Later years the Kapteyn universe

After Kapteyn's retirement from the University of Groningen in 1920, he took a part-time position at the University of Leiden, where he had carried out some research during the dismal early days of his career at Groningen, and where his former student de Sitter was director of the observatory. As a favor to de Sitter, Kapteyn filled a post in positional astronomy until university officials could find a permanent replacement. His bimonthly trips to Leiden allowed him to visit with Henrietta, Hertzsprung, and granddaughter Rigel, as Hertzsprung became a professor there in 1921. Henrietta's marriage to Hertzsprung dissolved in 1922, however.

Kapteyn devoted a large part of his energy at this time to his own final big project, a synthesis of all his research into the distribution of stars. He collaborated with Pieter van Rhijn at Groningen, his former student. Together they assembled the data from the Plan of Selected Areas on star counts and luminosities, and analyzed them with the assumption that space is free of any absorbing material. Their first paper on the subject appeared in 1920.

Kapteyn and van Rhijn were able to derive the density of stars—the number of stars per volume of space—as a function of distance from the middle of the plane. Within the plane of the Milky Way, they found that the density of stars decreased with distance. Around the Sun, the density is about one star per 300 cubic light-years. Their data implied that, at 2000 light-years from the Sun, the density decreased to 60 percent that of the solar neighborhood, or one star per 500 cubic light-years. Beyond that, their results were less certain, but an extrapolation of the density function indicated that the density fell to 1 percent of the solar neighborhood density, or about 1 star per 30 000 cubic light-years, at a distance of 30 000 light-years. They concluded

Figure 7.6 The ''Kapteyn Universe.'' Top panel: 1920 model of the distribution of stars in our galaxy, derived by Kapteyn and his student van Rhijn from an analysis of star-counts. The system is assumed to be symmetric, so only the ''top half'' of the galaxy is shown. The line AB represents the plane of the Milky Way. The Sun is at S, the center of the system. Distances are given along the x axis in parsecs; 1 parsec is equivalent to 3.26 light-years. The lines represent contours of equal density. Bottom panel: 1922 version of the ''Kapteyn Universe.'' Kapteyn no longer placed the Sun at the center of the system, but at a distance of 650 parsecs or about 2000 light-years. (In fact, the Sun is some 26 000 light-years from the center of the galaxy; Kapteyn was misled by assuming that interstellar absorption of light was not significant.) Kapteyn's universe is about five times as wide as it is thick, and includes about 50 billion stars. (Credit: Adapted from the originals in Astrophysical Journal 1920, 52, 23 and 1922, 55, 302.)

Figure 7.6 The ''Kapteyn Universe.'' Top panel: 1920 model of the distribution of stars in our galaxy, derived by Kapteyn and his student van Rhijn from an analysis of star-counts. The system is assumed to be symmetric, so only the ''top half'' of the galaxy is shown. The line AB represents the plane of the Milky Way. The Sun is at S, the center of the system. Distances are given along the x axis in parsecs; 1 parsec is equivalent to 3.26 light-years. The lines represent contours of equal density. Bottom panel: 1922 version of the ''Kapteyn Universe.'' Kapteyn no longer placed the Sun at the center of the system, but at a distance of 650 parsecs or about 2000 light-years. (In fact, the Sun is some 26 000 light-years from the center of the galaxy; Kapteyn was misled by assuming that interstellar absorption of light was not significant.) Kapteyn's universe is about five times as wide as it is thick, and includes about 50 billion stars. (Credit: Adapted from the originals in Astrophysical Journal 1920, 52, 23 and 1922, 55, 302.)

that the boundary of the disk of the Milky Way lay at about 60 000 light-years; perpendicular to this plane, the Milky Way extended only about 8000 light-years. The system as a whole, they estimated, included some 50 billion stars.

Kapteyn and van Rhijn illustrated the density function graphically using a contour plot (see figure 7.6, top panel). The Sun occupied the central position. Ellipse-shaped curves around the Sun indicated lines of constant density, rather like lines of constant altitude on a topographic map.

This 1920 model was static—it did not incorporate the information Kapteyn himself had gleaned on star-streaming. In 1921, then 70 years old and in failing health, he summoned the last of his strength to revise his ''Kapteyn Universe'' to remedy this flaw. His academic duties were finally at an end, and he looked forward to a restful retirement. Still, Henrietta wrote, ''An important new theory based on the results of his work of the last few years so enthralled him and kept him so busy that his books and papers accompanied him on his vacation to Switzerland.''26

Kapteyn called his last effort, ''a first attempt at the theory of the arrangement and motion'' of the stellar system. He considered that the star-streaming phenomenon might be due to stars in concentric rings orbiting the center of the system. The Sun, according to this theory, must be in one such ring, orbiting the center of the stellar system at a distance of about 2000 light-years.

Thus, he removed the Sun from the center of the stellar system in accordance with his theory for the cause of star-streaming, although he displaced it only about 3 percent of the way to the edge of the system (see figure 7.6, bottom panel). He knew that the central position of the Sun in the 1920 model had caused some concern among his peers, who looked with suspicion on any model that placed the Sun and its accompanying solar system in a special or unique point in the universe. At the same time, he did not take into account new data from Shapley, the subject of our next chapter, which correctly indicated that the Sun might be even further removed from the center of the stellar system. By this time, the Kapteyn Universe and Shapley's ''big galaxy'' model stood in opposition to each other, and astronomers were lining up with one or the other. Kapteyn, always seeking harmony, hoped that the difference between the two models might eventually be attributable to their entirely different approaches, and that further refinements to both models might bring them closer together. He wrote to Shapley in 1919, ''You are building from above, while we are up from below. You start from the general system in its greatest extension, we try to struggle laboriously up from our nearest surroundings. When will the time come that we thoroughly mesh?''27 In 1920, Kapteyn added, ''I hope to live in order to see your and my studies meet.''28

Kapteyn presented his results before publication to a gathering of astronomers in Edinburgh in 1921, and again at an informal gathering in Leiden that included Einstein. The paper appeared in print in 1922. Shapley visited Leiden in May 1922, but Kapteyn was too ill to take advantage of the opportunity to meet his principal challenger face-to-face.

Kapteyn died in June 1922 at the age of 71. A lifetime of slow, methodical work sampling the stars and ''grinding huge masses of fact into law'' had come to an end. Perhaps he still wished, as he had remarked in earlier times, to be reincarnated as a graceful and fast-flying swallow, his favorite bird. He lived to see his ''Kapteyn Universe'' model come to light, but not long enough to see the perplexing differences between his model and Shapley's unravelled by new discoveries.

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