The discovery of the galaxy

At the start of this century, a surge of observational data generated new tactics for unmasking the layout of the Galaxy. Astronomers photographed a large part of the sky. Such photographs provided a valuable resource for improving upon Herschel's star-count method to map out the shape of the Galaxy.

The Kapteyn Universe In 1901 the Dutch astronomer Jacobus C. Kapteyn (1851-1922) employed statistical and secular parallaxes to find the average distances of stars in the Galaxy. Kapteyn's study provided the distance scale for an outline of the Galaxy given by the star counts. Consequently, the Galaxy attained the grand dimensions of 8000 pc in diameter and 2000 pc in thickness, with the sun within 650 pc of the center. This is smaller than the true dimensions, but much larger than anyone had previously imagined.

Kapteyn did have one worry that later turned out to be important: the absorption of starlight in space. If absorption did occur, distant stars would be so faint that they would not be seen. Kapteyn was right to worry; interstellar dust does absorb starlight. The evidence for interstellar absorption by dust came later than Kapteyn's work and served to reset the boundaries of the Galaxy. In particular, the cutting off of the starlight caused Kapteyn to ascribe to our Galaxy a small, almost heliocentric character, which we now know is wrong. Why did it appear to Kapteyn that the sun was at the center of the Galaxy, when it fact it is far off-center? First of all, the obscuration by interstellar dust prevented Kapteyn from seeing more than a small fraction of the Galaxy. Second, the dust reduced the flux from the distant stars, making them seem fainter than they really are; hence they were judged more distant. Since the amount of dust increases with distance, the discrepancy between true distance and calculated distance also increases with distance. What is in fact a fairly uniform distribution of stars in the neighborhood of the sun appeared to Kapteyn as a distribution decreasing in density in all directions away from the sun.

The Cepheids: A New Distance Indicator A novel technique of surveying the stars came from an unexpected quarter in 1908. While studying variable stars in the Magellanic Clouds-the two large star systems in the southern sky now known to be other galaxies physically connected with our own Galaxy-Henrietta Swan Leavitt (1868-1921) discovered that when the apparent magnitudes of variable stars of a certain type were plotted against their periods, a definite relationship appeared. Somehow the periods of these variables were related to their luminosities: the longer the period, the greater the luminosity.

The next year Hertzsprung pointed out that the variables Leavitt had discovered had light curves a definite relationship appeared similar to that of the star Delta Cephei. A star whose light varies in a regular fashion is known as a periodic variable; Delta distance from the sun, the fact that the apparent Cephei sets the standard for one such class of variables-called cepheid variables or cepheids-distinguished by the special shape of their light curves. [Today we know that there are actually three types of what used to be clumped together as cepheid variable: Type I (classical] cepheids, Type II cepheids (W Virginis stars], and RR Lyrae stars. Type I cepheids are Population I stars, Type II are Population II. RR Lyrae stars, also Population II, are commonly found in globular clusters.] Hertzsprung deduced from Leavitt's data the relationship between the absolute magnitude (or luminosity] of a cepheid variable and its period. This connection is called the period-luminosity relationship. (Note that the relationship is slightly different for Population I and Population II cepheids.] This was a very important discovery, for we can use the relationship to find distances to cepheids. Here's the method.

1. Find a cepheid (identifying it by its light curve].
2. Measure its period (a relatively easy task that does not depend on any knowledge of the star's distance or spectral class].
3. Find the star's luminosity (absolute magnitude] from the period-luminosity relationship.
4. Measure the star's flux (apparent magnitude].
5. Calculate its distance from the inverse-square law.

The period-luminosity relationship played a vital and versatile role in surveying the Galaxy. With detection of only one cepheid, we can find the distance to some object with which the cepheid is associated (assuming no absorption by interstellar dust]. Since using the period-luminosity relationship to determine the distance to cepheids is so important, let's work out one example in detail. Note that only two measurements are needed: the star's average apparent magnitude and its period. This technique assumes that dust does not diminish the light from the cepheid. If it did, the apparent magnitude would be fainter than it actually is, and you would estimate the star and the cluster to be farther away than the actual distance. To get the correct distance, you would have to correct for the extinction, perhaps by measuring the color excess of the stars in the cluster.

Photometric Distances of Star Clusters

Actually, the modern approach is to turn the foregoing technique around, using clusters of known distance to calibrate the luminosity scale for the cepheids. For once we know the distance of any one cluster, we can get the distances to other clusters (including those containing cepheids) by comparing the fluxes from their main-sequence stars and using the inverse square law. Here's the technique. Recall that the H-R diagrams of galactic clusters are similar in that though the young clusters contain luminous main-sequence stars and the old clusters do not, they all have stars on the lower part of the main sequence. Stellar models show that stars of the same composition and mass have the same luminosity and radius (and therefore the same surface temperatures) during their main-sequence stage of core hydrogen burning. Spectroscopic studies indicate that galactic clusters do have pretty much the same chemical composition, so the main-sequence luminosities of all clusters should be the same, for stars of the same temperature. We can use this to find the relative distances of clusters.

Suppose we measure the apparent magnitudes (or fluxes) and color indices (or temperatures) for the stars in two different clusters, and plot an H-R diagram for each. If necessary, we correct the magnitudes and colors for the extinction and reddening by interstellar dust. Then we superimpose the two diagrams so that the main sequences coincide, and read off the average apparent magnitudes corresponding to the same temperatures along the main sequence. The difference in apparent magnitudes tells us the ratio of the distances of the two clusters.

Since this method relies on measurements of the magnitudes (or fluxes) of the stars in the clusters made with a photometer distances determined in this way are referred to as photometric distances.

The Moving Cluster Method for Distance Determination

The photometric technique gives only relative distances of clusters. To get absolute distances in par-sees, we need to find the distance of at least one cluster by some other means. One way is to compare the fluxes of cluster stars with those of nearby main-sequence stars whose distances are known through trigonometric parallax. Another, more accurate, technique involves using the proper motions of the stars in a nearby cluster to determine the change in its angular size of (it really works for only one cluster-the Hyades). The principle is fairly simple.

Shapley Dethrones the Sun In the second decade of this century, Harlow Shapley (1885-1972) proposed a radical idea about the size of the Galaxy and the sun's position in this island of stars. The observational foundation of Shapley's model rested on using the period-luminosity relation of cepheids. His model evicted the sun from its center status in the Galaxy, the second (Copernicus produced the first) significant move of humankind away from special status in the universe.

Shapley worked for his doctorate at Princeton University under Henry Norris Russell, becoming familiar with techniques for observing variable stars. With his new Ph.D., he was offered and accepted a position at Mount Wilson Observatory. During 1914 Shapley published two papers that foreshadowed his work on the size of the Galaxy. One paper dealt with the nature of variable stars, the other with the variable stars in the globular cluster M13 (M13 stands for the thirteenth object listed in a catalog of nonstellar objects put together by Charles Messier in 1781). When Shapley recognized that the variables he observed in globular clusters had the characteristics of cepheids, he adopted the technique of deriving the distance to the cluster by using a calibrated period-luminosity relation.

Here Shapley faced a difficult and crucial problem. Leavitt and Hertzsprung had shown that there was a relationship between the luminosity and period of cepheids, but because the distance of the Magellanic Clouds was unknown at that time, they had not been able to calibrate the relationship in terms of a specific luminosity to be associated with a specific period. How was he to get the calibration? That's difficult, because no cepheid is close enough to the sun to have its heliocentric parallax measured! To overcome this lack, Shapley examined the proper motions of a number of nearby cepheids. He then applied the statistical parallax method to estimate the distance to the cepheids. With this estimate, he could translate apparent magnitudes into absolute magnitudes, hence luminosities, and so calibrate the period-luminosity relation (as has been done for Fig. 23.21).

Then he could use this relation to get the distance of the globular clusters. In the closer globular clusters, he could distinguish what he thought were cepheid variables of the same kind as the ones nearby which he had used for the calibration of the period-luminosity relation. With his calibration, Shapley found these closer clusters to be at a distance about 12,000 pc from the sun. Later he estimated M13 to be 30,000 pc distant. This number was staggering, for it placed the globular clusters outside the boundaries of the Galaxy as mapped by Kapteyn.

It turns out that Shapley made two mistakes in his procedure. First, he was wrong in assuming that the variables in globulars were the same as those in the disk of the Galaxy. They are not; the variables in globulars actually are RR Lyrae stars and W Virginis stars, which have a different period-luminosity relationship. Second, his calibration was off, so he underestimated the luminosities of nearby cepheids by about 4. By coincidence, the first mistake-which overestimated the variables luminosities by 4-just about canceled out the second error. But Shapley also was unaware of another problem that caused him to overestimate the distance to globulars-he ignored interstellar absorption by dust.