Stellar distances and motions

Kapteyn found the years around the turn of the twentieth century, when he was in his fifties, to be among his busiest and most productive. In 1900, he began publishing regular updates on his laboratory's findings—often in English, which he expected would become astronomy's lingua franca. In 1901, he had the satisfaction of witnessing the graduation of his first doctoral student, Willem de Sitter. (De Sitter later became famous for applying Einstein's theory of general relativity to the question of the evolution of the universe—see chapter 9.)

Kapteyn's own children, meanwhile, were making their way in the world. He had sent both his daughters and his son to a boy's school, and his daughters helped set a precedent for women by studying medicine and law at university.

In his scientific work, Kapteyn stuck to ''the grinding of huge masses of fact,'' while trying not to forget the larger questions that had drawn him into the effort in the first place. He doggedly pursued clues to the precise distances and distributions of stars, even as many of his contemporaries jumped ahead to the next step and advanced hypotheses about the nature of the stellar system based on scanty information or tentative analogies.

During this period, his peers argued both for and against the island universe hypothesis. The historian of astronomy Agnes Clerke represented a popular if not majority view when she wrote in 1886 that the Milky Way system was so vast, as astronomers had learned from parallax measurements, that the idea of ''island universes'' on a comparable scale to ours was untenable. But Julius Scheiner cast doubt on this view in 1898 when his longexposure photograph of the Andromeda nebula's spectrum (the spectrum that eluded William and Margaret Huggins' attempt to photograph it) emerged as decidedly star-like, suggesting that this could be an ''island universe.'' Shortly after the turn of the century, the Dutch science writer Cornelis Easton suggested our stellar system might look like a spiral system, similar to the spirals discovered by Lord Rosse, if we could see it from afar — but he based his prescient opinion on speculation rather than on observational clues. In short, the situation was confused, and called for more data.

Kapteyn needed to probe the greatest possible distances and the greatest number of distances to determine the structure of the stellar system. Initially, he naturally assumed he would proceed by accumulating the parallaxes of individual stars. The measurement of parallaxes was something of a growth industry in astronomy near the turn of the century: in 1882, only 34 parallaxes were in hand, while by 1914, thanks to the efforts of Kapteyn and other astronomers around the world, some 100 000 had been measured. But even this growth in the accumulation of parallax data was not enough for the man who would solve the ''sidereal problem.''

Kapteyn turned his attention to stars' proper motions. Astronomers had built up a database of many stars with measurable proper motion, i.e., a shift in position due to their real motion through space. Sometimes a given star had both its parallax and proper motion measured, as was the case for 61 Cygni, the fast-moving binary system Bessel had found success with. Kapteyn's main effort around the turn of the century was to try to use this relatively abundant proper motion data to lead him to more information about stellar distances. He attempted to correlate stars' proper motions with their parallaxes, so that, for stars for which only proper motion was known, he could derive some estimate of their parallax distances.

His reasoning was basically like that of Piazzi, the astronomer who first suggested 61 Cygni might be nearby, and a good candidate for parallax measurements, because of its high proper motion (see chapter 5). Assume that the stars, scattered about in space, have random motions in all directions. In that case, a sample of relatively nearby stars will have a higher average proper motion than will a group of distant stars. In the same way, a car moving past our window at 40 miles per hour on a street running by our house will have a higher proper motion than a car traveling 40 miles per hour on a distant street that we can just see on the horizon. The nearer car covers a greater angle in space in a given unit of time, so that, all other things being equal, the nearer car has a higher proper motion (see figure 7.2).

The argument does not apply to individual stars, because we have assumed that they might have any randomly given velocity. A distant star could, by chance, have a higher velocity and demonstrate the same proper motion as a nearer, slower star. However, the average proper motion of a sample of stars will tend to accurately reflect the distance of stars in the sample. Thus Kapteyn applied statistical methods — he used average values for subsets of the entire population of stars to gain insight into the overall pattern of their distribution and characteristics.

Working with his brother Willem at the University of Utrecht, Kapteyn compared the proper motions and parallaxes of stars for which both quantities were measured, and found a formula relating them. Then, for a star whose proper motion only was known, he could compute what he called the ''mean parallax'' — the parallax or distance he thought it should have, according to the formula.

Figure 7.2 Mean parallax — a tool to estimate distances. The center of the diagram shows the position of an observer; encompassing circles divide the stars into three distance zones. If the velocities of the stars are random, an observer would measure a higher average velocity for stars in the inner circle, which are closer and which therefore appear to move faster than stars at greater distances. This establishes a connection between a star's typical distance (or mean parallax) and its average velocity; subsequently, if an observer acquires data about a given star's velocity, he can assign to it a distance, based on the distance-velocity relation. (Credit: Layne Lundstrom.)

Figure 7.2 Mean parallax — a tool to estimate distances. The center of the diagram shows the position of an observer; encompassing circles divide the stars into three distance zones. If the velocities of the stars are random, an observer would measure a higher average velocity for stars in the inner circle, which are closer and which therefore appear to move faster than stars at greater distances. This establishes a connection between a star's typical distance (or mean parallax) and its average velocity; subsequently, if an observer acquires data about a given star's velocity, he can assign to it a distance, based on the distance-velocity relation. (Credit: Layne Lundstrom.)

This ''mean parallax'' tool was one of the ways by which Kapteyn studied the distribution of stars in space. Through its use he could in principle measure distances to about 1500-3000 light-years, while the technique of parallax (trigonometric parallax) was limited to about 300 light-years. Kapteyn no doubt expected that his mean parallax analysis would push back the limits of the known universe as it could be probed with any degree of accuracy, adding more distant stars to the sample of well-studied objects. To his surprise, however, his first results concerned not stellar distances but the organization of stars on a grand scale.

Kapteyn thought he was proceeding with all due caution in probing the parallax-proper motion relationship. In fact, he introduced refinements such as calculating separate formulas for stars of different colors, or spectral types. The key assumption he made, that stars' velocities are random, would have passed muster with any of his peers. And yet in 1902, he came to the conclusion that something was wrong with his study, or that the universe was not what he and his fellow astronomers had imagined. His results suggested that, contrary to all expectations, the motions of the stars are not random. Kapteyn was in the habit of visualizing his data by plotting points or drawing vectors with white chalk on globes covered with blackboard-material, and when he did this with the velocities of the stars in his study, he saw a distinct pattern emerging on the celestial sphere.

Today we understand that the phenomenon he uncovered is explained (in a rather complicated way) by the rotation of our galaxy. To Kapteyn, the results simply suggested that there was some large-scale systematic motion of the stars. It was a bizarre but possibly very significant conclusion, he knew.

Kapteyn waited until 1904 to present and explain his findings to the astronomical community and to the public. He was waiting for the publication of more extensive data that he might use to verify his results—data that he believed had already been acquired at some American observatories, but was not yet made available. But in 1904, he decided to go ahead and present his results as they stood. That year he received an invitation to lecture at an astronomers' convention that his American friend Simon Newcomb planned for September, in conjunction with the World Exhibition or World's Fair in St. Louis, Missouri.

Kapteyn was about to make a big splash in a country that had lagged behind in astronomical clout, but was rapidly catching up to Europe. American observatories made a rather belated emergence on the international scene. In 1825, President John Quincy Adams bemoaned the lack of observatories in his country. ''It is with no feeling of pride, as an American, that the remark may be made, that, on the comparatively small territorial surface of Europe, there are existing upward of one hundred and thirty of these light houses of the skies; while throughout the whole

American hemisphere, there is not one,'' he told Congress. ''If we reflect a moment upon the discoveries, which, in the last four centuries, have been made in the physical constitution of the universe, by means of these buildings, and of observers stationed in them, shall we doubt of their usefulness to every nation?''16

By the time Kapteyn made his first visit to the United States in 1904, however, stops at several astronomical observatories were de rigeur for someone of his stature. The first to achieve some measure of prominence, as mentioned earlier, was the Harvard College Observatory. Pickering assumed the directorship in 1876, and made it his life's mission to expand on the promise of spectroscopy. With funds from Henry Draper's estate—the endowment that so frightened William Huggins, because it threatened to put him out of business—Pickering established Harvard as a center for the analysis of photographic stellar spectra.

Two other major American observatories made their mark before the turn of the twentieth century. In 1888, Lick Observatory unveiled the largest lens-based or refracting telescope of its time, 36 inches in diameter, atop Mount Hamilton near San Jose, California. Lick observatory was and is operated by the University of California. Yerkes Observatory, on the shores of Lake Michigan, operated by the University of Chicago, opened in 1897. Its 40-inch diameter refracting telescope improved on Lick's.

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