|T Cr B*||8.6||VF||300|
|* recurrent||** repeated outburst"|
The information available from observation gives only a very general indication of how well the novae conform to this theoretical pattern, but the little that is available is clearly in agreement with the theory. Most of the novae with large magnitude ranges are in the very fast category, and there is a general trend toward the next lower rating, the fast class, as the range decreases. Only one nova with a range greater than 11 magnitudes is definitely classified as fast. Below this magnitude level, the fast group outnumbers the very fast by about three to one. This is consistent with the theoretical conclusion that the earliest outbursts of the largest novae should have the maximum magnitude range, that this range should be less for the smaller novae, and that in all cases the range should decrease as time goes on and the outbursts are repeated.
While the slow novae are not concentrated at the lower end of the list as strongly as the very fast are concentrated at the upper end, there is a definite increase in the proportion of slow novae as the magnitude range decreases. If we omit the two stars of the larger class (identified as recurrent), the proportion of slow novae in the group with magnitude range 9.0 or below is 64 percent. In the group with ranges above this level it is only 24 percent. In between the extremes there are some relatively slow novae that are quite high on the list, and some of the very fast class that are quite low. Theoretically, the latter should be quite small stars and the former quite large. This cannot be confirmed observationally, as matters now stand.
The novae that are observed to have repeated are at the low end of the list; that is, they have the lowest magnitude ranges. Of course, these are not the only novae in the list that have repeated; they are merely the white dwarfs that are approaching the end of the nova stage of their existence, and are repeating their outbursts at short enough intervals to have had at least two within the time interval during which observations have been made. Their position at the low end of the list is another agreement with the theory.
At this point we need to take into account the fact that the possible speeds in the intermediate speed range do not constitute a continuous succession of values, but are confined to eight distinct levels, a characteristic of this speed range that we have already had occasion to recognize in applications such as the explanation of the relation known as Bode's Law. As noted earlier, four of the eight speed levels are on the spatial side of the dividing line, and correspond to identifiable locations in equivalent space. In the planetary stars, which are in the gaseous state throughout, the particles moving at the different speed levels are well mixed, and there is a continuous density gradient from the outer to the inner regions. Here the build-up of pressure and eventual escape of the compressed gas follows essentially the same pattern irrespective of the size of the star. The situation in the ordinary white dwarf stars is quite different because the outer shell of these stars is in the condensed gas state. In this state, as in a liquid, matter of different densities stratifies. The outer shell is therefore not homogeneous, but consists of a number of layers, initially four. Since the white dwarf aggregate is a time structure, rather than a space structure, the gas bubbles in the center of the star (space structures) remain in the aggregate, rather than separating from it. Thus they accumulate in the lowest of the four layers, and are confined by the weight of the three overlying denser layers.
Smaller stars of the same surface temperature have lower internal temperatures, and at some point in the mass range the fourth speed level is vacant. The compressed gas in the central regions of these smaller stars is located in the third level, and is subject to the weight of only two overlying denser levels. This very substantial reduction in the weight that is confining the gas results in a corresponding reduction in the pressure that has to be built up before the compressed gas can break through. It can be expected, therefore, that at some definite level of white dwarf mass the nova type of outburst will be replaced by a different type of eruptive behavior in which the outbursts are more frequent but less violent.
This theoretical expectation is fulfilled observationally. While the white dwarf stars that reach the main sequence at the higher luminosities are observed as novae during the conversion from motion in time to motion in space, those that are smaller, and less luminous in their final state, follow what may be described as a nova pattern in miniature, with less violent outbursts and much shorter periods, ranging from about a year downward. These small scale novae, of which SS Cygni and U Geminorum are the type stars, are classified together with the true novae, the recurrent novae, and certain nova-like variables, as cataclysmic variables.
The magnitude at which the change in behavior occurs is a critical level that, on the basis of the considerations previously discussed, should be related to the other critical levels of the CM diagram by integral numbers of natural (compound) units. We have identified the difference between points B and C on the spatial main sequence, 2.8 magnitudes, as one such natural unit. The explanation just given for the transition from nova to a less violent type of outburst suggests that it should take place one natural unit below the upper limit of the normal, or classical novae, which coincides with the lower limit of the planetary stars at point B on the diagram, magnitude 4.6. This puts the boundary between the two types of cataclysmic variables at 7.4 magnitudes on the spatial main sequence. The corresponding mass is 0.65 solar units. Thus the ordinary white dwarf in the range above 0.65 solar masses follows the nova pattern in its conversion to motion in space, while those in the range immediately below 0.65 solar masses are SS Cygni variables in the conversion stage.
We have identified the novae as white dwarfs that have component particles with speeds in all four of the levels on the (equivalent) spatial side of the dividing line, and the SS Cygni variables as white dwarfs in which the component speeds are limited to three of these four levels. On the basis of the same considerations that are applicable to the novae, the magnitude range of the SS Cygni stars, after conversion to motion in space, should be between 7.4 and 10.2, and the mass range should be from 0.65 to 0.40 solar units. Inasmuch as there are white dwarfs with still smaller masses, it follows that there should exist a class of these stars in which component speeds occupy only two levels. Since this leaves only one level overlying the one in which the gas is accumulating, it can be expected that the gas bubbles in these stars will break out at a relatively early stage before they reach any substantial size. The observations indicate that this third theoretical class of cataclysmic variable can be identified with the flare stars. These are theoretically stars of from 0.40 to 0.25 solar masses, with main sequence magnitudes, after conversion to motion in space, in the range from 10.2 to 13.0.
The 0.25 lower limit of the mass of the flare stars leaves room for some white dwarfs with only one speed level, as the minimum mass of the ordinary white dwarfs is somewhat lower, probably around 0.20. There is no significant amount of resistance to escape of gas from these stars, other than the viscosity of the condensed gas through which it has to make its way, but since the gas comes out in the form of bubbles, it is probable that there are visible flares from these stars similar to those from the two-level class, known to the astronomers as UV Ceti stars. The flare stars are not usually included in the classification of cataclysmic variables but they share the distinguishing characteristic of those variables, periodic outbursts of very energetic matter, and differ mainly in the magnitude of the outbursts. As indicated in the preceding paragraphs, there is a specific place for them in the pattern of the cataclysmic variables that has been derived from the theory of the universe of motion. the pattern that applies also to the novae and the SS Cygni stars.
Turning now to a consideration of the information that is available from observation, we find that the average magnitudes reported by the observers are within the theoretical limits, but these limits are so wide that the agreement with observation is not very significant. The mean absolute magnitude of the SS Cygni stars is reported as 7.5+0.7 (reference 149) and that of the UV Ceti flare stars as 13.1 (reference 150). The cataclysmic variable stage begins at about magnitude 16, the low limit of the ordinary white dwarfs, and extends to the level of the galactic main sequence, 0.8 magnitudes above the limiting magnitudes on the undisplaced basis as noted above. Since the conversion process accelerates, the average position of these variable stars, as observed, should be well below the midpoint of the magnitude range. The 13.1 magnitude reported for the UV Ceti stars is consistent with this prediction. The 7.5 magnitude of the SS Cygni stars is too high, near the upper end of the theoretical range, but it is likely that this value includes a large contribution from the after effects of the interior heat released during the outbursts.
Other data on the smaller classes of cataclysmic variables are scarce. Unlike the novae, which are spectacular, but rare because of the long intervals between outbursts, the SS Cygni stars are dim and hard to detect. It is reported that about 100 of them have been located, but only a few of them have been studied in detail. These are found to have a period-amplitude relation whereby the stars of longer period show the more violent outbursts, 151 thus continuing the pattern of the true novae, noted earlier. The maximum observed magnitude range is near 6 magnitudes, about one magnitude below the minimum of the true novae indicated in Table III.
Very little is known about the properties of the flare stars, aside from those that they share with the other cataclysmic variables. A. H. Joy describes them as extremely faint M-type dwarfs in which the light curve rises to maximum in a few seconds or minutes of time and declines to normal in less than a half hour. 152 These light curves are similar in form to the light-curves of novae, 153 an observation that supports the theoretical identification of the flare stars as junior members of the group headed by the novae.
The heterogeneous group of stars known as the nova-like variables do not constitute a separate class, but are members of the classes already identified, with some special characteristics that distinguish them from the type stars of their respective classes. For instance, R. Aquarii and similar stars differ from SS Cygni mainly in that in SS Cygni both components of the binary system are dwarfs. whereas R. Aquarii combines a red giant and a hot blue dwarf.154 Z Andromedae is the prototype of a group of stars that undergo outbursts of about three magnitudes, and combine the features of a low temperature red giant and a hot bluish B star which is probably a subdwarf. 155 The terms applied to the dwarf components in these quoted descriptions of the binary systems are appropriate for the white dwarf members of cataclysmic variable pairs. A blue dwarf is simply a hot white dwarf. while a subdwarf is a dwarf star below the spatial main sequence in the area in which the cataclysmic variables are theoretically located. As noted previously, a combination of a red giant and white dwarf is not unusual; it is an early evolutionary stage that in time evolves into the more familiar combination of main sequence star and white dwarf
It is now generally accepted that all cataclysmic variables are binary systems, as required by the theory developed herein. The following is an expression of the current view:
A dwarf nova, like all cataclysmic variables (novae, recurrent novae, dwarf novae, and novalike variables) is a close binary system in which the primary component is a white dwarf. The secondary is a normal star. 156
The current tendency is to ascribe the explosive behavior to this binary nature of the system. The sudden outbursts of the SS Cygni stars, says Burnham, are undoubtedly connected in some way with the duplicity of the system, but the exact details are uncertain. 157 Notwithstanding the use of the word undoubtedly in this statement, our findings are that the binary nature of the cataclysmic variables, which we confirm, has no connection with their explosive behavior. This is why the astronomers have not been able to explain how their hypothetical process operates. These systems are binary because they originate in supernova explosions powerful enough to accelerate some of their products to intermediate speeds, and the white dwarf member of the binary system is explosive because the intermediate speed component of the supernova products goes through an explosive stage on its way back to the normal speeds of the material sector. The theoretical conclusions agree with the observed fact—the binary nature of these objects—but they disagree with the prevailing assumption as to the nature of the process responsible for the explosive outbursts.
The situation with respect to the location of the cataclysmic variables on the CM diagram is similar. We deduce from the theory that these objects are on the way from the white dwarf status to positions on the spatial main sequence, and therefore occupy intermediate positions. The observers agree as to the positions.
From their luminosities, which are similar to the sun on the average, we are forced to conclude that they [the novae] are small superdense stars somewhat like white dwarfs, but not so extreme.78 (D. B. McLaughlin) Virtually all known post-nova stars are objects of the same peculiar type, hot bluish subdwarfs of small radius and high density, apparently intermediate between the main sequence stars and the true white dwarfs. 158 (R. Burnham) The prenova is below the main sequence intermediate between white dwarf and main sequence stars.159(E. Schatzman)
Where our findings differ from astronomical theory is in the direction of the evolution of the cataclysmic variables. The prevailing astronomical opinion is that the evolutionary direction is down the CM diagram from some location above the main sequence, generally identified as the red giant region, toward the white dwarf stage. The white dwarf is seen as the last form in which the less massive stars are observable, the penultimate stage on the way to extinction as black dwarfs. This leaves the planetaries and the cataclysmic variables dangling without any clearly identified role. Shklovsky calls them freaks.''
Our analysis now shows that here again the astronomers' evolutionary sequence is upside down. The white dwarfs of both classes (planetaries and ordinary white dwarfs) enter the field of observation at the left of the CM diagram from an unobservable condition analogous to that of the earliest of the protostars that eventually enter the diagram in the red giant region. Just as these giants move to the left and down the diagram to the equilibrium positions on the spatial main sequence, the white dwarfs move to the right and up the diagram to reach similar equilibrium positions on that sequence. The upward movement takes place in the cataclysmic variable stage.
As the foregoing survey of the results of observation of the cataclysmic variables indicates, existing empirical knowledge is much too limited to provide a clear picture of these objects. But each of the isolated bits of information currently available fits into the general pattern derived from the theory of the universe of motion. While the theoretical pattern of behavior conflicts to some extent with current astronomical thought, it is really not accurate to say that the results of this present investigation contradict the astronomers' theory of the cataclysmic variables, because, aside from the rather vague idea of a giant star shedding mass and moving toward the hypothetical black dwarf status along an unspecified route, the astronomers have no theory of these objects. Severe problems remain, 142 in arriving at an understanding, says H. M. Van Horn. A. H. Joy describes the situation with respect to the stars of the SS Cygni class in this manner:
The general problem of the SS Cygni stars is so complicated that little progress has been made toward its solution . . . No satisfactory explanation of the novalike outbursts which occur at semi-regular intervals in the variable stars of this class has been proposed, and their relationship to other groups has yet to be determined. 160
Gallagher and Starrfield give us a similar assessment of the current state of knowledge with respect to the novae.
It is clear that there are few problems relating to the novae that we may consider as solved, and many phenomena for which we have yet even to identify the nature of the underlying physical processes.161
Dean B. McLaughlin views the nova problem even more pessimistically. He sees little prospect of improvement.
The cause of nova outbursts is not likely to be identified directly by observation. At best we can only hope to arrive at an idea of the cause by devising hypotheses, calculating their consequences, and comparing the expected results with the observed facts.162
The development in this work, based on deductions from the postulates that define the universe of motion, has now provided the kind of a complete and consistent theory of the cataclysmic variables that has heretofore been lacking. In the course of this development we have identified the three basic errors that have diverted astronomical thinking about the white dwarfs into the wrong channels: (1) the assumption that conversion of hydrogen into heavier elements is the energy production process in the stars, (2) the assumption that speeds in excess of that of light are impossible, and (3) the assumption that the white dwarf is a dying star. Correction of these errors and application of the physical principles governing motion at speeds greater than light, derived in the preceding volumes of this work, have arrived at a logical and consistent theory of the entire class of cataclysmic variables.
These results show that Shklovsky's characterization of the cataclysmic variables as freaks is totally wrong. These stars (and the planetaries as well) are in the direct line of one of the two coordinate branches of the stellar evolutionary cycle. They are all white dwarfs, differing only in the properties that are affected by the particular evolutionary stage at which each type of object makes its appearance, and they all go through the same general processes of cooling to a critical temperature level and then converting from motion in time to motion in space. Meanwhile the companions of these white dwarfs are going through the successive stages of the giant evolutionary cycle. The two stars of each of these binary systems are at comparable evolutionary stages, regardless of the difference in their properties, and they ultimately arrive at the same kind of a gravitationally and thermally stable state. When they're relatively short excursion away from the main sequence is ended, both of the partners will settle down for another long stay in that equilibrium condition.