THE STRUCTURE OF THE UNIVERSE*

P. ten Bruggencate, Potsdam

The advances achieved by astronomers in studies of the structure of the universe over the last 20 years have aroused among non-specialists less interest than the powerful development of physics that took place during the same interval of time and overturned our former conceptions. The reason for this, apparently, lies in the fact that quantum theory and wave mechanics touched the foundations of the exact sciences and led to the creation of entirely new methods of investigation.

The situation in astronomy is quite different. Here the methods of investigation have, in the main, remained the same, but different objects have begun to be studied. Two decades ago the question of the distribution of stars in the vicinity of the Sun stood at the center of attention in stellar astronomy. At the present time, by similar methods, we are studying the spatial distribution of spiral nebulae. This grandiose expansion of the field of astronomical research, the general picture of which I shall try to outline, can best be illustrated by the following example. At the astronomical congress held in Hamburg in 1912, the founder of modern stellar astronomy, Seeliger, could say that there were not sufficiently weighty reasons to admit the existence of island universes resembling our Galaxy. At present we know that spiral nebulae must in this sense be regarded as island universes. We now know that on a photographic plate taken with a long exposure by means of the large reflector of the Mount Wilson Observatory, in a region of the starry sky the size of the lunar disk, one can count up to 300 such island universes.

However, we shall begin our survey with the structure of our stellar system. In stellar astronomy it is customary to specify the position of an object in the sky by its galactic coordinates, i.e. by coordinates measured from the great circle whose position on the celestial sphere coincides with the position of the Milky Way. Galactic longitude corresponds to geographic longitude, and galactic latitude to geographic latitude. It was found that the distribution on the sky

* Phys. Z., 37, No. 22/23, 780–785, 1936; translated by S. A. Shorygin.

bright stars, and consequently, first of all, the distribution of stars visible to the naked eye, is symmetric with respect to the Milky Way; more precisely, it was established that it depends only on galactic latitude. As for the spatial distribution of these brightest stars, from this we can draw the conclusion that the Sun is located near the center of a “local” stellar system, more or less symmetric with respect to the axis of rotation of this system. However, after the extension of work on stellar statistics to much fainter stars, and after the repetition of analogous investigations for stars from the 12th to the 18th magnitude, the picture of the mean distribution of stars over the sky changes significantly. In such a case the spatial density of stars (i.e., the frequency of their distribution) will depend not only on galactic latitude but also on galactic longitude. These faint stars outline a stellar system in which the Sun occupies a strongly eccentric position. True, in this case too the plane of the Milky Way remains the plane of symmetry; however, this larger stellar system extends much farther in the direction of \(325^\circ\) galactic longitude (the constellation Sagittarius) than in the opposite direction, \(145^\circ\) galactic longitude (the constellation Orion). The asymmetry of galactic latitudes, revealed in the transition to faint stars, arises from the fact that the spatial density of stars is influenced by the star clouds that form part of the Milky Way. The faintest stars among those that make up the visible appearance of the Milky Way are precisely stars of approximately the 12th magnitude. In surveying the distribution of the brightness of individual regions of the Milky Way along its entire extent, this asymmetry at once becomes striking. The brightest clouds that form the Milky Way are located in the constellations Scutum, Ophiuchus, Sagittarius, and Scorpius. From there, the brightness of the Milky Way gradually decreases in both directions and reaches its smallest value at the opposite point of the celestial sphere—in the constellation Orion. This characteristic asymmetrical course of the brightness of the various regions of the Milky Way is also clearly revealed in the numbers of faint stars. The attention of anyone who for the first time sees the southern hemisphere of the starry sky is attracted, first of all, not by unfamiliar bright stars, but by the structure of the Milky Way, so unlike the structure of the part of it visible in the northern hemisphere (Fig. 1). The imagination of the ancient Greeks united the brightest stars of the northern hemisphere into constellations,

Fig. 1. Star clouds in the part of the Milky Way visible in the southern hemisphere (after Barnard)

embodied the figures of the heroes of their myths; the inhabitants of the island of Java, in the bright clouds and dark gaps of the southern part of the Milky Way (in the constellations Ophiuchus and Scorpius), discerned the figure of the giant Bhima, who is the central figure of Javanese religious legends.

Does such a structure of the Milky Way have as its cause an alternation in space of regions extremely rich in stars with regions almost starless, or is this structure, to a considerable extent, due in its origin to clouds of cosmic dust existing in world space and causing the absorption of light? Today we decidedly incline to the second view. It should not, however, be passed over in silence that, for the final solution of this question, it will be necessary to carry out a whole series of further investigations concerning particular details. And if the first supposition were to prove correct, then the spatial distribution of faint stars would have to deviate considerably from uniformity.

Let us turn to the methods that make it possible to judge the mean distribution of stars in space. The direct and, in a certain sense, most exact method of determining the spatial distribution of stars would undoubtedly have to consist in measuring the distances of as large a number of individual stars as possible. In fact, the method of direct measurements of stellar distances, consisting in the measurement of so-called trigonometric parallaxes, has provided us with a firm foundation for our knowledge of the structure of the universe. It will therefore be appropriate to say a few words about it. The tiny ellipse described in the sky by each star as a result of the Earth’s revolution around the Sun—this is what the astronomer tries to measure. A star situated at the pole of the ecliptic describes a path which, in its form, is an exact representation of the Earth’s orbit; this motion along an ellipse for a star situated on the ecliptic degenerates into an oscillatory motion taking place along a straight line. However, this parallactic motion, already for distances that are insignificant in comparison with the dimensions of the universe, very quickly becomes immeasurably small; and therefore this first direct method of investigating the spatial distribution of stars does not lead to the goal. True, the present degree of accuracy of measurements might prove sufficient to carry out measurements of this kind within a sphere of radius 150 light-years, at the center of which is the Sun. But the distance which light manages to traverse in 150 years is, on astronomical scales, so small that there would be little benefit from this.

For this reason attempts were made to form an idea of the spatial distribution of stars by a statistical route. The problem is then posed in the following way. We determine (by counting) the number of stars of a definite brightness located in some region of the sky chosen by us arbitrarily. Can we from this draw a conclusion regarding the spatial distribution of these stars, which are projected onto the region we have chosen

region of the sky? If the luminosities (brightnesses) of all stars were equal to one another, then the problem posed would be easily solved. Then (in the case that no absorption of light occurred in space) the apparent brightness of stars would be a measure of their distance. In such a case we could assert with complete confidence that stars of the 7th magnitude are farther from us than stars of the 5th magnitude, and so on. However, the assumption made about the equality of the luminosities of all stars is in fact by no means justified. We know stars that send into space 10,000 times more light than the Sun, and also stars that emit scarcely 0.0001 of the Sun’s light. Therefore we are quite unable to decide at first sight why one star appears brighter to us than another: whether because it is nearer to us, or because it has a greater absolute brightness. The number of stars of a given apparent brightness located in a given region of the sky therefore depends not only on the spatial distribution of the stars, but also on the relative frequency of occurrence of stars possessing large and small absolute brightnesses.

In the present case the astronomer is faced with a problem which—from the mathematical point of view—can be exactly likened to the problem a physicist must solve when he wishes to derive the energy curve of some source of light from its observed spectrobologram. If the physicist had at his disposal a spectral instrument possessing unlimited resolving power, then the solution of the problem would present no difficulty. In reality, however, the physicist must take into account the limited resolving power of his spectral instrument; first he obtains the spectrobologram experimentally, and only then must he derive from it the energy curve. For the astronomer, the role of this spectrobologram, which has first to be determined, is played by the distribution function of the absolute brightnesses of stars; only after establishing it can he decipher the true numbers characterizing the spatial distribution of the stars. But, unfortunately, the distribution function of absolute brightnesses corresponds to a spectral instrument of very low resolving power. A physicist who wished, with the aid of such an instrument, to determine the energy curve of a source of light would be called incautious. In the same way, stellar statistics gives us only a very rough picture of the mean spatial distribution of the stars. As for the local stellar system of Seeliger and Kapteyn, determined from the positions of the brighter stars, we may briefly characterize it as follows (Fig. 2): the plane of the Milky Way is the plane of symmetry of a strongly flattened system. In this plane the spatial density of stars, at distances of approximately 30,000 light-years, falls to one-hundredth of their frequency of occurrence in the neighborhood of the Sun; in the direction perpendicular to the plane of symmetry, such a small spatial density

of stars is reached much earlier, namely: already at a distance of approximately 6,000 light-years. To this system belong all stars that appear to us brighter than the 11th magnitude, and the Sun is situated rather close to the center of this system. Its extent in the plane of the Milky Way, as we now know, is apparently somewhat smaller, owing to the necessity of taking into account the absorption of light.

Labels in the figure: parsecs; Milky Way; 60°; 30°; 23; 5; 10; 15; 20; 30; 25.

Fig. 2. Section of the local stellar system: the course of curves of equal frequency of occurrence of stars according to Seeliger

of light. When an attempt is made to extend these investigations to faint and very faint stars, the methods of stellar statistics prove insufficient for determining the dimensions of this system of large size. As for Shapley’s investigations of the distribution

Labels in the figure: 10,000; 5,000; 0; 5,000; 10,000.

Fig. 3. Distribution of the spatial densities of stars in the large Galaxy according to Shapley. The slow fall of the frequencies in the direction \(\lambda\) 325°, and the rapid fall in the opposite direction. An attempt was made to decompose the observed distribution (upper curve) into a symmetric local distribution and an asymmetric distribution (the two lower curves)

of stars from the 12th to the 18th magnitude, they make it possible, quite reliably, to draw the following two conclusions (Fig. 3): 1) the large stellar system is sharply asymmetric with respect to galactic longitudes, and 2) the “local” stellar system of Seeliger and Kapteyn must be regarded as a more or less clearly expressed local stellar cloud situated on the periphery of this large system.

A very fortunate circumstance is that we possess deeper knowledge of the structure of the galactic system. This knowledge is based on studies of the spatial distribution of star clusters. We know of two types of star clusters: open (scattered), or galactic, star clusters (for example, the Pleiades) and globular star clusters (for example, Messier 13 in the constellation Hercules; Fig. 4). The distribution of objects of both these types over the celestial sphere already reveals characteristic differences. All open

Fig. 4. Globular star cluster Messier 13

Fig. 5. Distribution of open (white circles) and globular (black dots) star clusters by galactic latitudes

star clusters are found either in the Milky Way itself or, in any case, in its immediate vicinity. Globular star clusters, on the contrary, show a rather uniform distribution in galactic latitudes. But the distribution of star clusters also proves to be unequal in galactic longitudes. Whereas open star clusters show a uniform distribution in galactic longitudes, globular star clusters, in a sharply pronounced way, prefer galactic longitudes in the neighborhood of \(325^\circ\) (Figs. 5 and 6). Already on this basis it is possible to draw deep parallels with the distribution of bright and faint stars. We may say that open star clusters form the skeleton of the “local” stellar system, while globular star clusters outline the contours of a system of much larger dimensions. This large system is clearly revealed in the numbers expressing the spatial density of faint stars. We must conceive of the local stellar system as a stellar cloud located on the periphery of this large system. As for the star clusters, whose total number is limited,—the number of open…

...open star clusters is less than 500, and the number of globular star clusters is less than 100—then we are able, for each separate cluster, to derive its distance in a reliable way. Thanks to this, we obtain the possibility of constructing, on the proper scale, spatial models of the systems of open star clusters and globular star clusters. Having constructed such models, we become convinced that the system of open star clusters has the form of a round disk, the plane of this disk almost exactly coinciding with the plane of the Milky Way. This disk has a diameter of about 30,000 light-years, and the Sun is located near the center of this system. The situation is different with the system defined by the distribution of globular star clusters. This system is much less flattened. Its plane of symmetry coincides with the plane defined by the distribution of the star clouds that form part of the Milky Way. In this plane, the system under consideration has an extent of approximately 160,000 light-years, and in the direction perpendicular to this plane—an extent of approximately 120,000 light-years. The Sun is situated in the system of globular star clusters in a sharply eccentric position, separated from its center by a distance of somewhat less than

Fig. 6. Distribution of globular star clusters by galactic longitude

Fig. 7. Spiral nebula, the branches of which partly seem to have resolved into stars

35,000 light-years. The center of this system is located from the Sun in the direction toward the large star cloud in the constellation Sagittarius.

On the basis of certain discrepancies obtained in determining the distances of open star clusters, Trumpler concluded that, at least in the immediate vicinity of the plane of the Milky Way, a noticeable absorption of light takes place. The effect of this absorption of light has already been taken into account in the above-cited figures expressing the dimensions of the stellar systems.

As for the globular star clusters, Shapley succeeded, with the aid of stars of the δ Cephei type occurring in these clusters, in obtaining quite reliable values for the distances of these clusters. (Stars

of the $\delta$ Cephei type form a definite class of variable stars, in which a connection is found between their luminosity, on the one hand, and the period of variation of their brightness, on the other. In 1926 Hubble succeeded in proving the presence of stars of the $\delta$ Cephei type in the outer parts of the great spiral nebula Messier 33, which for the first time made it possible to determine the distances of spiral nebulae (Fig. 7) without resorting to any hypotheses. This made it possible to resolve the old question of whether these objects belong to our Galaxy, or whether these nebulae form independent island universes. The second solution was recognized as correct. In recent years Hubble, with the aid of the 100-inch and 60-inch reflectors of the Mount Wilson Observatory, has carried out a systematic survey of the sky in search of extragalactic nebulae. Our present knowledge of the distribution of these objects in the sky is based on counts of the number

Fig. 8. Distribution of extragalactic nebulae in the sky

of nebulae (44,000 objects) photographed on 1283 plates. The regions of the starry sky covered by these photographs are distributed over galactic latitudes and longitudes, on the whole, uniformly over the entire celestial sphere. Fig. 8 shows the distribution of nebulae in the sky. This figure may serve as a visual proof of the existence of light-absorbing matter grouped in the plane of the Milky Way. Near the poles of the Galaxy, owing to the insignificant extent of the layer of this matter in a direction perpendicular to the plane of the Galaxy, the absorption of light becomes barely noticeable. There we observe regions with normal numbers of extragalactic nebulae. But already at galactic latitudes $\pm 40^\circ$ there are regions with much smaller numbers of extragalactic nebulae, and in the belt of the Milky Way, about $20^\circ$ wide, there are almost no such regions in which extragalactic nebulae would be found. This occurs because in the plane of the Milky Way the absorption of light is so strong that

our view does not penetrate beyond the limits of our galactic system. The strongest absorption of light is observed at galactic longitude \(325^\circ\), in the direction in which the center of the “large Galaxy” is located. In regions of the sky where no absorption of light occurs, the average number of nebulae falling on one square degree is 460; this number is obtained when the sky is photographed at the Newtonian focus of the 100-inch reflector with an exposure of 1 hour under the best seeing conditions. The limiting stellar magnitude of the objects appearing on such plates is approximately \(20^m.0\). The number of 460 nebulae per 1 square degree corresponds, in round numbers, to 100 nebulae falling on an area equal to the lunar disk. Hubble estimated the number of nebulae appearing on photographs made with the 100-inch reflector with many-hour exposures as reaching 1780 per square degree. As the brightnesses of the photographed objects decrease, the number of nebulae increases so rapidly that upon reaching the 21st stellar magnitude as many nebulae appear on the plate as stars. But in the final analysis what interests us is the distribution of nebulae in space. The first step that must be taken in order to solve this far more difficult question consists in a reliable determination of the apparent brightnesses of the nebulae. Here, however, from the very beginning we encounter a serious difficulty, consisting in the need to tie together photographic photometry of points (images of stars) and photographic photometry of areas (images of nebulae). At present we stand only on the threshold of establishing an indisputable photometric system of nebular brightnesses, as a result of which estimates of brightnesses below 19.5 stellar magnitude must now be regarded as very approximate.

Nevertheless, apparently, the following important regularity can be established. If we restrict ourselves to nebulae whose apparent brightnesses are not so small that it would be necessary to take into account the influence of the red shift or possible curvature of space in deriving the luminosities of these nebulae, we become convinced that the following relation turns out to be approximately valid:

\[ \lg N_m = 0.6m + \mathrm{const}, \tag{1} \]

in which \(N_m\) is the number of nebulae, beginning with the brightest and extending to those having stellar magnitude \(m\). An essential role in this equation is played by the coefficient 0.6 standing before \(m\). From it follows the necessity for the existence of a uniform distribution of nebulae in space. The fact that, as a first approximation, we can regard this conclusion as real proves to be very significant for cosmological investigations concerning the structure of space, which we shall briefly mention in the conclusion. But before this it is necessary to speak of entirely different investi-

observations that contributed to just as great a degree to the expansion of our ideas about the structure of the universe. We shall be concerned with the improvement of methods for photographing faint nebulae with the aid of the enormous reflectors of the Mount Wilson Observatory. For this purpose it was especially important, as far as possible, to increase the aperture ratio of the spectrograph camera. A decisive step in this direction was taken in 1930, when Peighton succeeded in constructing for this camera an objective with an aperture ratio of \(1:0.6\). The following numerical summary may serve as a vivid illustration of the successes that have since been achieved in determining the radial velocities of faint nebulae:

Largest velocities of nebulae (by year, in km/sec)

In this summary are compared the largest measured velocities of nebulae, taken from the annual reports of the Mount Wilson Observatory. It is especially noteworthy that nebulae displaying a red shift of the order of 40 000 km/sec (i.e., about \(1/8\) the speed of light) have such low brightnesses that, in the Cassegrain focus of the 100-inch reflector, they can no longer be observed visually; consequently it is not possible to keep them directly on the slit of the spectrograph. In this case the observations are made as follows: on a negative obtained in the Newtonian focus, a suitable object is selected for guiding the reflector, and its position relative to the faint nebula is measured exactly. Then a system of micrometric screws makes it possible to set the cross-hairs of the guiding tube in the Cassegrain focus, relative to the slit of the spectrograph, in such a way that the image of the nebula falls on the spectrograph slit when the object selected for guiding is on the cross-hairs. In Fig. 9 several spectra of nebulae are reproduced in order of increasing red shift. Beside the spectra are reproduced negative images of these same nebulae, taken with approximately equal exposures. As we see, the increase in red shift proceeds in parallel with the decrease in the diameters and apparent brightnesses of the nebulae. This serves as direct proof of the existence of a connection between red shift and distance. In the tiny spectra, whose length does not reach 3 mm, the lines in the interval between \(\lambda 3900\) and \(\lambda 5000\) are distinguishable only with difficulty. Therefore, when large shifts are present, it is necessary to expose the spectra long enough for the characteristic absorption lines H and K (the doublet of the resonance lines of \(Ca^+\)) to appear on the plates, easily distinguishable from all the others.

To the extent that at present one can speak of this with some certainty, the red shift increases linearly with increasing distance of the nebulae, and moreover by 180 km/sec per \(10^6\) light-years. Consequently, a light ray flying from nebulae possessing radial velocities of the order of \(1/8\) the speed of light requires about 200 million years to reach us. At such distances, however, the red shift becomes so considerable that its effect on photographic brightnesses can no longer be neglected. This confronts

Fig. 9. On the left—the spectra of distant nebulae; the comparison spectrum belongs to helium.
On the right—negative images of the same nebulae

astronomers with a difficult problem, because, in addition, in order to introduce a correction corresponding to reality, it is necessary to estimate the amount of energy absorbed in various parts of the spectrum in the Fraunhofer lines. The solution of this latter problem is extraordinarily important also because, on the basis of corrected values of the brightnesses of nebulae, conclusions may ultimately be drawn about the structure of space.

I believe that we are faced with the solution of one of the greatest problems, namely the problem of the structure of the universe as a whole. We shall have to decide whether the red shift is a consequence of the expansion of the universe, i.e. of the non-static state of the universe (Lemaître, Eddington); or whether space is in reality static, while the connection between red shift and distance or the speed of light indicates the existence of a new fundamental physical law (Nernst).

In the first case, the influence of the red shift on the visible brightnesses of nebulae will be greater than in the second. This has its own pri-

The cause of this is the circumstance that, in the first case, alongside the usual Doppler effect, there must also be manifested the work which must be performed by radiation in the expansion of space. If we take a uniform distribution of nebulae in space as the most probable, then an exact investigation of the deviations of the observed frequencies of the distribution of nebulae from the values given by equation (1) will open before us a highly promising path toward resolving the question of the structure of space.