What is needed to chart the distribution of stars in space? Clearly the directions to the stars, but one also needs to know their distances. Then one can define the outline of the Milky Way. But astronomers have to be satisfied with much less. As Herschel found, one can never see all the stars; some are definitely too dim even for modern telescopes. Moreover, it is impossible to measure the distances to all stars. There were very few parallax (that is, distance) measurements in the nineteenth century, and even today we are limited to our local neighborhood in the Milky Way. Only when the space telescope Gaia of the European Space Agency (ESA) is launched in the next decade will we start to get distances to a representative sample over the disk of our Milky Way. Gaia's goal is to make the largest, most precise map of the Milky Way by surveying an unprecedented number of stars - more than a billion.1
A much easier task than the distance measurement is the measurement of the brightness, or magnitude, of a star (Chap. 8). It gives some indication about the distance. In the nineteenth century the estimation of magnitudes became a routine operation, and they were included in great star catalogs. The most famous one is Bonner Durchmusterung (The Bonn General Survey). It was compiled by Friedrich Arge-lander (1799-1875) and his associates. After working in the Turku and Helsinki observatories in Finland, Argelander became director of the Bonn observatory in 1836. While in Bonn, he studied all stars brighter than magnitude 9.5, determined their coordinates in the sky, and measured their magnitudes. The Survey was completed in 1859 and it contained 324,000 stars. This huge catalog has been useful up to recent times in the study of the Milky Way.
The German astronomer Hugo von Seeliger (1849-1924) developed Herschel's star count method further. He realized that it is better to study the change in the number counts of stars going to successively dimmer stars, rather than the total count number. The great star catalogs had exactly the right kind of material for this line of research.
What can the change in the star counts tell us? Let us make the assumption that all stars are equally bright, and consider looking at a uniform spherical star system from its center. We would find that there should be four times as many stars of magnitude 7 than of stars of magnitude 6. The same difference would apply to any increase of magnitude by one unit. This follows simply from the way the magnitude scale has been defined, together with the decrease of brightness and increase of available space with increasing distance. However, when we meet the stars at the edge of the system, the number count at the next magnitude level suddenly drops to zero. By finding the magnitude after which the counts drop suddenly, we can identify the edge of the system.
In studies like this, von Seeliger found in 1884-1909 that the successive number count ratio is not 4, but more like 3. Thus the star density is not uniform around us, but seems to decrease with distance. At the faintest magnitudes the number counts dropped even below 3. He concluded these faint stars are close to the edge of the system. He found that the overall shape of the Milky Way is much like what Herschel had found previously.
The first proper model of the Milky Way, including the distance scale, was constructed by the Dutch astronomer Jacobus C. Kapteyn (1851-1922). He was elected to the professorship of astronomy at Groningen University at the age of 27. After arriving there, he found that the university did not have an observatory. This lack redirected his efforts to the study of catalogs compiled by others. He also became a spokesman for international collaboration.
1 Gaia will be placed in an orbit around the Sun, at a distance of 1.5 million km further out than Earth. This special location ("L2") will keep pace with the orbit of the Earth; Gaia will map the stars from there. Its predecessor Hipparcos exceeded all expectations and cataloged more than 100,000 stars to high precision.
Kapteyn wanted to determine the structure of the Milky Way. Its shape was already known, but what about the scale? How far is the edge of the Milky Way that shows up in star counts? From the star counts astronomers had already identified a faint star at Milky Way's edge. If this star were as bright as the Sun, we could calculate its distance and thus determine the system size. But stars are not of equal brightness. Kapteyn studied nearby space and determined how the star brightness is distributed. For this, distances are needed. The parallax method was inadequate and Kapteyn used proper motions.
The distance of a star is revealed from the direction and the rate it moves across the sky, its proper motion (Chap. 8). These motions arise, not only from the stars' true space motions, but from the reflection of Sun's motion in space as well. Imagine driving at night through a snowstorm with snowflakes representing stars. Ahead of you, the flakes appear as dots as they come straight toward you with zero "proper motion." A similar view is seen through the rear window. However, to the sides, one sees streaks as the nearby flakes appear to move backward showing significant "proper motion."2
Today we know that the Sun moves at 20 km/s relative to nearby stars toward the constellation of Hercules. As discussed in our snowstorm example, depending on the size of the proper motion and the angle from the direction of the Sun's motion, we can estimate how far a star is from us. The tinier the motion appears, the greater is the distance likely to be. By using an ingenious analysis, Kapteyn derived statistical distance values and the brightness distribution of stars. Then he could derive the distance scale of the Milky Way. According to Kapteyn, the Milky Way is a disk with a diameter of 50,000 light years where the star density diminishes toward the edges (Fig. 20.5).
The problem with this model was that the Sun was only 2,000 light years from the center of the Milky Way, which seemed suspicious. As Kapteyn wrote himself in 1909:
This would place the Sun at a very exceptional position in the stellar system, i.e. where the stars are at their densest. - On the other hand, if we suppose that the decrease in density is only apparent and is caused by absorption of light, then the apparent decrease in density in all directions is perfectly natural.
Kapteyn realized that if space is not transparent, but filled with some medium that dims the light enough, then the star counts can give an incorrect picture of the Milky Way - what appears as the edge is the effect of absorbing dust. He studied the possibility of absorption in space by various methods, but was unable to prove its existence. Thus his model was for years the dominant view of the Milky Way. A change began in 1918 when Harlow Shapley studied the distribution of globular star clusters in space, much less affected by absorption. He concluded that the Milky Way is much bigger than the "Kapteyn universe" and that the Sun is situated 50,000 light years from its center. To see how Shapley came to his radical conclusion, we now discuss a new way of estimating distances using variable stars.
2 William Herschel estimated which way the Sun moves among other stars by looking at proper motions of just 13 stars. The first precise solar motion study, by Argelander, relied on 560 stars observed at Turku, Finland.
b 50 000 light years = 16000 parsecs
Fig. 20.5 (a) Jacobus C. Kapteyn studied the Milky Way using star counts. (b) "Kapteyn's universe" was the first model of the Milky Way with a distance scale. The Sun appeared to be almost at the center of the system
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