14.2 Measuring the Milky Way

Before the twentieth century, astronomers’ conception of the cosmos differed markedly from the modern view. The growth in our knowledge of our Galaxy, as well as the realization that there are many other distant galaxies similar to our own, has gone hand in hand with the development of the cosmic distance scale.

Star Counts

In the late eighteenth century, long before the distances to any stars were known, the English astronomer William Herschel tried to estimate the size and shape of our Galaxy simply by counting how many stars he could see in different directions in the sky. Assuming that all stars were of about equal brightness, he concluded that the Galaxy was a somewhat flattened, roughly disk-shaped collection of stars lying in the plane of the Milky Way, with the Sun at its center (Figure 14.3). Subsequent refinements to this approach led to essentially the same picture. Early in the twentieth century, some workers went so far as to estimate the dimensions of this “Galaxy” as about 10 kpc in diameter by 2 kpc thick.

Figure 14.3 Early Galaxy Model Eighteenth-century English astronomer William Herschel constructed this "map" of the Galaxy by counting the numbers of stars he saw in different directions in the sky. He assumed that all stars were of roughly equal luminosity and, within the confines of the Galaxy, were uniformly distributed in space. Our Sun (marked by the large yellow dot) appears to lie near the center of the distribution, and the long axis of the diagram lies in the plane of the Galactic disk.

In fact, the Milky Way Galaxy is several tens of kiloparsecs across, and the Sun lies far from the center. The flaw in the above reasoning is that the observations were made in the visible part of the electromagnetic spectrum, and astronomers failed to take into account the (then unknown) absorption of visible light by interstellar gas and dust. (Sec. 11.1) Only in the 1930s did astronomers begin to realize the true extent and importance of the interstellar medium.

The apparent falloff in the density of stars with distance in the plane of the Milky Way is not a real thinning of their numbers in space, but simply a consequence of the murky environment in the Galactic disk. Objects in the disk lying more than a few kiloparsecs away are hidden from our view by the effects of interstellar absorption. The long “fingers” in Herschel’s map are directions where the obscuration happens to be a little less severe than in others. However, perpendicular to the disk, where there is less obscuring gas and dust along the line of sight, the falloff is real.

Observations of Variable Stars

While astronomers’ attempts to probe the Galactic disk by optical means are frustrated by the effects of the interstellar medium, stars are visible to much greater distances in directions out of the Milky Way plane. An important by-product of the laborious effort to catalog stars around the turn of the twentieth century was the systematic study of variable stars. These are stars whose luminosity changes with time—some quite erratically, others more regularly. Only a small fraction of stars fall into this category, but those that do are of great astronomical significance.

Figure 14.4 Variable Stars (a) Light curve of the pulsating variable star RR Lyrae. All RR Lyrae-type variables have essentially similar light curves, with periods of less than a day. (b) The light curve of a Cepheid variable star called WW Cygni. (c) This Cepheid is shown here (boxed) on successive nights, near its maximum and minimum brightness; two photos, one from each night, were superposed and then slightly displaced. (Harvard College Observatory)

We have encountered several examples of variable stars in earlier chapters. Often, the variability is the result of membership in a binary system. Eclipsing binaries and novae are cases in point. However, sometimes the variability is an intrinsic property of the star itself, and is not dependent on its being a part of a binary. Particularly important to Galactic astronomy are the pulsating variable stars,1 which vary cyclically in luminosity in very characteristic ways. Two types of pulsating variable stars that have played central roles in revealing both the true extent of our Galaxy and the distances to our galactic neighbors are the RR Lyrae and Cepheid variables. (Following long-standing astronomical practice, the names come from the first star of each class to be discovered—in this case the variable star labeled RR in the constellation Lyra and the variable star Delta Cephei, the fourth brightest star in the constellation Cepheus.)

Figure 14.5 Variable Stars on H–R Diagram Pulsating variable stars are found in the instability strip of the H–R diagram. As a high-mass star evolves through the strip, it becomes a Cepheid variable. Low-mass horizontal-branch stars in the instability strip are RR Lyrae variables.
RR Lyrae and Cepheid variable stars are recognizable by the characteristic shapes of their light curves. RR Lyrae stars all pulsate in essentially similar ways (Figure 14.4a), with only small differences in period between one RR Lyrae variable and another. Observed periods range from about 0.5 to 1 day. Cepheid variables also pulsate in distinctive ways (the regular “sawtooth” pattern in Figure 14.4b), but different Cepheids can have very different pulsation periods, ranging from about 1 to 100 days. In either case, the stars can be recognized and identified just by observing the variations in the light they emit.

Pulsating variable stars are normal stars experiencing a brief period of instability as a natural part of stellar evolution. The conditions necessary to cause pulsations are not found in main-sequence stars. They occur in post-main-sequence stars as they evolve through a region of the Hertzsprung–Russell diagram known as the instability strip (Figure 14.5). When a star’s temperature and luminosity place it in this strip, the star becomes internally unstable, and both its temperature and its radius vary in a regular way, causing the pulsations we observe. As the star brightens, its surface becomes hotter and its radius shrinks; as its luminosity decreases, the star expands and cools. Cepheid variables are high-mass stars evolving across the upper part of the H–R diagram. (Sec. 12.4) The less luminous RR Lyrae variables are lower-mass horizontal-branch stars that happen to lie within the lower portion of the instability strip. (Sec. 12.3)

A New Yardstick

Astronomers can use pulsating variables as a means of determining distances, both within our own Galaxy and far beyond. Once we recognize a star as being of the RR Lyrae or Cepheid type, we can infer its luminosity. Then, by comparing the star’s (known) luminosity with its (observed) apparent brightness, we can estimate its distance using the inverse-square law. (Sec. 10.2)
Figure 14.6 Period–Luminosity Plot A plot of pulsation period versus average absolute brightness (that is, luminosity) for a group of Cepheid variable stars. The two properties are quite tightly correlated. The pulsation periods of some RR Lyrae variables are also shown.

How do we infer a variable star’s luminosity? For RR Lyrae variables, this is simple. All such stars have basically the same luminosity (averaged over a complete pulsation cycle)—about 100 times that of the Sun. For Cepheids, we make use of a close correlation between average luminosity and pulsation period, discovered in 1908 by Henrietta Leavitt of Harvard University and known simply as the period–luminosity relationship. Cepheids that vary slowly—that is, have long periods—have high luminosities, while short-period Cepheids have low luminosities.

Figure 14.6 illustrates the period–luminosity relationship for Cepheids found within a thousand parsecs or so of Earth. Astronomers can plot such a diagram for relatively nearby stars because they can measure their distances, and hence their luminosities, using stellar or spectroscopic parallax. Thus, a simple measurement of a Cepheid variable’s pulsation period immediately tells us its luminosity—we just read it off the graph in Figure 14.6. (The roughly constant luminosities of the RR Lyrae variables are also indicated in the figure.)

Figure 14.7 Variable Stars on Distance Ladder Application of the period–luminosity relationship for Cepheid variable stars allows us to determine distances out to about 15 Mpc with reasonable accuracy.
This distance-measurement technique works well provided the variable star can be clearly identified and its pulsation period measured. With Cepheids, this method allows astronomers to estimate distances out to about 15 million parsecs, more than enough to take us to the nearest galaxies. Indeed, the existence of galaxies beyond our own was first established in the late 1920s, when American astronomer Edwin Hubble observed Cepheids in the Andromeda Galaxy and thereby succeeded in measuring its distance. The less luminous RR Lyrae stars are not as easily detectable as Cepheids, so their usable range is not as great. However, they are much more common, so, within limited range, they are actually more useful than Cepheids.

Figure 14.7 extends our cosmic distance ladder, begun in Chapter 1 with radar ranging in the solar system and expanded in Chapter 10 to include stellar and spectroscopic parallax, by adding variable stars as a fourth method of determining distance.

The Size and Shape of Our Galaxy

Figure 14.8 Globular Cluster Map Our Sun does not coincide with the center of the very large collection of globular clusters. Instead, more globular clusters are found in one direction than in any other. The Sun resides closer to the edge of the collection, which measures roughly 30 kpc across. We now know that the globular clusters outline the true distribution of stars in the Galactic halo.
Many RR Lyrae variables are found in globular clusters, those tightly bound swarms of old, reddish stars we first met in Chapter 11. (Sec. 11.5) Early in the twentieth century, the American astronomer Harlow Shapley used observations of RR Lyrae stars to make two very important discoveries about the Galactic globular cluster system. First, he showed that most globular clusters reside at great distances—many thousands of parsecs—from the Sun. Second, by measuring the direction and distance of each cluster, he was able to determine their three-dimensional distribution in space (Figure 14.8). In this way, Shapley demonstrated that the globular clusters map out a truly gigantic, and roughly spherical, volume of space, about 30 kpc across.2 However, the center of the distribution lies nowhere near our Sun. It is located nearly 8 kpc away from us, in the direction of the constellation Sagittarius.

In a brilliant intellectual leap, Shapley realized that the distribution of globular clusters maps out the true extent of stars in the Milky Way Galaxy—the region that we now call the Galactic halo. The hub of this vast collection of matter, 8 kpc from the Sun, is the Galactic center. As illustrated in Figure 14.9, we live in the suburbs of this huge ensemble, in the Galactic disk—the thin sheet of young stars, gas, and dust that cuts through the center of the halo. Since Shapley’s time, astronomers have identified many individual stars—that is, stars not belonging to any globular cluster—within the Galactic halo.

Figure 14.9 Stellar Populations in Our Galaxy Artist’s conception of a (nearly) edge-on view of the Milky Way Galaxy, showing the distributions of young blue stars, open clusters, old red stars, and globular clusters.
Shapley’s bold interpretation of the globular clusters as defining the overall distribution of stars in our Galaxy was an enormous step forward in human understanding of our place in the universe. Five hundred years ago, Earth was considered the center of all things. Copernicus argued otherwise, demoting our planet to an undistinguished place removed from the center of the solar system. In Shapley’s time, the prevailing view was that our Sun was the center not only of the Galaxy but also of the universe. Shapley showed otherwise. With his observations of globular clusters, he simultaneously increased the size of our Galaxy by almost a factor of 10 over earlier estimates and banished our parent Sun to its periphery, virtually overnight!

1Note that these stars have nothing whatsoever to do with pulsars.

2The Galactic globular cluster system and the Galactic halo of which it is a part are somewhat flattened in the direction perpendicular to the disk, but the degree of flattened is uncertain. The halo is certainly much less flattened than the disk, however.

Concept Check

Can variable stars be used to map out the structure of the Galactic disk?