CHAPTER 12
Ordinary White Dwarfs
The previous discussion of the white dwarf stars has been directed at the products of the Type I supernovae, the explosions that take place at the temperature limit to which matter is subject. As already mentioned, a similar explosion, known as a Type II supernova, takes place when matter reaches an age limit. This is intrinsically a more violent process, and in its extreme manifestations it produces results that are quite different from those of the Type I supernovae. Discussion of these results and the manner in which they are produced will be deferred to the later chapters. At this time we will want to note that under less extreme conditions the results of the Type II supernovae are identical with those of Type I, except that the products are smaller.
The explanation is that the unique character of the products of the extreme Type II supernovae is due to the ultra high level of the speed imparted to these products by the combination of a large explosion (that is, one involving a large star) and an extremely energetic process. The products of Type I supernovae do not reach this speed level, even though the exploding star is one of maximum size, because the process is less violent. Similarly, the products of a Type II supernova do not reach the ultra high level if the exploding star is small, even though they have the benefit of the very energetic process.
Although the age limit can be reached by stars of any size, and the white dwarf products of Type II explosions extend through a wide size range, the great majority of those that exist in the outer regions of the galaxies are small, simply because the great majority of the stars in these regions are small. Many of these small white dwarfs are below the minimum size of 1.1 solar masses that applies to the central stars of the planetary nebulae. Our next objective will be to examine the evolutionary course of these smaller stars, ordinary white dwarfs, as we will call them.
As we saw in Chapter 11, the 1.1 lower mass limit of the planetary nebula region is the white dwarf mass below which the energy content of the star is not sufficient to maintain a gaseous structure in gravitational equilibrium. This is analogous to the critical density of the giant stars. It should be understood that the term “giant” refers to the volume, not to the mass. Most of these giants are low mass stars. Such stars, whose first stage of evolution carries them along the path OA, are unable to reach the critical density in the dust cloud (gaseous) condition, and have to call upon the compressive forces of the aggregate in which they are located to aid in developing a compact, gravitationally stable, core in order to increase the average density to the required level. What exists here is a situation in which the inward-directed forces operate to force the matter of the star into a gravitationally stable condition. When the star is too small for this condensation to take place in a single operation, applicable to the star as a whole, it proceeds on a two-component basis, in which one component, the central core, is compressed to the condensed gas state, while the remainder of the stellar aggregate continues on the gaseous basis, gradually converting to condensed gas as the star moves down toward the main sequence.
In the case of the white dwarfs there is no gravitational problem, as the white dwarf aggregate is always under gravitational control, but the smaller stars those with masses less than 1.1 solar units, do not have enough energy content to maintain the surface temperature at 100,000 K in the gaseous state. Hence they, too, have to proceed on a two-component basis, developing a condensed gas component like that of the smaller stars of the giant class. However, the fact that the motion of the constituents of the white dwarf is in time rather than in space introduces some differences. Because of the inverse density gradient in the white dwarf stars this relatively heavy condensed gas component takes the form of an outer shell, rather than that of an inner core. Then, the presence of this shell reduces the radiation temperature to that of a condensed gas surface. This is the same surface condition that exists along the line B’B, the 30,000 K temperature line of the planetaries. Thus the 100,000 K line above point A’ becomes a 30,000 K line below that level.
The existence of an outer shell has been recognized observationally, but because of the prevailing theory of white dwarf structure this has been interpreted as a zone of ordinary matter surrounding the hypothetical degenerate matter of which the white dwarf, according to current astronomical theory, is composed. Greenstein reports that there is a non-degenerate envelope about 65 miles deep.135 On the basis of our findings, the thickness of the shell at the time of entry into the observable region depends on the size of the star. A white dwarf just below the critical 1.1 mass needs only a thin shell, but the required thickness increases as the mass of the star decreases.
As brought out in Chapter 11, the central star of a planetary nebula moves down the CM diagram along the line A’B’, or a parallel line above it, to the level at 30,000 K where the energy content of the outer thermal units of this gaseous aggregate is on the boundary between motion in time and motion in space. Here the transition from units of temporal motion to units of spatial motion takes place. But since the ordinary white dwarfs have to develop an outer shell of condensed gas before they become observable, the energy content of their outer thermal units is already below the unit speed boundary. A transition to motion in space on the basis of the full-sized unit is therefore impossible. These small stars have to cool to a lower critical temperature at which their outer thermal units are at the level of the smaller compound units of the condensed gas state, a state in which the atoms occupy equilibrium positions inside unit distance, in what we have called the time region.
The 30,000 K and 100,000 K temperatures along the line at the left of the CM diagram are critical values in the sense in which this term was used in the discussion of the luminosity scale of the diagram. We may therefore deduce by analogy with the situation in the region above the main sequence that the drop from 100,000 K to 30,000 K at the point A’ involves one of the compound natural units of luminosity. The 30,000 K equivalent of the line APB’ is then a parallel line one unit lower in the diagram. This line constitutes the lower boundary of the zone occupied by the ordinary white dwarfs.
Above point A’ the constituents of the white dwarf stars are moving freely in time; that is, they constitute gaseous aggregates in time. It follows that they radiate from the surface corresponding to an inverse volume. The more massive stars of this group (the hot subdwarfs and the planetary stars) have the greater inverse volume and are therefore the more luminous. Below point A’ the outer layers of the stars are in the condensed gas state, in which they are confined within limited volumes of space. These stars radiate from the spatial surface, the surface corresponding to a direct volume. The more massive stars of this class have the larger inverse volume, and therefore the smaller direct volume (a theoretical conclusion that, as we have noted earlier, is confirmed observationally). Consequently, they are less luminous than the smaller stars of the same class.
There may be some question as to why there should be a difference between the radiation pattern of the gaseous state and that of the condensed gas state when the motion is in time, since we do not encounter any such difference in dealing with motion in space. The stars on or above the spatial main sequence radiate in space regardless of their physical state. The answer to this seeming contradiction is that condensed gas aggregates radiate in time if they are condensed in time, whereas they radiate in space if they are condensed in space. The outer shells of the white dwarfs condense in space.
From their initial locations along the entry line, the cooling ordinary white dwarfs move down the CM diagram along lines parallel to the spatial main sequence in the same manner, and for the same reasons, as the planetary stars, within the relatively narrow band between APB’ and the lower zone boundary. Since the radiation from these stars is in space, the color-temperature relation applicable to this radiation is the same as that which applies to the stars of the spatial main sequence. The evolutionary lines of the ordinary white dwarfs therefore continue to their individual temperature limits, rather than terminating at the extension of the low temperature limit of the planetaries.
Consideration of the question as to the location of these low temperature limits of the ordinary white dwarfs will be deferred to the next chapter. At this time we will merely note that the evolutionary lines followed in the cooling of these stars do not reach the position of the lower portion of the spatial main sequence, which bends sharply downward beyond 4000 K. James Liebert reports that there is a cut-off between magnitudes 15 and 16. This fact that the range of the white dwarfs stops short of the main sequence has come as an unwelcome surprise to the astronomers. Greenstein makes this comment:
An anomaly has been found in the number and relative frequency of cool, red white dwarfs. It has been expected that these would be very common, but, in fact, objects more than 10,000 times fainter than the sun are rare.136
Main sequence dwarfs are observed all the way down to about magnitude 19, and it has been anticipated that the white dwarf population would extend to comparable levels. The observed cut-off at a higher luminosity confronts astronomical theory with an awkward problem. The evolutionary sequence, according to orthodox ideas, is protostar to main sequence star to red giant to white dwarf to black dwarf. One of the biggest problems that arises in the attempts to reconcile this theoretical sequence with the observations is how to account for the changes in mass that are required if this sequence is followed. As already noted, the theorists are experiencing major difficulties in accounting for the reduction in mass that is necessary if the red giant is to evolve into a white dwarf. They have no explanation at all for an increase in mass during the evolution of the star. The existence of main sequence stars smaller than the white dwarf minimum thus puts them into a difficult position. Liebert, arguing from the premises of accepted theory, states that the observed cut-off implies either (1) an error in the calculations, or (2) a decreased white dwarf birthrate about 1016 years ago.137
In the context of the theory of the universe of motion aggregates of intermediate speed matter are produced in all sizes from the maximum downward. But the smaller aggregates are unable to complete their consolidation into single compact entities. As explained in Chapter 7, in connection with the formation of planetary systems, the pattern of gravitational forces in the aggregates of intermediate speed matter favors complete consolidation of the larger aggregates, but becomes more favorable to multiple products as the total mass decreases. On this basis, the reason for the absence of white dwarfs below a mass of about 0.20 solar units is not that white dwarf aggregates of smaller sizes do not exist, but that these smaller aggregates are not able to complete their consolidation, and remain as groups of objects of less than stellar size.
The existence of this lower mass limit applying to the white dwarfs is one of the reasons for the big difference in luminosity between the planetary stars and the ordinary white dwarfs that has puzzled the observers. As Richard Stothers puts it, there is a “luminosity gap” between the coolest planetary star and the hottest of the ordinary white dwarfs.138 Some attempts have been made to explain this gap in terms of stellar composition. Greenstein, for instance, tells us that
The only possible explanation of their low luminosity is that hydrogen must now comprise less than 0.00001 of the mass of a dwarf star.135
Like so many other astronomical pronouncements, what this assertion really means is that its author is unable to find any other explanation within the limits of currently accepted theory. From the theory of the universe of motion we find that the “gap” between the luminosities is mainly due to the reduction in the luminosity of the ordinary white dwarfs by reason of the outer shell of condensed gas that characterizes these stars. The luminosity difference is increased by the existence of the mass minimum, as this eliminates the small stars that would be the most luminous members of this class.
We can now see the significance of the group of planetary nebulae immediately below the line APB’ on the CM diagram. These are stars that are small enough to require an outer shell, but so close to the dividing line that the shell is too thin to block much of the radiation from the interior. These out-of-place planetaries are found only in a very limited region of the diagram, because as soon as they cool a little more and move down the evolutionary path a short distance the shell thickness increases enough to cut off the planetary type of radiation.
In our examination of the behavior of ordinary white dwarfs we will, as usual, draw upon various sources in the astronomical literature for the observational information that is needed, but the specific comparisons with the theoretical pattern will deal mainly with a group of 60 white dwarfs on which all of the major physical properties have been determined—absolute magnitudes and color indexes by J. L. Greenstein (reference 139), and masses and temperatures by H. L. Shipman (reference140). Figure 21 is the CM diagram for this group of stars.
All but three of the masses of the sample group fall within the evolutionary band that has been identified. The average decrease in luminosity is more rapid than that indicated by the theoretical evolutionary lines, but this faster drop is due to known causes. At the upper end of the evolutionary band the entire distribution of masses is shifted upward to some extent. In this early white dwarf stage, when the outer shells are relatively thin, some of the radiation from the interior is evidently penetrating the shell, increasing the luminosity beyond the normal levels. This is a weaker form of the same effect that was noted in connection with the existence of planetary nebulae below the line A’B’. In the remainder of the band the average luminosity gradually drops away from the theoretical line in the same manner, and for the same reason,
that the spatial main sequence turns downward in its lower sections. This is a result of the gradual decrease in the frequencies of the radiation from the stars, which shifts more and more of the radiation into the optically invisible ranges as the temperature drops.
The general relation between mass and luminosity is definitely inverse, as required by the theory. While the positions of the individual members of the three mass groups identified by symbols in Figure 20 are somewhat scattered, those of the smaller stars are all in the upper portion of the populated areas of the diagram, while those of the group with masses above 0.8 solar units are all in the lower portion. Most of the stars of the intermediate group, those with masses between 0.4 and 0.8, are close to the average.
As noted earlier, the lower section of the evolutionary band of the ordinary white dwarfs is not cut off at the 0.4 color index in the manner of the planetary stars, but continues on to a limit somewhere in the neighborhood of magnitude 16. The faintest star in the sample group has magnitude 15.73. The number of stars below the 0.4 color index in this sample group is rather small, but this is undoubtedly a matter of observational selection. All of the white dwarfs are relatively dim, and the observational difficulties resulting from this cause increase as the stars age and become less luminous. The available data on these objects therefore come preferentially from the earlier, more luminous, stars. As we will see later, “the most numerous kind of white dwarf” is the cool, dim type of star that populates the lower luminosity range, beyond a color index of 0.3 or 0.4, the same range that is so poorly represented in the sample group. The question as to what happens to the stars that reach the lower limit of this white dwarf evolutionary path will be the subject of discussion in the next chapter.
The foregoing findings as to the evolutionary course of the ordinary white dwarfs now enable us to extend the theoretical CM diagram of the planetary stars, Figure 19, to include the stars of this smaller class, and to show how the zone occupied by these ordinary white dwarfs is related to the positions of the other classes of stars. For comparison, this enlarged diagram, Figure 22, also indicates the location of the ordinary white dwarfs as identified in the illustration accompanying the previously cited article by M. and G. Burbidge.102
The spectra of the white dwarfs show a considerable amount of variation, and on the basis of this variability these stars are customarily assigned to a number of different classes. Greenstein distinguishes nine classes, and the designations that he has applied in his tabulation141 are in general use. However, the basic distinction appears to be between the hydrogen-rich stars, designated as Class DA, a few hybrid classes, particularly DAF, and the balance, which are helium-rich. Much of the discussion in the literature is carried on in terms of DA and non-DA. H. M. Van Horn, for instance, comments that “The existence of white dwarfs with non-DA (hydrogen deficient) spectra has not yet been satisfactorily explained.”142
Because of this lack of an acceptable explanation, the astronomers have not reached any consensus on the question as to whether the observed differences that have led to the distinction between the various classes reflect actual differences in composition, or are products of processes that take place during the evolution of the stars. The theoretical development in this work leads to the conclusion that these differences are primarily evolutionary. Before discussing these theoretical reasons why changes take place in the atmospheres of the white dwarfs as they age, we will first examine the evidence which demonstrates that these stars do, in fact, undergo significant changes as they progress along their evolutionary paths.
In this case, as is usual in astronomy, the observations give us only what amounts to an instantaneous picture, and do not specifically indicate whether the regularities that are observed are time related. This is the reason for the existing uncertainty. But the new information developed in the foregoing pages has now provided a basis from which we can approach the question. As shown in Figure 21, the ordinary white dwarfs of different masses follow parallel cooling lines on the CM diagram, with the smaller stars at the top of the luminosity range and the larger ones at the bottom. From this demonstrated fact that the lines parallel to the main sequence in the white dwarf region of the diagram are lines of equal mass, as the theory requires them to be, it follows that on a plot of mass against the B-V color index, Figure 23, where the lines of equal mass are horizontal, the distance from the left side of the diagram along any one of these lines represents time; that is, it measures the amount of evolutionary development. The general trend obviously is from the hydrogen-rich stars, Class DA, to the classes marked x on the diagram, the DC group, we might call them, all of which are classified by Shipman as helium-rich.
At temperatures above a dividing line in the vicinity of 8000 K the great majority are DA stars, with only about ten percent in the DC group. Below this temperature all of the stars fall into the DC group or a transitional class. A specific segment of the general transition from the DA status to that of the DC group can be recognized in the larger stars. Greenstein defines a class DAF, in which the hydrogen lines characteristic of the DA spectrum are weaker, and Ca II lines are present. Class DF, in which Ca II appears follows this, but hydrogen does not. Evolution through the entire sequence DA, DAF, DF is taking place in stars with mass above 0.50.
Next let us turn to the question as to what causes this shift from a hydrogen atmosphere to a helium atmosphere as the white dwarf ages. The astronomers have no answer to this question. As explained by James Liebert in a 1980 review article, “The existence of nearly pure helium atmosphere degenerates over a wide range of temperatures has long been a puzzle.”137 The “cooler helium-rich stars,” he reports, are “the most numerous kind of white dwarf.” Furthermore, the concentration of still heavier elements in the atmospheres of these stars is also too high to be explainable on the basis of current astronomical theory. Since the interior of the white dwarf is in an unusual physical state (this is true regardless of whether the matter is “degenerate,” as seen by conventional theory, or expanding into time, as seen by the theory of a universe of motion), the matter in the atmosphere, which is normal, must have been accreted from the environment. Liebert points out that
The metals in the accreted material should diffuse downward, while hydrogen should remain in the convective layer. Thus the predicted metals-to-hydrogen ratios would be at or below solar (interstellar) values, yet real DF-DG-DK stars have calcium-to-hydrogen abundance
ratios ranging from about solar to well above solar.137
The only possibility that Liebert is able to suggest as a solution to the “puzzle” is that the hydrogen accretion must be “blocked by some mechanism.” This is clearly a “last resort” kind of hypothesis, lacking in plausibility, and wholly without factual support. On the other hand, the explanation of the structure of the white dwarf derived from the postulates that define the universe of motion requires just the kind of a situation that is found by the observers. As Liebert says, on the basis of conventional theory, “the metals in the accreted material should diffuse downward.” But on the basis of the theory described in this work, the center of the white dwarf is the region of least density. According to this theory, then, the hydrogen should “diffuse downward,” and the metals should remain in the outer regions. The helium, too, should remain behind while the lighter hydrogen sinks. The observed distribution of the three components, hydrogen, helium, and metals, in the classes of stars identified by Liebert is exactly what the theory of the universe of motion tells us it should be in the older white dwarfs.
The presence of hydrogen atmospheres in the earlier stars, and the gradual nature of the transition to helium atmospheres are due to slow transmission of physical effects across any boundary between motion in space and motion in time. Originally, the white dwarf, located in the middle of the debris left by the supernova explosion, was able to accrete matter at a relatively rapid rate. Inasmuch as these accreted explosion products consisted mainly of hydrogen, the accretion gave the white dwarf a hydrogen atmosphere. But there was a small proportion of helium and other heavier elements in the accreted matter. Long-continued preferential movement of hydrogen into the stellar interior therefore resulted in a gradual increase in the proportion of heavier elements in the atmosphere. Meanwhile the accretion rate was decreasing as the white dwarf and its giant companion swept up the residue from the explosion. Eventually the incoming hydrogen passed into the interior of the star as fast as it arrived. Beyond this point, which we located in the vicinity of 8,000 K, the atmosphere of the white dwarfs is predominantly helium. In view of the complete inability of the astronomers to find any tenable explanation of these helium atmospheres within the limits of accepted physical and astronomical theory. the agreement with the theory of the universe of motion is impressive.
This is an appropriate point at which to emphasize one of the most significant aspects of a general physical theory, one that derives all of its conclusions in all physical fields by deduction from a single set of basic premises, independently of any information from observation. The development of such a theory not only produces explanations for known phenomena that have hitherto resisted explanation, but also, because of its purely theoretical foundations, is able to supply explanations in advance for phenomena that have not yet been discovered. Items of this anticipatory character have had only a minor impact on the presentation in the preceding pages of this volume, as the subject matter thus far covered has been confined almost entirely to phenomena that were already known prior to the first publication of the theory of the universe of motion in 1959. But the remainder of this volume will deal mainly with astronomical phenomena that have been discovered, or at least recognized in their true significance, since 1959. The explanations that will be given for these phenomena will be taken directly from the 1959 publication, or derived by extension of the findings described therein. One entire chapter (Number 20) will be devoted to describing the predictions made in 1959 with respect to the origin and properties of a then unknown group of objects that are now identified with the quasars, pulsars, and related objects.
The phenomenon that we are now considering, the existence of helium atmospheres in certain classes of white dwarf stars, is a more limited example of the same kind of anticipation of the observational discoveries. Here the explanation was provided before the need for it was recognized. The essential feature of this explanation is the inverse density gradient. The existence of this inverse gradient is not an ad hoc assumption that has been formulated to fit the observations, in the manner of so many of the “explanations” offered by conventional theory. It is something that is definitely required by the basic postulates of the theory of the universe of motion, and was so recognized, and set forth in the published works, long before the existence of the helium atmospheres was reported by the observers, and the need for an explanation of this seeming anomaly became evident. “The 1959 publication stated specifically that ”The center of a white dwarf star is the region of lowest density .”
Once the existence of the inverse density gradient was recognized, the presence of helium atmospheres in the older white dwarf stars could have been deduced, independently of any observations, if the investigations had been extended into more detail. This was not feasible as a part of the original project, because of the limited amount of time that could be allocated to astronomical studies in an investigation covering the fundamentals of all major branches of physical science. The answer to the problem of the helium concentration was, however, available for immediate use as soon as the problem was specifically recognized. In the pages that follow, this experience will be repeated time and time again. We will encounter a long succession of recent discoveries—some of a minor character, like the helium atmospheres; others that have a major significance to astronomy—and we will find simple and logical explanations of these discoveries ready and waiting in the physical principles that were previously derived from the postulates of the theory of the universe of motion.
This ready availability of deductively derived answers to current problems is something that conventional astronomical theory does not have. The astronomers first have to make the discovery, and then look for an explanation of what they have found. Almost all-important new discoveries come as surprises. Thus it is to be expected, in a rapidly growing field of knowledge, that there will be many phenomena that are still unexplained, or not satisfactorily explained, in terms of accepted theories and concepts. This situation is not looked upon as particularly serious, inasmuch as explanations of a more or less plausible character can reasonably be expected to be forthcoming for most of these items as more observations are made and the general level of knowledge in the relevant areas rises. But the prevalence of these issues of a work-in-progress nature tends to obscure the fact that among the unexplained phenomena there are some that clearly cannot be reconciled with the accepted theories, and therefore provide definite proof that there is something seriously wrong in the currently prevailing structure of theory.
Spontaneous movement of heavy atoms against the density gradient does not occur in the real world. Technetium cannot rise from the core of a normal star to the surface through an overlying volume of hydrogen. Helium and the metals cannot remain on the surface of a normal star, or a highly condensed star, while hydrogen sinks to the center. Inasmuch as the observations show that technetium is present in the surface layers of some stars, and the heavier elements do remain in the surface layers of some of the white dwarfs, it is evident that the current theories are wrong in some essential respects. In the first of these cases, there is adequate evidence to show that technetium is present in stars of normal characteristics; that is, matter is not being ejected from the interiors explosively. It then follows that the technetium is not produced in the core of the star in accordance with the prevailing ideas. In the white dwarf situation, there is adequate evidence to demonstrate that the concentration of heavy elements in the outer layers of certain classes of these stars is greater than that in the matter that is being accreted from the environment. Here, then, the hydrogen is preferentially sinking into the stellar interior. In this case it necessarily follows that the white dwarf is not a normal star, or a star composed of “degenerate” matter, but a star with an inverse density gradient.