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Criteria of Nebular Distances

Since a reliable scale of distance is of vital importance in the exploration of space, the simple principles on which the scale was established will be discussed at some length. If the intrinsic luminosity (or candle-power) of an object is known, the apparent faintness indicates the distance. Conversely, if the distance is known, the apparent faintness indicates the intrinsic luminosity. On these principles the development of distance criteria proceeded step by step.

Fundamental distances are derived from certain easily recognized types of giant stars whose intrinsic luminosities are well known from investigations within the galactic system. These stars, among which the Cepheid variables are the most important, range from 1,000 to 4,000 times as bright as the sun. They have been identified in several of the neighbouring systems, which, together with the galactic system, form a local group, more or less isolated in the general field. The existence of this local group is a fortunate chance. The members constitute a small sample collection of nebulae whose distances are well determined by familiar, established methods.

A study of the sample collection furnished by Cepheid variables demonstrated that the very brightest stars in the different nebulae are about equally luminous. They average about 50,000 times as bright as the sun, and the individual deviations are small. Thus the brightest stars furnish a second criterion which indicates the distances of all nebulae in which any stars can be detected, regardless of whether or not the particular types can be recognized. The distances are not individually accurate, but mean values of even small groups should be reliable. The `resolved' nebulae, about 150 in all, form a second, larger sample collection which is believed to be fairly representative.

Analysis of this second collection leads to a third criterion of distance, namely, the total luminosities of the nebulae themselves. The nebulae average about 1,700 times brighter than their brightest stars - in other words, about 85 million times brighter than the sun. The scatter is rather large. The brightest giants are about ten times brighter than the average, and the faintest dwarfs, about ten times fainter. Nevertheless, the majority fall within the narrow limits from one-half to twice the average of them all. Thus the criterion is essentially statistical. Individual distances are very uncertain, but mean results for large numbers of nebulae are quite reliable.

Total luminosities form the general criterion which, in a statistical sense, applies to all the millions of nebulae that can be recorded with existing telescopes.

Two additional criteria should be mentioned, because, although their application is limited, they furnish individual distances of nebulae in which stars cannot be detected. One is the law of red-shifts which, as will be explained later, are displacements of spectral lines towards the red from their normal positions. Red-shifts are directly proportional to the distances of the nebulae in which they are observed. The law was, established with the aid of statistical distances previously available, but, once established, it furnishes reliable individual distances for all nebulae whose spectra can be recorded. The data are important because they do not depend upon resolution. For instance, the individual distances derived from red-shifts indicate clearly that the different types of nebulae are strictly comparable. There is no appreciable systematic variation in total luminosities in the sequence of nebular types.

Finally, there are the brightest nebulae in clusters. Some twenty or more great clusters of nebulae are known, each containing several hundred individual members. They are remarkably similar. We find large clusters of large bright nebulae, small clusters of small faint nebulae, and tiny clusters of tiny, extremely faint nebulae. They appear as though we were observing a single cluster from appropriately different distances. Thus their relative distances are readily estimated from their apparent characteristics, and the actual distance of any one - for instance, the nearest cluster - would lead directly to the actual distances of them all. The actual distances are important because, among other reasons, each cluster is a large sample collection of nebulae. The score or more of clusters furnishes a sample collection containing several thousand individual nebulae of all types. Analysis of this collection should indicate the absolute characteristics of nebulae in general.

The clusters are so similar that the mean luminosity of, say, the ten brightest members, or even the individual luminosity of, say, the fifth brightest nebulae, forms a precise and convenient measure of distance. The criterion has been calibrated; for instance, the fifth brightest nebulae are about 650 million times as bright as the sun, and the variation among different clusters is almost negligible. Therefore, the brightest nebulae in clusters furnish the criterion which applied over the greatest range in distance. The great clusters are the most remote objects to which precise individual distances can be assigned.

The step-by-step development of distance criteria is rather impressive. We start with familiar methods, currently used for investigations within the galactic system, and assemble a small sample collection of nebulae. The collection, as a whole, calibrates a second method, individually less precise, but ranging to much greater distances. With the second method we assemble a fairly large sample collection of nebulae. This second collection, as a whole, calibrates a third criterion, still less precise for individual cases, but ranging out to the very limits of the telescope.

The greatest uncertainty lies in the second step. The brightest stars are a certain number of times brighter than the Cepheids in the particular nebulae which form the first sample collection; but the collection is small, and we cannot be sure that it represents a fair sample of nebulae in general. Nevertheless, it is the only sample we have and, since the data are internally consistent, we must make the best of it. Otherwise, the procedure seems to be thoroughly reliable. Resolved nebulae are a certain number of times brighter than their brightest stars, and unresolved nebulae are strictly comparable. Red-shifts and data from clusters emphasize the consistency of the general picture.



The great clusters are the most remote objects to which individual distances can be assigned with confidence. For this reason they play a leading role in the formulation of the law of red-shifts. The clusters are all very much alike. Each contains several hundred members, among which the elliptical types predominate. The fifth brightest nebula averages about 650 million times as bright as the sun (very nearly the same as the mean of the ten brightest members), and serves as a convenient criterion of distance.

In the Coma cluster the fifth nebula appears about 2,000 times fainter than the faintest naked-eye stars, and, consequently, the distance is about 45 million light-years. The average red-shift in the cluster is dlambda / lambda = 0.245, corresponding with a velocity of recession of about 4,500 miles per second.

The cluster consists of perhaps a thousand nebulae scattered over several square degrees. The plate covers an area of 190 square minutes of arc, and shows about 85 members of the cluster. The most conspicuous nebulae are N.G.C. 4874 (globular) and N.G.C. 4884 (elongated).

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