flash. Stop! How many pulses were there?  [12.] If there were ten pulses in 30 days, how long did each pulse last? [2.5 days.]

So the period of this Cepheid variable star is 12 days. As you can see, the period is related to the brightness.

Henrietta Leavitt studied Cepheid variables in a large group of stars that she knew were all about the same distance away. She found that brighter ones always pulse slower than dimmer ones. In fact, by measuring the pulsing rate of a Cepheid variable star, she can accurately gauge its absolute brightness. 

The Cepheid variables that we have been observing so far, we have pretended are very close to us and are all exactly the same distance from us. To see how Cepheid variables act as “standard light bulbs” for us, let’s look at another Cepheid variable. 

DIGITAL EFFECT: Variable C On
Turn on Cepheid variable C at Beta Cephei and begin pulsing immediately. It should pulse as slowly as A did, but between the same brightness levels as B did.

What can you tell about this Cepheid variable? 

[Accept any response.]

Let’s compare it with Cepheid variable A.

DIGITAL EFFECT: A/C Pulse
Show variable stars A and C simultaneously. Should be done after the audience notices A and C appear to have the same rate, though C is dim.

A fascinating fact that is not well known is that the North Star (Polaris) is a Cepheid variable star that changes between magnitudes 2.5 and 2.6 with a period of 4 days.

Fade off the all the variable star dots and the stick figure of Cepheus.

What is similar about them? 

[They have the same period.] 

If they have the same period, how do their absolute brightnesses compare? 

[The absolute brightness must be the same.]

Even though we know their absolute brightness are equal, which one actually looks dimmer to us? [C.] 

So, if their absolute brightnesses are equal, which one must be farther away from us? [C.]

To summarize: by measuring the period of a Cepheid variable star, we can know what its peak absolute brightness is. Then by measuring how much dimmer its peak apparent brightness is, we can figure out how far away it is. This discovery was a major milestone in our understanding of the size of our Universe. Cepheid variables have become our “standard light bulbs.” 

If we see a Cepheid variable star in a cluster of distant stars, we can find the distance to the cluster of stars by figuring out the distance to the Cepheid variable.

Observations of Cepheid variable stars have allowed us to map large sections of the Universe. We now realize that most of the individual stars we see with the naked eye are relatively nearby: within a few hundred light-years. 

Many of these stars probably have systems of planets orbiting them just as the 9 planets in our solar system orbit the Sun. The name of our Sun is Sol, and the system of planets orbiting Sol is called the Solar System. This star is Vega. [Point it out.]

If Vega has a system of planets, what should we call it? (The Vegan System.)

Use light pointer to point out stars all over the sky.

The study of very distant Cepheid variable stars has led to some remarkable findings.
For instance, all of the stars near us are orbiting in a giant mass of stars that we call a galaxy.

Point out Milky Way galaxy. 
If your planetarium does not have a Milky Way projection, ask if anyone has seen the Milky Way and what does it look like.

What looks to us like a beautiful nighttime cloud extending all the way across the sky is really made of millions upon millions of stars. A long time ago, this cloud was named The Milky Way. Now we know that if we could see the Milky Way from a great distance, we would see that it is a galaxy that is a huge pancake-shaped collection of dust, gas clouds and stars. Our Sun is about 2/3 of the way out to the edge of the pancake. Since we are inside the pancake, we are always looking at it edgewise, so it appears as a lovely cloud-like band that stretching all the way across our sky.

Do you think that all the stars in the Milky Way are orbiting around our Sun? 

[No. They orbit the center of the pancake.] 

Cepheid variable stars have been used to help find out how big our Milky Way galaxy really is. Current estimates are that the Milky Way has as many as 400 billion stars spread out over a region of space nearly 100,000 light-years across. (Aren’t you glad we’re using light-years instead of kilometers or miles?) If a star were to blow up on the other side of our galaxy, we wouldn’t know about it for 100,000 years!