02 Galaxies



From the finding that the initial product of the large-scale aggregation process in the material sector of the universe is the globular cluster, it follows that galaxies are formed by consolidation of globular clusters. This conclusion is in direct conflict with the prevailing astronomical opinion, which is described by John B. Irwin as follows:

The Milky Way system, like other galaxies, is thought to have originated from a condensation or collapse of the intergalactic medium, which event resulted in a system of stars. The reason for the collapse is not known, and the details of the process are uncertain.13

As might be expected where neither the antecedents of the process nor the details are in any way understood, this explanation has encountered serious difficulties, and is currently in deep trouble. As expressed by Virginia Trimble in a report of a conference, at which this situation was discussed at some length, “The conventional wisdom concerning galaxy formation and evolution is beginning to leak badly at the seams.” In the concluding portion of her report she notes that” Fall, Hogan, and Rees (Cambridge) have considered the case of a galaxy assembled entirely out of pre-existing star clusters,” and she makes this comment:

The discerning reader will long since have noticed where we are headed—if there are problems making the biggest things (clusters of galaxies) first, then perhaps we should try making the smallest things (stars or clusters of stars) first.14

Such a reversal of thinking on the subject is difficult in the context of present-day astronomical theory because so much of that theory has been specifically tailored to fit the “big things first” viewpoint but, as we will see in the following pages, if the observational evidence is taken at its face value and not twisted to conform to the prevailing theories, the problems disappear. In the universe of motion the galaxies are, in fact, “assembled entirely out of preexisting star clusters,” as the Cambridge astronomers suggested.

Unlike the individual stars, whose spheres of gravitational control meet at locations of minimum gravitational force, so that each star is outside the gravitational limits of its neighbors, the original boundaries of the aggregate that ultimately becomes a globular cluster meet those of its neighbors at locations of maximum gravitational force. The contraction of the aggregates leaves the gravitational effect at these locations unchanged, while the increase in mass due to the influx of material from the cosmic sector adds a significant increment. Each of the globular clusters is thus well within the gravitational limits of the adjoining clusters. Consequently, there is a general tendency for the clusters to move toward each other and combine. When such a combination does occur, the combined unit exerts a stronger gravitational force within wider spatial limits, and both the accretion of diffuse material and the attraction of nearby clusters are speeded up. Like the contraction of the pre-cluster aggregate, the contraction of the group of clusters leading to combination is thus a self-reinforcing process.

It should be noted in this connection that consolidation of two clusters is inevitable if their mutual gravitational attraction continues to act without interference from outside sources (that is, gravitational forces of other aggregates). There has been a rather general belief that because of the immense distances between the stars in a cluster, or other aggregate; two such structures could pass through each other with little or no actual contact. Fred Hoyle expresses this general opinion in this statement:

Think of the stars as ordinary household specks of dust. Then we must think of a galaxy as a collection of specks a few miles apart from each other, the whole distribution filling a volume about equal to the Earth. Evidently one such collection of specks could pass almost freely through another. 15

Our finding that the stars occupy equilibrium positions throws a considerably different light on this situation. A stellar aggregate such as a cluster has the general characteristics of a viscous liquid and collision of two such aggregates involves an inelastic impact similar to the impact of one liquid aggregate upon another. In each case there is a certain amount of penetration while the kinetic energy of the incoming mass is being absorbed, but the eventual result is consolidation. The incurring mass meets a wall, not a passageway.

This liquid-like nature of the aggregates of stars, deduced theoretically and confirmed observationally by the behavior characteristics of the galaxies and star clusters that will be examined in the subsequent pages, has a major effect on the phenomena in which these objects participate. It invalidates many of the conclusions such as the one expressed by Hoyle in the statement just quoted, and a great many mathematical calculations that rest on the hypothesis of free movement of the constituent stars of an aggregate.

Consolidation of two globular clusters produces an aggregate which not only has double the mass of a cluster, but also, because the impact is not exactly central in the usual case, has a rotational motion that was absent in the original cluster. Instead of an oversize cluster, we may therefore regard the combination as an aggregate of a new type: a small galaxy. For a period of time after its formation such a galaxy has a rather confused and disorderly structure, and is therefore classified as irregular, but in time the disruptions due to the collision are smoothed out, and the galaxy assumes a more regular form. By reason of the rotational motion that is now present, the galactic structure deviates to some extent from the nearly spherical shape of the original clusters, and it is now classed as an elliptical galaxy.

If some larger unit does not capture this small elliptical galaxy it continues growing by accretion of dust and gas, and occasionally picks up another globular cluster. In the earlier stages, each such capture of a cluster disorganizes the galactic structure and puts the galaxy back into the irregular class for a time, but as it increases in size the galaxy gradually becomes able to swallow a cluster without any major effect on its own structure. By this time, however, some combinations of small galaxies begin to take place. Here, again, a structural irregularity develops, and persists for a time. In this stage the aggregates are reported to be “several hundred times larger than the dwarf elliptical galaxies.18

As long as the captured clusters are mature—that is, fully consolidated into stars—the amount of dust in an elliptical or small irregular galaxy is relatively minor. Eventually, however, one or more of the captives is a cluster of dust and gas clouds an immature globular cluster, rather than a mature cluster of stars. The mixing of this large amount of dust and gas with the stars of the galaxy alters the dynamics of the rotation, and causes a change in the galactic structure If the dust cloud is captured while the galaxy is still quite small, the result is likely to be a reversion to the irregular status until further growth of the galaxy takes place. Because of the relative scarcity of the immature clusters, however, most captures of these objects occur after the elliptical galaxy has grown to a substantial size. In this case the result is that the structure of the galaxy opens up and a spiral form develops.

There has been a great deal of speculation as to the nature of the forces responsible for the spiral structure, and no adequate mathematical treatment of the subject has appeared. But from a qualitative standpoint there is actually no problem, as the forces, which are definitely known to exist—the rotational forces and the gravitational attraction—are sufficient in themselves to account for the observed structure. As already noted, the galactic aggregate has the general characteristics of a heterogeneous viscous liquid. A spiral structure in a rotating liquid is not unusual; on the contrary, a striated or laminar structure is almost always found in a rapidly moving heterogeneous fluid, whether the motion is rotational or translational. Objections have been raised to this explanation, generally known as the “coffee cup” hypothesis, on the ground that the spiral in a coffee cup is not an exact replica of the galactic spiral, but it must be remembered that the coffee cup lacks one force that plays an important part in the galactic situation: the gravitational attraction toward the center of the mass. If the experiment is performed in such a manner that a force simulating gravitation is introduced, as, for instance, by replacing the coffee cup by a container that has an outlet at the bottom center, the resulting structure of the surface of the water is very similar to the galactic spiral.

In this kind of a rotational structure the spiral is the last stage, not an intermediate form. By proper adjustment of the rotational velocity and the rate of water outflow the original dispersed material on the water surface can be caused to pull in toward the center and assume a circular or elliptical shape before developing into a spiral, but the elliptic structure precedes the spiral if it appears at all. The spiral is the end product. The manner in which the growth of the galaxy takes place has a tendency to accentuate the spiral form, but the rotating liquid experiment shows that the spiral will develop in any event when the necessary conditions exist. Furthermore, this spiral is dynamically stable. We frequently find the galactic spirals characterized as unstable and inherently short-lived, but the experimental spiral does not support this view. From all indications, the spiral structure could persist indefinitely if the mass and rotational velocity remained constant.

The conclusion that the spiral arms are quasi-permanent features of the galaxies is currently contested on other grounds, as in the following quotation from an astronomy textbook:

The trouble is that this idea predicts the arms should be nearly fixed structures almost as old as the galaxy itself, whereas actually they are young regions only a few million years old.16

The assertion that the spiral arms are “young regions” is based on the presence of hot, massive stars, currently considered to be young, on the strength of the prevailing assumption as to the nature of the stellar energy generation process. The evidence that invalidates this hypothesis, which will be presented at appropriate points in the pages that follow, thus cuts the ground from under this argument.

A spiral galaxy consists of a nucleus, approximately spherical, and a system of curving arms extending outward from the nucleus. In the smaller and younger objects the nucleus is small, the arms are thick and widely separated, and the general structure can be described as loose. As these galaxies grow older and larger, the nucleus becomes more prominent, the rotational velocity increases, and the greater velocity causes the arms to thin out and wind up more tightly. Ultimately the arms disappear entirely and the nearly spherical nucleus becomes the galaxy. At this stage the shape of the galaxy is the same as that of the smallest and youngest of the galaxies that have attained a stable form, and these giant old galaxies are generally included in the elliptical category. But putting such widely different aggregates into the same class simply on the basis of their form leads to confusion, and cannot be considered good practice. Fortunately, the term “spheroidal” is being used to some extent in this connection, and since it is quite appropriate, we will classify these oldest and largest of the stellar aggregates as spheroidal galaxies.

As the foregoing discussion brings out, the primary criterion of the age of galaxies is size, with shape as a secondary characteristic varying in direct relation to size. It must be realized, of course, that accidents of environment and other factors will affect this situation to some extent, so that there are some deviations from the normal pattern, but in general the ages of the various types of galactic structures stand in the same order as their sizes. The passage of time also brings other observable results that confirm the ages indicated by the sizes of the galaxies. One of these is a decrease in abundance. In the evolutionary course as outlined, each aggregate is growing at the expense of its environment. The smaller units are feeding on atoms, small particles, and stray stars. The larger aggregates pull in not only all material of this kind in their vicinity, but also any of the small aggregates that are within reach.

As a result of this cannibalism the number of units of each size progressively decreases with age. Observations show that the existing situation is in full agreement with the theoretical expectation, as the order of abundance is the inverse of the age sequence indicated by the galactic size and shape. The giant spheroidal galaxies, the senior members of the galactic family, are relatively rare, the spirals are more common, the elliptical galaxies are abundant, and the globular clusters exist in enormous numbers.

It is true that the observed number of small elliptical galaxies, those in the range just above the globular clusters, is considerably lower than would be predicted from the age sequence, but it is evident that this is a matter of observational selection. When the majority of galaxies are observed at such distances that only the large types are visible, it is not at all strange that the number of small elliptical galaxies actually identified is less than the number which, according to the theory, should exist. The many additional elliptical galaxies discovered within the Local Group in very recent years, increasing the already high ratio of elliptical to spiral in the region accessible to detailed observation, emphasizes the effect of the selection process.

Conventional astronomical theory neither requires nor excludes the existence of large numbers of these dwarf galaxies, and because they are too inconspicuous to demand attention from an observational standpoint, little notice has been taken of them until recently. Since our development leads to the conclusion that they are, next to the globular clusters, the most numerous of the astronomical aggregates, it is worth noting that the astronomers are beginning to recognize their abundance. For instance, a recent (1980) comment suggests that these dwarfs “may be the most common type of galaxy in the universe.”17 This is what the theory of the universe of motion says that they must be.

Other observational indications of age will be examined later, after some more foundations have been laid, but these will merely supply additional confirmation. At this time it should be noted that all three of the criteria thus far discussed are in agreement that the observed galaxies and sub-galaxies can be placed in a sequence consistent with the theoretical deduction that there is a definite evolutionary path in the material sector of the universe extending from dispersed atoms and sub-atomic particles through multi-molecular dust particles, clouds of atoms and particles, stars, clusters of stars, elliptical galaxies, and spiral galaxies to the giant spheroidal galaxies which constitute the final stage of the material phase of the great cycle of the universe. It is possible, of course, that some of these units may have remained inactive from the evolutionary standpoint for long periods of time, perhaps because of a scarcity of available “food” for accretion in their particular regions of space, and such units may be chronologically older than some of the aggregates of a more advanced type. Such variations as these are, however, merely minor fluctuations in a well-defined evolutionary pattern.

”One of the continuing mysteries,” says Virginia Trimble, “is why galaxies should have the range of masses they do.”14 The foregoing explanation of the evolution of the galaxies shows why. The galaxies originate as globular clusters and grow by capture until they reach a size limit at which their existence terminates. Galaxies therefore exist in all sizes between these two limits.

Next we turn to a different kind of evidence that gives further support to the theoretical conclusions. In the preceding discussion it has been demonstrated that the deductions as to continual growth of the material aggregates by capture of matter from the surroundings are substantiated by the definite correlation between the size, shape and relative abundance of the various types of galaxies and clusters. Now we will examine some direct evidence of captures of the kind required by the theory. First we will consider evidence which indicates that certain captures are about to take place, then evidence of captures actually in progress, and finally evidence of captures that have taken place so recently that their traces are still visible.

The observed positions and motions of the globular clusters provide the most abundant evidence of impending captures, but the total amount of information about these clusters now available is sufficient to justify a separate chapter. The capture of clusters by galaxies will therefore be discussed in Chapter 3 , in connection with the general consideration of the role of these objects.

Capture of galaxies by larger galaxies is much less common than capture of globular clusters, simply because the clusters are very much more abundant. We may deduce, however, that there should be a few galaxies on the road to capture by each of the giant galaxies. This is confirmed by the observation that the nearer large spirals have “satellites,” which are nothing more than small galaxies that are within the gravitational range of a larger aggregate, and are being pulled in to where they can be conveniently swallowed. The Andromeda spiral, for instance, has at least eight satellites: the elliptical galaxies M 32, NGC 147, NGC 185, and NGC 205, and four small galaxies that have been named Andromeda I, II, III, and IV. The Milky Way galaxy is also accompanied by at least six fellow travelers, the largest of which are the two Magellanic Clouds and the elliptical galaxies in Sculptor and Fornax. The expression “at least” must be included in both cases, as it is by no means certain that all of the small elliptical galaxies in the vicinity of these two large spirals have been identified.

As one report summarizes the situation, the dwarf galaxies “cluster in swarms about the giant galaxies.” The author goes on to say, “Why this should be is not yet understood; but theorists believe that it could be telling us much about the way galaxies form.”18 In the light of the information presented in the foregoing pages, it should be evident that what these observations are telling us is simply that the original products are undergoing a process of consolidation into larger aggregates.

Some of these galactic satellites not only occupy the kind of positions required by theory, and to that extent support the theoretical conclusions, but also contribute evidence of the second class: indications that the process of capture is already under way. The so-called “irregular” galaxies were not given a separate place in the age-size-shape sequence previously established, as it appears reasonably certain that these galaxies, which constitute only a small percentage of the total number of galaxies that have been observed, are merely galaxies belonging to the standard classes which have been distorted out of their normal shapes by factors related to the capture process. The Large Magellanic Cloud, for instance, is big enough to be a spiral, and it contains the high proportion of advanced type stars that is characteristic of the spirals. Why, then, is it irregular rather than spiral? The most logical conclusion is that the answer lies in the proximity of our own giant system; that the Cloud is in the process of being swallowed by our big spiral, and that it has already been greatly modified by the gravitational forces that will eventually terminate its existence as an independent unit. We can deduce that the Large Cloud was actually a small spiral at one time, and that the “rudimentary” spiral structure, which is recognized in this galaxy, is actually a vestigial structure.

The Small Cloud has also been greatly distorted by the same gravitational forces, and its present structure has no particular significance. From the size of this Cloud we may deduce that it was a late elliptical or early spiral galaxy before its structure was disrupted. The conclusion that it is younger than the large Cloud, which we reach on the basis of the relative sizes, is supported by the fact that the Small Cloud contains a mixture of the type of stars found in the globular clusters, currently called Population II, and the type found in the spiral arms, currently called Population 1, whereas the stars of the Large Cloud are predominantly of Population 1.

The long arm of the Large Cloud, which extends far out into space on the side opposite our galaxy is a visible record of the recent history of the Cloud. The gravitational attraction of the Galaxy is exerted on each component of the Cloud individually, as well as on the structure as a whole, since the Cloud is an assembly of discrete units in which the cohesive and disruptive forces are in balance. This balance is precarious at best, and when an additional gravitational force is superimposed on the equilibrium within the Cloud some of the stars are detached from the aggregate. The difference between the forces exerted by our galaxy on the nearest stars of the Cloud and those exerted on the most distant stars was unimportant when the Cloud was far away, but as it approached the Galaxy this force differential increased to significant levels. As the main body was speeded up by the increasing gravitational pull some stragglers failed to keep up with the faster pace, and once they had fallen behind, the force differential became even greater. The Cloud therefore left a luminous trail behind it marking the path alone, which it had traveled.

Galactic Trails: NGC 4038 & NGC 4039

Figure 1 Photo 1
Figure 1 Photo 1

This is no isolated phenomenon. Small galaxies may be pulled into larger units without leaving visible evidence behind, as the amount of material involved is too small to be detected at great distances, but when two large galaxies approach each other we commonly see luminous trails of the same nature as the one that has just been discussed. Figure 1 is a diagram of the structural details that can be seen in photographs of the galaxies NGC 4038 and 4039. Here we can see that one galaxy has come up from the lower right of the diagram and has been pulled around in a 90 degree bend. The other has moved down from the direction of the top center and has been deflected toward the first galaxy. When the action is complete there will be one large spiral moving forward to its ultimate destiny, leaving the stray stars trailing behind the galaxies to be pulled in individually, or be picked up by some other aggregate that will come along at a later time. Several thousand “bridges” that have developed from interaction between galaxies are reported to be visible in photographs taken with the 48-inch Schmidt telescope on Mount Palomar. Some of these are trailing arms similar to those in Figure 1. Others are advance units that are rushing ahead of the main body. The greater velocity of these advance stars is also due to the gravitational differential between the different parts of the incoming galaxy, but in this case the detached stars are the closest to the source of the gravitational pull and are therefore subject to the greatest force.

Irregularities of one kind or another are relatively common in the very small galaxies, but these are not usually harbingers of coming events like the gravitational distortions of the type experienced by the Magellanic Clouds. Instead, they are relics of events that have already happened. Capture of a globular cluster by a small galaxy is a major step in the evolution of the aggregate. Consolidation with another small galaxy is a revolutionary event. Since the relatively great disturbance of the galactic structure due to either of these events is coupled with a slow return to normal because of the low rotational velocity, the structural irregularities persist for a longer time in these smaller galaxies. The number of small irregular aggregates visible at any particular time is correspondingly large.

Although the general spiral structure of the larger galaxies is regained relatively soon after a major consolidation because of the high rotational velocities that speed up the mixing process, there are features of some of these structures that seem to be correlated with recent captures. We note, for instance that a number of spirals have semi-detached masses, or abnormal concentrations of mass within the spiral arms, that are difficult to explain as products of the recent development of the spiral itself, but could easily be the result of recent captures. The outlying mass NGC 5195 seemingly attached to one of the arms of M 51, for example, has the appearance of a recent acquisition (although there is some difference of opinion as to the true status of this object). The lumpy distribution of matter in M 83 gives this galaxy the aspect of a recent mixture which has not yet been thoroughly stirred; NGC 4631 looks as if it contains a still undigested mass; and so on.

A study of the “barred” spiral galaxies also leads to the conclusion that these objects are galactic unions that have not yet reached the normal form. The variable factor in this case appears to be the length of time required for consolidation of the central masses of the combining galaxies. If the original lines of motion intersect, the masses are no doubt intermixed quite thoroughly at the time of contact, but an actual intersection of this kind is not required for consolidation. All that is necessary is that the directions of motion be such as to bring one galaxy into the general vicinity of the other. The gravitational force then accomplishes the change of direction that is necessary in order to bring about a contact of the two objects. Where the gap to be closed by gravitational action is relatively large, the rotational forces may establish the characteristic spiral form in the outer regions of the combination before the consolidation of the central masses is complete, and in the interim the galactic structure is that of a normal spiral which a double center.

M51 Photo 3

M 51

  Photo 2

NGC 1300

Figure 2(a) shows the structure of the barred spiral galaxy NGC 1300. Here the two prominent arms terminate at the mass centers a and b, each of which is connected with the galactic center c by a bridge of dense material that forms the bar On the basis of the conclusions in the preceding paragraph, we may regard a and b as the original nuclei of galaxies A and B. the two aggregates whose consolidation produced NGC 1300. The gravitational forces between a and b are modifying the translational velocities of these masses in such a manner as to cause them to spiral in toward their common center of gravity, the new galactic nucleus, but this process is slowed considerably after the galaxy settles down to a steady rotation, as only the excess velocity above the rotational velocity of the structure as a whole is effective in moving the mass centers a and b forward in their spiral paths. In the meantime the gravitational attraction of each mass pulls individual stars out of the other mass center, and builds up a new galactic nucleus between the other two. As NGC 1300 continues on its evolutionary course, we can expect it to gradually develop into a structure such as that in Figure 2(b), which shows the arms of M 51. Figure 2(c) indicates how M 51 would look if the central portions of the arms were removed. The structural similarity to NGC 1300 is obvious.

Additional evidence of relatively recent captures will be developed in Chapter 8 after some further groundwork has been laid. Meanwhile the evolutionary pattern of the constituent stars of the clusters and galaxies will be defined, and it will be shown that the stellar evolution corresponds with the pattern of evolution of the galaxies, as described in this present chapter. All in all, the results obtained from these various lines of inquiry add up to an overwhelming mass of evidence confirming the validity of the theoretical process of galactic evolution beginning with dispersed matter and ending with the giant spheroidal galaxies.

This picture of continuous growth from globular cluster to spheroidal galaxy extending over a period of many billion years is in direct conflict with the prevailing astronomical view, which regards the galaxies as having been formed directly from dispersed matter in an early stage of an evolutionary universe, and having remained in essentially the same condition in which they were originally formed. The difference between this view and that derived from the Reciprocal System of theory is graphically illustrated by an argument offered by Shklovsky in support of the contention that a process of star formation must be operative in the Galaxy. He points out that at least one of the stars of the Galaxy “dies” each year in a supernova explosion, and then argues that “In order that the stellar tribe should not become extinct, just as many new stars on the average must be formed annually in our Galaxy.”19 While our findings portray the Galaxy as not only pulling in single stars on a continuous basis, but also periodically swallowing a globular cluster, and even an occasional small galaxy. Shklovsky is not even willing to concede the capture of one star per year.

The same viewpoint is reflected in the current tendency to try to explain the globular clusters detected in inter-galactic space as outgoing rather than incoming. These “intergalactic tramps,” says one text, “may actually be globular clusters that escaped from our Galaxy.”20 Even the halo stars surrounding the Galaxy tend to be regarded as escapees from the original galactic system rather than as incoming matter.

In a strange juxtaposition alongside this uncompromising orthodox view, there is a widespread and growing recognition of the prevalence of galactic cannibalism. For example, Joseph Silk tells us that “It seems that the giant galaxies have grown at the expense of other galaxies in their cluster,21 M. J. Rees elaborates on the same theme:

We can see many instances where galaxies seem to be colliding and merging with each other, and in rich clusters such as Coma the large central galaxies may be cannibalizing their smaller neighbors… Many big galaxies—particularly the so-called CD galaxies in the centers of clusters—may indeed be the result of such mergers.22

There is also an increased willingness to recognize the observational indications of galactic collisions. After a number of years during which the collision hypothesis applied earlier to such powerful radio emitters as Cygnus A was regarded as a mistake, it has resurfaced, and is now widely accepted. We now frequently encounter unequivocal statements such as this: “Several hundred collisions or near collisions between galaxies have been photographed in the past 20 years.23

The concepts of galactic cannibalism, of galaxies “growing,” of “capture,” and of “collision,” are the concepts appertaining to the theory developed in this work, not to the theory currently accepted by the astronomers. Whether or not the investigators who are using these concepts realize that they are striking at the foundations of orthodox theory is not clear, but in any event, that is the effect of the present trend of thought. These present-day investigators and theorists are providing an increasing amount of significant support for the conclusions detailed in this volume.

One more question about the aggregation process remains to be considered. We have found thus far in our examination of this process that the original stellar aggregates, the globular clusters, enter into combinations, which continue growing until they reach the status of giant spheroidal galaxies. The question now arises, is this the end of the aggregation process, or do the galaxies combine into super-galactic aggregates? The existence of many definite groups of galaxies with anywhere from a dozen to a thousand members would seem to provide an immediate answer to this question, but the true status of these groups or clusters of galaxies is not as evident as that of the stars or the galaxies. Each of the stars is a definite unit, constructed according to a specific pattern from subsidiary units that are systematically related to each other. The same can be said of the galaxies. It is by no means obvious, however, that this statement can be applied to the clusters of galaxies. So let us turn to a theoretical examination of the question.

The globular cluster, we found, originates as a contracting aggregate of diffuse matter in which numerous centrally concentrated sub-aggregates are forming. Because of their central concentration these sub-aggregates, which eventually become stars, meet their neighbors at locations of minimum gravitational effect, and their net movement is therefore outward away from each other. Dispersed aggregates of near uniform density, on the other hand, meet their neighbors at locations where the gravitational effect is at a maximum. They exist as separate entities only because of competition between the various centers, which limits each aggregate to the minimum stable size. When open space is made available by reason of contraction of the individual units, these aggregates, the globular clusters, move inward toward each other.

If we now consider a still larger volume of space, there are no large-scale aggregates corresponding to the stars; that is, centrally concentrated aggregates that are outside the gravitational limits of their neighbors. But in their original condition, the assemblage of globular clusters constitutes a dispersed aggregate similar to the dispersed aggregate of gas and dust particles, but on a larger scale. Applying the same principles as before, we can deduce that there exists a gravitationally determined limiting size of the aggregates of clusters (which we will call groups) corresponding to the limiting size of the aggregates of gas and dust (the globular clusters). We could continue this hierarchy of aggregates, and contemplate an aggregate of groups, but before this next level of structure has time to materialize, the life span of the constituent stars has terminated. Thus the groups of globular clusters, which eventually become groups of galaxies, are the largest structural units. The hierarchical theory, in which there are clusters, clusters of clusters, and so on indefinitely, is thus excluded. This theory has maintained a certain amount of support in astronomical circles over the years, but on the basis of the foregoing findings it is no longer tenable.

The theoretically defined groups of galaxies are not necessarily, or even usually, coincident with the currently recognized aggregates called clusters of galaxies The members of each of the classes of aggregates that we have defined, clusters and groups, are moving inward toward each other. The inward motion of the smaller units, the clusters, is much the faster. It follows that the net motion of the outer clusters of adjoining groups carries them away from each other, even though the groups of which they are components are moving inward. Consequently, the amount of empty space between groups continually increases. Ultimately the inward motion of the groups would reverse this trend, if it continued, but before this can happen the time limit intervenes.

Inasmuch as the new groups form in the regions of space left empty by the recession or disintegration of previously existing groups of galaxies—the “holes” in space reported by the astronomers—the sizes of the resulting aggregates of galaxies are determined by the sizes of the vacant spaces. This is a matter of chance, and the individual values are no doubt distributed over a considerable range, but we can conclude that there is an average size, probably including some hundreds of visible galaxies and many hundreds of invisible dwarfs, to which most aggregates will conform approximately, with a relatively small number substantially above or below this average.

On this basis, the largest units in which gravitation is effective toward consolidation of its components are the groups of galaxies. Each such group is formed jointly with a number of adjoining groups. These groups begin separating immediately, but until the outward movement produces a clear-cut separation, their identity as distinct individuals is not apparent to observation. Here, then, is the explanation of the large “clusters” and “superclusters” of galaxies. These are not structural units in the same sense as stars or galaxies, or the groups of galaxies that we have been discussing. Each consists of a number of independent groups, formed simultaneously in the same general region of space, and separating so slowly that the processes of galaxy formation and growth are well under way before the units have moved far enough apart to be recognized as separate entities. Some of the mathematical aspects of these cluster relationships will he explored further in Chapter 15 .

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