Ever since Carl Wirtz and Edwin Hubble in the 1920s discovered that the universe is expanding, astronomers have used Cepheids as the yardstick of choice for measuring how far away galaxies are. Cepheids are one type of variable star. As the term suggests, variable stars change in brightness over time. Astronomers have cataloged over 30,000 variables. In fact most stars, including the Sun, vary if you look closely enough.
Cepheids vary in brightness because they are yellow supergiants. Such stars expand and contract because their gases become unstable as radiation passes through them. Polaris, the North Star, is a good example. Every four days it goes through a complete cycle of brightness variation. The length of the cycle, known as the period, depends on how powerful the star is. By measuring the period, astronomers can work backwards to deduce the power of the star. Then they compare the power to the brightness that they actually see, and calculate how far the star must be in order to appear as bright as it does.
This is how astronomers, using the Hubble Space Telescope and a large ground-based telescope, estimated the so-called Hubble constant that determines how big and old the universe is (see figure 6). The result splashed onto the front pages of major newspapers, namely, that the universe appears to be younger than its contents. This conundrum has yet to be resolved, but astronomers aren't too unhappy because they love a good mystery.
Cepheid variable. These are blow-ups of pictures taken by the Hubble Space Telescope last year. Notice how the star fades in and out. Astronomers were thrilled when Hubble found this star in the spiral galaxy M100, because it allowed them to calculate the distance from Earth to that galaxy. The distance turns out to be 51 million light-years. Photo courtesy of Wendy L. Freeman, Carnegie Institution of Washington, and NASA.
As it happens, variable stars are an area of astronomy where backyard observers are absolutely essential. Variables are so numerous and so unpredictable that only a network of skilled amateurs -- who don't have to worry about reserving telescope time -- can keep track of them. Variable stars are an ideal way to get high-school students doing real science, with real data, from the real sky. They make great lab exercises, science-fair projects, and science-club activities.
The following activity illustrates how to study a variable star. It deals with the granddaddy of them all: Delta Cephei. Students will have to find the star Delta Cephei, watch it change brightness over the course of a month, and plot up their data. Once they get the hang of taking measurements, students need to spend just a few minutes each evening making observations. The activity is best done in groups so that students can share ideas and results with each other -- just as scientists do in practice.
Each student or team will need the following:
During this experiment, some of the stars in Cepheus -- those that don't change in brightness -- will serve as comparison stars. See Figure 7 for a blow-up diagram of the constellation.
Cepheus. On the left is what you actually see in the sky. On the right is a diagram of the official constellation. Delta Cephei, so named because it is the fourth brightest star in Cepheus, is at the bottom left. Students can use the nearby stars to estimate the magnitude of Delta. Photo and diagram courtesy of O. Richard Norton, Science Graphics, Bend, Ore.
2. Locate the star Delta in Cepheus and estimate its brightness
Record the exact time and date in the log book. Then find Delta in the sky and compare it to its two neighboring stars, Zeta and Epsilon. From this, you can estimate the magnitude of Delta.
Magnitude is the astronomers' way of specifying brightness: the brighter the star, the smaller the magnitude. Zeta has a magnitude of 3.4 and Epsilon has a magnitude of 4.2. Delta varies from being slightly brighter than Zeta to slightly fainter than Epsilon. If Delta appears very slightly fainter than Zeta, its magnitude would be 3.7. If it were intermediate in brightness between Zeta and Epsilon, its magnitude would be 3.9. And so on.
The other stars in the constellation can also help as references. Gamma or Beta are magnitude 3.2, which makes them a tad brighter than Zeta. Pi, with a magnitude of 4.4, is a smidgen dimmer than Epsilon.
In our experience, students can estimate the brightness to within 0.2 magnitude. It helps to practice identifying and measuring Delta Cephei and the comparison stars on a 35 mm slide of the constellation. An excellent set of constellation slides is available from the ASP catalog or from Science Graphics in Bend, Ore.
If you like, you can convert the time to the standard system used by astronomers, Universal Time, also known as Greenwich Mean Time. If you are on Daylight Saving Time, subtract one hour to get Standard Time. Then convert this to Universal Time by adding 4, 5, 6, 7, or 8 hours, depending on whether you live in the Atlantic, Eastern, Central, Mountain, or Pacific time zone. If you live elsewhere in the world, consult the telephone directory or newspaper for instructions on how to convert to Universal Time. If the conversion takes you past midnight, you have to advance the date by one day. For example, Nov. 1 at 8 p.m. EST is Nov. 2 at 1 a.m. UT. Finally, for the highest accuracy, you could express the data in terms of fractional days; that is, Oct. 1 at 9 p.m. is Oct. 1.875.
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