Thus far we have been concerned with the globular clusters and their successors as aggregates of stars. Now we will turn our attention to the individual stars of which these aggregates are constructed. As we saw in Chapter 1, the stars originate as dust and gas clouds. There is no clear line between dust cloud and star. Until comparatively recently stars could be detected only by means of their radiation in the visible range, and this established a low limit at about 2500 K. During the last few decades instruments of greatly extended range have been developed, and stars of normal characteristics are now being observed down to the neighborhood of 1000 K. Infrared objects of a nature not yet clearly determined, with surface temperatures as low as 300 to 700 K, have been reported.
From theoretical considerations we deduce that at some point after the interior of a contracting cloud of dust and gas has been raised to a high temperature by gravitational energy, a relatively rapid rise in the temperature of the entire aggregate occurs when the destructive limit of the heaviest element present is reached in the central regions, and conversion of mass to energy begins. As explained in Volume II, both the thermal energy of the matter in the star and its ionization energy are space displacements, and when the total of these space displacements reaches equality with one of the rotational time displacements of an atom, the opposite displacements neutralize each other, and the rotation reverts to the linear basis. In other words, both the ionization and a portion of the matter of the atoms are converted into kinetic energy. Inasmuch as all atoms are fully ionized before the temperature limit is reached, and the heavier atoms are capable of acquiring a greater degree of ionization than the lighter ones, the amount of thermal energy required to bring the total space displacement up to the limit is less for the heavier elements. The limiting temperature is therefore inversely related to the atomic mass.
Production of increasingly heavier elements is a continuing process that begins with the original entry of primitive matter from the cosmic sector. The pre-stellar dust cloud therefore contains a small proportion of newly formed heavy elements, together with whatever heavy element content there may have been in the fragments of older matter incorporated from the surroundings. Inasmuch as the entire structure of the cloud is fluid, the heavy elements make their way to the center. As the temperature in the central regions rises, successively lighter elements reach their destructive limits and are converted to energy.
Activation of this second energy source necessitates an immediate and substantial increase in the temperature of the aggregate in order to produce enough radiation to reach equilibrium with the greater energy generation. Thus there is not a gradual rise of the surface temperature of the aggregate from the near zero of inter-stellar space up to the levels recognized as those of stars, but rather a long period of no more than minor warming, followed by a quite sudden jump to the temperature of an infrared star. The objects cooler than 1000 K generally display some peculiar characteristics that distinguish them from normal stars, and make it difficult to draw definite conclusions as to their true nature.
The most significant evolutionary changes that take place in the stars, as they grow older can conveniently be shown on a graph in which the luminosity (expressed as magnitude) is plotted against some measurement representing the surface temperature. In its original form, this Hertzsprung-Russell, or HR, diagram utilized an arbitrary spectral classification as the temperature variable, but the present tendency is to use a color index, which accomplishes the same result. The textbooks still retain the H-R diagram, probably for historical reasons, but the color-magnitude, or CM, diagram is now in general use by the observers.
The CM diagram of the globular cluster M3 is shown in Figure 3. In this diagram the points representing the magnitudes applicable to the individual stars fall mainly within the crosshatched area. Identification of the locations marked O, A, B and C has been added to the conventional diagram for purposes of this present discussion.
The mass, density, and central temperature of the globular cluster stars are related to the variables of the CM diagram, and although they are subject to modification by other factors, so that they cannot be represented accurately in this two-component diagram, they can be located approximately, and adding them to the framework of the diagram for reference purposes facilitates understanding of the theoretical development. Accurate measurements of magnitudes in the area of the diagram occupied by the globular cluster stars are difficult to obtain. S. J. Inglis points out that “There is no red giant whose mass we know with any degree of certainty.”36 But we can relate these magnitudes to the evolutionary pattern of the stars, and thus arrive at approximations of their values.
We know, for instance, that the line BC, the main sequence, is the location of gravitational equilibrium. The stars on this line are therefore at approximately the same density. The density at C is actually greater than that at B by a factor of 3 or 4, because of the compression due to the larger stellar mass, but since the equilibrium densities along the main sequence are more than a million
times greater than those in the early portions of area O. the difference between B and C is negligible on the scale of the diagram. We may therefore draw lines parallel to BC and treat them as lines of equal density for analytical purposes. Similarly, the line AB theoretically represents a condition of constant mass. The theory further indicates that the central temperatures are determined by the stellar mass. Lines parallel to AB can thus be regarded as lines of equal mass and central temperature. On the basis of the explanation of the line AC that will be developed in the following pages, this line represents a condition in which condensation of a dust cloud of nearly uniform density is proceeding at a rate determined by gravitational forces. We may call it a line of constant growth.
Figure 4 is a reproduction of the M 3 diagram with the lines representing these other variables added. These lines provide a good indication of the way in which the several variables are related in different regions of the diagram, and reference to the pattern of this illustration will be helpful in interpreting the CM diagrams that will be introduced later. The relations represented by the auxiliary lines in Fig. 4 apply to the stars of the globular cluster type only. As we will see later, the corresponding relations—the lines of equal mass, for instance—are altogether different for other classes of stars. This is a fact that has not heretofore been recognized, an oversight that is responsible for many
errors in the orthodox interpretations of the CM diagrams.
All of the stars of a globular cluster condensed from the same dispersed aggregate of primitive material, but the conditions affecting the rate of condensation varied, and the evolutionary stages of the stars therefore differ. Consequently, the stars of a cluster such as M 3 are spread out over a range of the stellar evolutionary pattern on the CM diagram. The earliest of the visible stars are the coolest but, by reason of the immense area from which they are radiating, their luminosity is relatively high. These stars therefore occupy positions in the upper right of the diagram, in the general area marked O. The remainder of this chapter will give a general description of the paths that these stars follow when they leave this area. Further details will be added in Chapter 8, after some additional groundwork has been laid.
The stars of these globular clusters exist in two size ranges. The great majority are small, in the neighborhood of the solar mass or below. Another portion of the total consists of stars that are substantially larger. We can identify the latter as stars that had a fragment of preexisting material as a nucleus for condensation of the pre-stellar dust and gas cloud. The smaller stars are those that did not enjoy this advantage. The fragments incorporated into the stars were usually small, as the explosions that scattered them into space were violent enough to reduce the greater part of the original structure to dust, gas, and small aggregates. The growth of the stellar structure follows essentially the same course whether or not it contains a small fragment as a nucleus. The important difference is that it takes a very long time to build a dust particle up to an aggregate of fragment size. A pre-stellar aggregate that has a fragment to start with therefore has a big head start over those that have to build all the way from dust particles, and it is able to establish gravitational control over a larger volume of the protocluster. Thus, even though the stars of both of these groups are nearly alike at their points of origin in area O, those of one group have a much greater potential for growth.
The supply of dust and gas available for capture is, in effect, exhausted for the first group by the time they reach the vicinity of point A. These stars then cease to grow, and they no longer continue on the path OC. Instead they make a sharp turn and move downward on a relatively steep slope, reaching gravitational equilibrium on the main sequence at point B. Along the path AB the gravitational contraction continues, but because the mass is no longer increasing, the central temperature remains approximately constant. The decrease in the size of the radiating surface results in an increase in the surface temperature, but coincidentally the corresponding increase in density increases the resistance to the flow of heat from the center of the star to the surface. These two oppositely directed processes just about counterbalance each other, and the net result, including the effect of the energy contributed by the contraction, is a small increase in surface temperature. The combination of a decrease in the radiating surface and a relatively small temperature change results in a rapid decrease in the luminosity.
With the benefit of this information as to the nature of the changes that take place along the evolutionary path OAB of the small stars, it can now be seen that the stars on the path OAC are subject to the same factors, except that there is a continuous addition of more matter, and a consequent increase in the central temperature. As a result, the increase in surface temperature is much greater than that along the line AB, and the decrease in luminosity is smaller, leading to a nearly horizontal movement across the CM diagram.
Arrival at the main sequence, at either point B or point C, eliminates any further generation of energy from gravitational contraction. Each star then has to establish a thermal equilibrium on the basis of the atomic energy generation alone. For this purpose it moves up or down the main sequence to the point where the dissipation of energy by radiation is in balance with the energy production. The main sequence is the location where the stars spend most of the latter part of their lives. It has been estimated that about 95 percent of the observable stars are on this sequence (although it should be understood that the observable stars do not constitute a representative sample of the stars as a whole). For convenient reference in the subsequent discussion we will designate the stars on the evolutionary paths OAB or OAC as Class A, and those of the main sequence as Class B. The stars of Class A and Class B coincide, in general, with those currently called Population II and Population I respectively. The reason for the reversal of the sequence is that it puts the classes into the correct evolutionary order. The younger stars are currently called Population II. The A classification is more appropriate.
In the context of the star and cluster formation process deduced from the postulates that define the universe of motion, the foregoing explanation of the CM diagram of the globular clusters is essentially self-evident, but the astronomers cannot take this simple and logical view of the situation. They did so in an earlier era, but they have changed their ideas. As one author states, “Present knowledge has forced a nearly complete reversal of this view.” This “knowledge,” he says, is partly observational and partly theoretical. The “observational” items that he cites are (1) “red giants are common in globular clusters and elliptical galaxies, systems which are known to be of great age… and in which star formation has ceased countless ages ago,” and (2) “red giants do not appear in greater numbers in the nebulous regions of the Galaxy, as they would certainly do if they had been formed recently from the great gas and dust clouds of space.”37
As can easily be seen, these so-called “observational” items are, in fact, purely theoretical. Their application to the points at issue depends entirely on the prevailing theories of stellar formation and of stellar ages. As long as the astronomers were basing their conclusions on the evidence from their own field, they arrived at an understanding of the evolutionary course of the globular cluster stars very similar to that which we now derive from the Reciprocal System of theory. But it became evident that this conclusion is inconsistent with the physicists contention that the stellar energy is generated by the hydrogen conversion process (this is the “present knowledge” cited in the quotation above). This pure assumption by the physicists is the only basis for the assertion that the globular clusters “are known to be of great age.” There is no astronomical basis for that conclusion. But since the astronomers are unwilling to challenge the physicists assertions, they have, as indicated in the quoted comment, “completely reversed” their own ideas, and have accommodated their theories to the requirements of the hydrogen process.
On this basis, the stars of the globular clusters are old stars. The evolutionary path obviously has to start in region O of the diagram, since the protostars are necessarily diffuse and cool. It is generally recognized that the red giant stars of the globular clusters are stars of the same type as the protostars. Shklovsky, for instance, concedes that the massive protostars in a late stage of their evolution “have all the characteristics of giant stars.”38 But since the astronomers now see the red giants of the globular clusters as old stars they cannot accept the conclusion that these are identical objects.
As a consequence of this inability to recognize the identity, astronomical theory first has to put the stars through the evolutionary process as protostars, and then, after a hypothetical sojourn on the main sequence, bring them back for another experience as giant stars. These giants then have to make their way, in some, as yet unexplained, manner, directly from their position in region O of the CM diagram to the region of the early white dwarfs, which is located in the diametrically opposite corner of the diagram. As expressed by L. H. Aller in an understatement of classic proportions, “the details of its [the giant star’s] evolution are uncertain.”39
When the stars of the globular clusters and dwarf galaxies are recognized as relatively young objects, only one step beyond the dense dust cloud, or protostar, stage, the necessity for these contortions in the theoretical evolutionary path is eliminated. The infrared protostars are precursors of the red giants; they are already giants and on the way to becoming red. From this cool and diffuse state they follow one or the other of the two alternate paths to gravitational equilibrium on the main sequence.
After a star has achieved both gravitational and thermal equilibrium, and has settled down to a somewhat stable condition, its subsequent course depends on the environment. If this environment is relatively free from dust and gas, the star may not be able to generate enough energy to replace that lost by radiation, because of a shortage of heavy elements. In that case it moves slowly down the main sequence to the point where the radiation has been reduced enough to balance input and output. Whether or not this movement ever continues far enough to lower the central temperature below the lowest destructive limit, so that the star loses its energy supply and ceases to be a star, is not clearly indicated at the present stage of the theoretical development. As matters now stand, however, it seems probable that any aggregate that is once able to attain the stellar status on the main sequence will remain a star.
The continual replenishment of the supply of heavy elements by means of the atomic building process described in Volume II is an important factor in this situation. It plays a major role even where there is a significant amount of accretion, as there is only a very small proportion of heavy elements in the accreted matter. Since the amount of atom building is proportional to the mass of the aggregate, the same rate of heavy element formation that maintains the stellar status of the smaller stars is sufficient to add materially to the fuel supply of a larger star.
The automatic reduction in the amount of radiation which takes place in response to a decrease in the generation of energy enables a star to adjust to a rather wide range of environmental conditions, and since changes in these conditions occur only on an extremely long time scale, many of the main sequence stars maintain approximately the same pattern of thermal behavior for extended periods of time (fortunately for the human race). But accretion from the environment plays a very important part in the general evolutionary picture in the globular clusters the growth comes entirely, or almost entirely from the remaining portions of the original pre-stellar dust and gas cloud. But accretion of matter also takes place from whatever environments the stars enter after consolidation of the original dust and gas is complete. Such accretion is common in the post-globular cluster stages, and has a significant effect on many astronomical phenomena, as we will see in the pages that follow.
For reasons that will be discussed in Chapter 8, the accretion by the average star in the outer regions of a spiral galaxy exceeds the losses due to radiation, and this star therefore moves up the main sequence. Stars in regions of greater dust and gas concentrations evolve still more rapidly, and the process also speeds up, as the stars become more massive, since the stronger gravitational forces draw material from larger regions of space.
As the stars increase in mass, the central temperatures increase accordingly, and successively higher destructive limits are reached, making additional elements available as fuel for the energy generation process. Since none of the heavy elements is present in more than a relatively small quantity in a region of minimum accretion, the availability of an additional fuel supply due to reaching the destructive limit of one more element is not sufficient to cause any significant change in the energy balance of the stars in the lower half of the main sequence. The rate of accretion increases as the stars move up the sequence, but because of the corresponding increase in mass and total energy content, they are able to absorb greater fluctuations. The main sequence stars are therefore relatively quiet and unspectacular as they gradually make their way along the evolutionary path.
The chemical composition of the stars and the distribution of elements in the stellar interiors are debatable subjects, but the deductions that have been made from the principles established in the earlier development of theory do not conflict with actual observations; they merely conflict with some interpretations of those observations. While the gravitational segregation of the stellar material which theoretically puts a high concentration of the heavier elements into the central core is not entirely in agreement with current astronomical thought, it should be emphasized that such a segregation is the normal result in a fluid medium subject to gravitational forces, and a theory which requires the existence of normal conditions is never out of order where the true situation is observationally unknown.
Furthermore, even though the conclusions that have been reached as to the amount of heavy elements present in the stellar interiors are beyond the possibility of direct verification, it will be brought out in the subsequent discussion of the solar system that some strong evidence as to the internal constitution of the stars can be obtained from collateral sources. Current ideas as to stellar composition are based almost entirely on spectroscopic information. These data are useful, but they have a limited applicability, as they only tell us what conditions prevail in the outer regions of the stars. Even from this restricted standpoint the evidence may actually be misleading, as the spectroscopic results are affected to a significant degree by the character of the material currently being picked up through the accretion process. The observed differences in the stellar spectra that can be attributed to variations in chemical composition are probably more indicative, in many cases, of the environments in which the stars happen to exist at the moment than of the true composition of the stars themselves.
The presence of substantial amounts of elements such as technetium, for example, in the outer regions of some stars poses a formidable problem if we are to regard this as an actual indication of the composition of the stars. It is doubly difficult for present-day astronomical theory. If the technetium is manufactured in the regions of maximum temperature in the center of each star, in accordance with the majority opinion at the moment, there is a serious problem in explaining how this material gets to the surface against the density gradient. L. H. Aller makes this comment:
How the star gets the heavy elements from the core to the surface without exploding provides an impressive challenge to theoreticians.40
Shklovsky regards this emergence from the central regions as impossible, and contends that “Only nuclear reactions in the surface layers of the stars can account for the presence of technetium lines in type S stellar spectra.”41 But this merely replaces one question with another. Just how the conditions necessary for initiating atomic reactions can be attained in these surface layers is an equally difficult problem. On the other hand, the technetium content at the surface of the star is easily explained on the basis that the observed amounts of this material have been derived from the captured material. This element is stable, according to the findings detailed in Volume II, wherever the magnetic ionization level is zero, and relatively heavy concentrations could be produced in areas that are left undisturbed for long periods of time.
As indicated earlier, the gradual and uneventful progress of the growing stars up the main sequence is due to the relatively small size of the increments of energy that result from the attainment of the destructive limits of successively lighter elements. When the destructive limit of nickel is reached there is a change in the situation, as this element is present, both in the stars and in the interstellar matter, in quantities that are substantially greater than those of any heavier element. It could be expected, then, that the attainment of this temperature limit would result in some observable enhancement of the thermal activity of the stars that are involved. Such increased activity is observed in a special class of stars located near the top of the main sequence.
These Wolf-Rayet stars are somewhat less massive than the stars of the O class, the highest on the main sequence, but they have about the same luminosity, and they are associated with the O stars in the disk of the Galaxy. Their principal distinguishing characteristic is a very disturbed condition in their surface layers, with ejection of material that forms an expanding shell around each star. These special conditions lead to the existence of a distinctive spectrum. It appears probable that the Wolf-Rayet star is the one whose central temperature has reached the destructive limit of nickel. We may interpret its observed characteristics as indicating that arrival at this temperature limit has resulted in an increase in the production of energy that is large enough to cause violent internal activity, and ejection of matter from the star, without being enough to initiate a full-scale explosion. On this basis, the star remains in the Wolf-Rayet condition until the greater part of the nickel is consumed. It then resumes accreting mass (probably picking up most of what was ejected) and reverts to the O status.
The foregoing comments on the Wolf-Rayet stars apply only to those known as Population I Wolf-Rayets. The Wolf-Rayet designation is also applied to some of the central stars of planetary nebulae, but there is little justification for putting these two groups of stars into the same class. This issue will be discussed in Chapter 11.
When the temperature corresponding to the destructive limit of iron is reached, the situation is more drastically changed. This element is not limited to very small quantities, or even to moderate quantities like the nickel content. It is present in concentrations, which represent an appreciable fraction of the total stellar mass. The sudden arrival of this quantity of matter at its destructive limit activates a source of far more energy than the star is able to dissipate through the normal radiation mechanism. The initial release of energy from this source therefore blows the whole star apart in a tremendous explosion.
According to current estimates, iron is more than 20 times as abundant in the stars as nickel. If the amount of nickel is sufficient to bring the star to the verge of an explosion, as the behavior of the Wolf-Rayet stars appears to indicate, the amount of iron is far more than is needed in order to cause an explosion. The explosion thus takes place as soon as the first portions of this element are converted into energy. The remainder, together with the overlying lighter material, is dispersed by the explosive forces. The carry-over of material from one cycle to the next enables the amount of iron and lighter elements to continue building up as the age of the system increases, whereas the heavier elements have to start from scratch after the explosion, except for some limited quantities of the elements close to iron that have escaped destruction. This accounts for what George Gamow called the “surprising shape of the empirical curve [of abundance of the elements],”42 the existence of distinctly different patterns above and below iron.
The explosion that theoretically occurs at the destructive limit of iron is consistent with observation, as it can be identified with the observed phenomenon known as a Type I supernova. However, the characteristics of the supernova explosion, as derived from theory, conflict, in some respects, with current astronomical opinion. One of these conflicts concerns the kind of stars that are subject to becoming Type I supernovae. Inasmuch as the temperature of a star is a function of its mass, the temperature limit at which the explosion takes place is also a mass limit. According to our theory, then, the stars that reach the destructive temperature limit and become Type I supernovae are hot massive stars, and they are all nearly alike.
The astronomers concede the existence of a stellar mass limit. Since there is a recognized relation between stellar mass and temperature along the main sequence, the existence of a mass limit carries with it the existence of a temperature limit, as required by the theory of the universe of motion. Neither limit has an explanation in terms of conventional astronomical theory, and the observed cut-off in the mass distribution function was unexpected. “It is a surprise,” say Jastrow and Thompson, “that there also appears to be an upper limit to the mass of a star.”43 These authors put the limit at about 60 solar masses. Other observers place it at about 100.
The astronomers also admit that all Type I supernovae are very much alike. The observations of these phenomena are thus consistent with our theoretical findings. Furthermore, the temperature limit can be reached in any galaxy, and Type I supernovae should therefore occur in all classes of galaxies. They are the only kind that can occur regularly, according to our findings, in elliptical and small irregular galaxies. Spirals, such as our Milky Way, and the giant spheroidal galaxies, contain both Type I and Type II supernovae, which result from a different kind of stellar explosion that we will examine in detail in Chapter 16. As we will see there, the Type II explosion is the result of reaching an age limit. Except where some stray old star has been picked up by a young aggregate, stars cannot reach the age limit in young galaxies. This accounts for the observed restriction of the Type II supernovae to the older and larger galaxies. All that is known about the Type I supernovae is thus entirely consistent with the theory of the universe of motion.
On the other hand, the observations are almost totally inconsistent with conventional astronomical theory. The astronomers have been almost completely baffled by the supernova phenomenon. Most investigators are reluctant to admit that they are up against a blank wall, and tend to describe the situation in ambiguous terms, such as the following, taken from a recent report on one aspect of the supernova problem: “The exact mechanism by which a star becomes a supernova is not yet known.”44 The insertion of the word “exact” into this statement implies that the general behavior of the supernovae is understood, and that only the details are lacking. But the truth is that the astronomers have nothing but speculations to work with, and some of the more candid observers admit this. R. P. Kirshner, for instance, concedes that the “models” thus far proposed for the origin of supernovae are no more than speculative, and adds this comment:
The train of events leading to a supernova of Type I is more mysterious than that leading to one of Type II, since a Type I supernova is expected to be the explosion of a star about as massive as the sun. Since such a star can comfortably settle down to being a white dwarf, something unusual must happen for it to explode as a supernova.31
This is a good example of the problems in astronomy that have been created by the elevation of the physicists assumption as to the nature of the stellar energy process to a status superior to that of the astronomical observations. As Kirshner brings out in his statement, the Type I supernova is mysterious not so much because little is known about it, but because that which is known from observation conflicts with two items that are “known” from deductions based on generation of energy by the hydrogen conversion process. The conclusion that a star of about one solar mass can “comfortably settle down to becoming a white dwarf” is wholly dependent on the status of the red giants as old stars. This, in turn, is based entirely on the assumption as to the nature of the energy generation process. The further conclusion that these “old” red giants develop into white dwarfs rests on the equally unsupported assumption that the white dwarfs are still older than the red giants, and that there must be some progression from one to the other. The astronomical evidence disproving these assumptions will be presented at appropriate points in the subsequent pages. The fact now being emphasized is that Kirshner’s “mystery” is simply a conflict between the astronomical observations and the consequences of the physicists assumption that the astronomers accept as gospel.
The same conflict exists with respect to the other item of “knowledge” cited by Kirshner, the identification of the Type I supernova with the explosion of a star of about one solar mass. This is another conclusion that rests entirely on the physicists hydrogen conversion hypothesis. On the basis of this hypothesis, it has been concluded that the stars of the elliptical galaxies and small irregulars are very old. Conventional theory indicates that the more massive stars (which, according to the theory, are short-lived) would have been eliminated from these old aggregates by evolutionary processes. The deduction, then, is that “before their outburst type I supernovae were very old stars whose mass was at most only slightly (say 10 to 20 percent) greater than the mass of the sun.”45
But this does not fit into the rest of conventional astronomical theory at all. As P. Maffei puts it, “This result has caused some problems to theoreticians.”46 Kirshner points out that the supernova explosion is not the fate that present-day theory predicts for the small stars. Furthermore, the identification of the supernovae with the small stars, whose mass varies over a wide range, leaves the theory without any explanation for one of the few things about the Type I supernovae that definitely is known; that is, these explosions are all very much alike.
In the light of the points brought out in the foregoing paragraphs, it is evident that the astronomers cannot legitimately claim to have a tenable theory of supernovae. In this case, then, as in so many of the others that have been, or will be, discussed in this volume, the deductions from the theory of the universe of motion are simply filling a vacuum, providing explanations that conventional astronomical theory has been unable to supply.