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.
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.
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 Herschels 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.
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 timesome quite erratically, others more regularly. Only a small fraction of stars fall into this category, but those that do are of great astronomical significance.
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 discoveredin 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.)
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 HertzsprungRussell diagram known as the instability strip (Figure 14.5). When a stars 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 HR 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 stars (known) luminosity with its (observed) apparent brightness, we can estimate its distance using the inverse-square law. (Sec. 10.2)
How do we infer a variable stars 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 periodluminosity relationship. Cepheids that vary slowlythat is, have long periodshave high luminosities, while short-period Cepheids have low luminosities.
Figure 14.6 illustrates the periodluminosity 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 variables pulsation period immediately tells us its luminositywe 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 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
In a brilliant intellectual leap, Shapley realized that the distribution of globular clusters maps out the true extent of stars in the Milky Way Galaxythe 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 diskthe thin sheet of young stars, gas, and dust that cuts through the center of the halo. Since Shapleys time, astronomers have identified many individual starsthat is, stars not belonging to any globular clusterwithin the Galactic halo.
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.
Can variable stars be used to map out the structure of the Galactic disk?