4. DISTANCES:

Measuring the distances of galaxies is one of the most challenging problems of astronomy. We have already discussed this problem in Lesson 8 in the context of measuring the size of the Milky Way. In the Milky Way, we can measure distances to about 1000 parsecs by measuring stellar parallaxes (see Lesson 4). But, to measure distances beyond 1000 parsecs, astronomers must rely mainly on the inverse square law of light. I repeat the idea here, since it is so important. If absorption by intervening dust clouds can be neglected, the brightness (B), is related to luminosity (L) and distance (D) by the inverse square law:

B = L/(4p D²)

Thus, if we knew the luminosity, L, of a star (or any other astronomical source) and we measured its brightness, B, we could solve this equation to determine its distance, D. The problem is: how can we know L? It turns out that there are certain types of sources for which we can infer L from some other observed property. We call these sources standard candles.

We have already discussed two examples of this method. The first is "main sequence fitting" (see Lesson 4). If we know that a star is a main sequence star, we can infer its luminosity from its spectral type (surface temperature). Astronomers use this method to measure distances in the Milky Way and the distances of the nearest galaxies -- out to a distance of about 200,000 light years. But beyond that, astronomers can only see the most luminous red and blue giants, and such stars are not likely to be main sequence stars.

Fortunately, nature has provided a more luminous kind of standard candle: Cepheid variable stars, which are a second type of standard candle. Cepheid variables are not main sequence stars -- they are probably helium core-burning stars. But they pulsate regularly, and their luminosities are related to their pulsation periods by the famous period-luminosity relationship, originally discovered by Henreitta Leavitt. We can infer the luminosities of such stars by measuring their pulsation periods (see Lesson 8). With the Hubble Space Telescope we can observe Cepheid variables in galaxies at distances of about 100 million light years.

Beyond 100 million light years, Cepheid variables are too faint to observe, even with the Hubble Space Telescope. But again, nature has kindly provided a luminous source that appears to be a reliable standard candle: Thermonuclear supernovae (also called Type Ia supernovae -- see Lesson 6). A few years ago, astronomers discovered that the maximum luminosity of a Thermonuclear supernova is correlated with the rate at which its light dims: the slower the dimming rate, the more luminous the supernova is at maximum (see below). So, if astronomers can find a supernova in time to observe its maximum brightness, observe its spectrum (to make sure it is Type Ia), and watch its decay rate, they know its maximum luminosity. Then they can use the inverse square law to infer the distance of the galaxy to which it belongs.

Two modern developments in astronomical instrumentation have made it possible for astronomers to do this. One is the development of wide-field CCD cameras on large ground-based telescopes. With such cameras, astronomers can obtain images of an area of sky containing thousands of galaxies. Comparing such images of the same region of the sky, taken a week or so apart, they can find a dozen or so supernovae. Then, with very large telescopes such as the Keck telescope (the second development), they can obtain spectra of all of these supernovae and identify those of Type Ia.

At maximum light, thermonuclear supernovae are so luminous that they can be seen at distances of 10 billion light years or more -- almost to the edge of the observable universe. They appear to be the most accurate standard candles by which we can map the distant universe. Because this technique is so promising, two international teams of astronomers (the High-Z Supernova Search Team and the Supernova Cosmology Project) are devoting a considerable fraction of observing time on the world's largest telescopes to observing them. Some of the results are described here: Hubble Pinpoints Distant Supernovae.

Only a few years ago, the distances to distant galaxies were uncertain to about a factor of 2 (e.g., we could only say that a certain galaxy must be at a distance between 1.5 and 3 billion light years). But with the techniques described above, enabled by the Hubble Space Telescope and large ground-based telescopes, we can determine the distance of a galaxy with an error of about +/- 15% (e.g., between 1.7 and 2.3 billion light years). That's a big improvement.

It's important to realize that the yardsticks by which we determine cosmic distance all depend on each other. For example, the period-luminosity relationship of the Cepheid variable stars must be calibrated by observing Cepheid variables in nearby galaxies (such as the Large Magellanic Cloud), whose distance can be determined by main sequence fitting. Likewise, the maximum luminosities of Type Ia supernovae must be calibrated by observing such supernovae in galaxies whose distances can be determined by observing Cepheid variables in them -- see Measuring the Expansion Rate of the Universe. Each of the techniques by which we develop reliable yardsticks to measure cosmic distances is a step on the cosmic distance ladder.

I have described four steps to measure cosmic distances: (1) parallax; (2) main sequence fitting; (3) Cepheid variable stars; (4) Type Ia supernovae. There are several other techniques for inferring cosmic distances, some fairly good and others rather unreliable and outdated. Another good method is (5) the "Tully-Fisher relation" -- by which astronomers can infer the luminosities of spiral galaxies from their rotation speeds. With redundant techniques, astronomers can cross check the various techniques against each other to see which ones are most accurate and reliable. That's important, because the uncertainty in the cosmic distance scale depends on the accumulated uncertainties from every step in the ladder. Prof. Ned Wright of UCLA gives a complete summary of all the methods to measure cosmic distances in The ABC's of Distances. You don't need to know all these methods, but you may wish to review the four that I have described above.

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Last modified March 30, 2002
Copyright by Richard McCray