The numerous variable stars in any one cluster are remarkable for their uniformity. Accepting variables of this type as a constant standard of absolute brightness, and assuming that the differences of average magnitude of the variables in different clusters are entirely due to differences of distance, the relative distances of many clusters were ascertained with considerable accuracy. Then it was found that the average absolute magnitude of the twenty-five brightest stars in a cluster is also a uniform standard, or about 1.3 magnitudes brighter than the mean magnitude of the variables. This new standard was employed in ascertaining the distances of other clusters not containing many variables.
Shapley further shows that the linear dimensions of the clusters are nearly uniform, and the proper relative positions in space are charted for sixty-nine of these objects. We can determine the scale of the charts, if we know the absolute brightness of our primary standard—the variable stars; and this is deduced from a knowledge of the distances of variables of the same type in our immediate stellar system.
The most striking of all the globular clusters, Omega Centauri, comes out the nearest; nevertheless it is distant 6.5 kiloparsecs. A kiloparsec is a thousand parsecs, and is the equivalent of 3,256 light-years. At the inconceivable distance of sixty-seven kiloparsecs, or more than 200,000 light-years, is the most remote of the globular clusters, known to astronomers as N.G.C. 7006, from its number in the catalogue which records its position in the sky, the New General Catalogue of nebulæ by Dreyer of Armagh.
The clusters are widely scattered, and their center of diffusion is about twenty kiloparsecs on the Galactic plane toward the region of Scorpio-Sagittarius. Marked symmetry with reference to this plane makes it evident that the entire system of globular clusters is associated with the Galaxy itself. But to conceive of this it is necessary to extend our ideas of the actual dimensions of the Galactic system. Almost on the circumference of the great system of globular clusters our local stellar system is found, and it contains probably all the naked-eye stars, with millions of fainter ones. Its size seems almost diminutive, only about one kiloparsec in diameter. The relative location of our local stellar system shows why the globular clusters appear to be crowded into one hemisphere only.
Shapley suggests that globular clusters can exist only in empty space, and that when they enter the regions of space tenanted by stars, they dissolve into the well-known loose clusters and the star clouds of the Milky Way. Strangely the radial velocities of the clusters already observed show that most of them are traveling toward this region, and that some will enter the stellar regions within a period of the order of a hundred million years.
The actual dimensions of globular clusters are not easy to determine, because the outer stars are much scattered. To a typical cluster, Messier 3, Shapley assigns a diameter of 150 parsecs, which makes it comparable with the size of the stellar cluster to which the sun belongs. Also on certain likely assumptions, he finds that the diameter of the great cluster in Hercules, the finest one in our northern sky, is about 350 parsecs, and its distance no less than 30,000 parsecs; in other words, the staggering distance that light would require 9,750,000 years to travel over. While these distances can never be verified by direct measurement, it lends great weight to the three methods of indirect measurement, or estimation, (1) from the diameter of the image of the clusters, (2) from the mean magnitude of the twenty-five brightest stars, and (3) from the mean magnitude of the short period variables, that they are in excellent agreement.
CHAPTER LV
MOVING CLUSTERS
Recent researches on the proper motions of stars have brought to light many groups of stars whose individual members have equal and parallel velocities. Eddington calls these moving clusters. The component stars are not exceptionally near to each other, and it often happens that other stars not belonging to the group are actually interspersed among them. They may be likened to double stars which are permanent neighbors, with some orbital motion, though exceedingly slow.