QUASARS - HOW BIG ARE THEY?

To recipients of the review article QUASARS-THREE YEARS LATER:

In the original draft of the above mentioned article the author included a supplement containing a detailed account of an analysis of the quasar luminosity data which he has carried out for the purpose of determining the range of sizes of the fast-moving galactic fragments that he has identified as the quasars. Inasmuch as the article, even without this supplement, was considerably longer than we had anticipated, we did not consider it feasible to add this much to the material intended for general distribution. It is, however, a significant extension of the previous theoretical work, and we have therefore reproduced it separately. We are sending copies to those of the recipients of the original article who we believe are particularly concerned with the subject matter.

In connection with your examination of this material you may be interested in an article by Dr. Allen D. Allen that is now receiving considerable attention. This article originally appeared in Foundations of Physics, Dec. 1973, and was rewritten for publication in the Intellectual Digest, June 1974. Dr. Allen points out that the conventional view which regards the universe as being composed of “elementary particles” of matter is encountering extreme difficulties, and that, as a consequence, an increasing amount of support is being given to “the concept that ultimately the world is constructed from principles rather than from units of matter” . This is the kind of a theory on which the quasar analysis is based, as the fundamental entity in Larson’s Reciprocal System of physical theory is not matter but the specific mathematical relation (or “principle” ) that he has identified as motion. Some of the conclusions that are reached with respect to the quasars no doubt seem strange, perhaps almost incredible, in the light of opinions and beliefs derived from orthodox thought, and it should therefore be helpful to know that these unconventional conclusions are not only fully in accord with the observed facts, as the results of this and previous studies show them to be, but are also products of a theory that is now, in Dr. Allen’s words, “an established (if competing) theory in the mainstream of theoretical physics.”

—North Pacific Publishers

In a universe of the kind postulated in the Reciprocal System of theory, one composed entirely of motion, matter is subject to a limit related to age, as a result of which the oldest and largest galaxies terminate their existence in a series of violent explosions. Some of the material ejected from the galaxies during these explosions comes out in the form of fragments that have been accelerated to speeds in excess of that of light by the enormous amount of energy released in the explosive process. As explained in the book Quasars and Pulsars, which, for convenient reference, will hereafter be designated as Q&P, these fast-moving fragments are the quasars.

The available information about most of the observable features of the quasars was examined in Q&P and in a supplement to that volume which covers developments subsequent to the time of the original publication. Inasmuch as this supplement will also be the subject of frequent reference, its title Quasars - Three Years Later will be abbreviated, for purposes of this discussion, to TYL. As shown in these two publications, the observational data in the quasar area are in full agreement, both qualitatively and quantitatively, with the deductions from theoretical premises, so far as the theoretical development has been carried. This is a report of a further extension of the theory which covers a quasar feature not heretofore studied: the range of sizes of the galactic fragments, an item which is very significant, since one of the important requirements that the theory must meet in order to be valid is that the sizes of the quasars, as determined from the observational data, must be consistent with their theoretical status as fragments of giant galaxies.

The analysis presented herewith will demonstrate that this requirement is met. It will show that the quasars range from about 2.5 x 10^-5 to about 1.5 x 10^-3 times the size of the galaxy of origin. This means that the original giant elliptical (spheroidal) galaxy, containing somewhere in the neighborhood of 10¹² stars, ejects fragments ranging from about 2.5 x 10⁷ stars, the mass of 50 or more large globular clusters, to about 1.5 x 10⁹ stars, which is the size of a small spiral galaxy.

While some consideration will be given to the emission at radio frequencies, the analysis will deal mainly with the optical luminosities and spectra. Measurements of the optical magnitudes are available for all of the quasars that have been definitely identified and it would seem rather obvious, therefore, that these data should be of great value in the study quasar characteristics. Thus far, however, correlations have been attempted between magnitude and other quantities -- distance, for example inconclusive. As Burbidges say, their book Quasi-stellar Objects, with reference to the correlations with redshifts, what little correlation there is shows a scatter of a similar order of magnitude to that of the total span of the relation” .

But the theoretical development outlined in Q&P has produced a large amount of additional information regarding the properties and evolutionary pattern of the quasars, and has given us some significant new insight that Can be brought to bear on the problem. In the light of the general explanation of the nature and origin of the quasars that was developed in Q&P, it is now clear that the principal reason for the wide scatter in the correlations between luminosity and other properties is the large variation in the sizes of the individual objects. Obviously, galactic fragments ejected by violent explosions can exist in a wide range of sizes, determined by the conditions existing in the galaxy before the explosive event, and by the magnitude of the explosion. Ultimately it may be possible to establish some upper and lower limits from purely theoretical considerations, but this will require a major extension of the theoretical structure beyond where it stands today. For the present, the objective is to determine these limits, and the general distribution of sizes, from the empirical luminosity data, interpreted in the light of the pertinent portions of the quasar theory as it now stands.

It will be convenient to work mainly with a representative sample of these data, rather than with the entire mass of information that is now available, and most of the tabulations that will constitute the basis for the discussion that follows will include only those quasars for which the required data are available in Table 3.1 of the Burbidge book Quasi-stellar Objects, a compilation that covers those for which redshifts had been measured up to early 1967. Reference will be made to later observations where the additional information has a bearing on the points at issue.

The distinguishing characteristic of the quasar phenomenon, according to the theory, is that the enormous amount of kinetic energy imparted to the quasar by the galactic explosion has accelerated it to a speed greater than unity (the speed of light), and the special features of the quasar, those that have made it the “mystery” of present-day astronomy, are due mainly to the space-time inversion that takes place whenever the unit level is crossed in either direction. (The concept of space-time inversion, a basic feature of the Reciprocal System of theory, is discussed at length in the two previous publications). The ultra-high speed manifests itself most clearly by a range of redshifts that extends far beyond the maximum reached by the redshifts of any other class of astronomical objects. According to the theory developed from the basic postulates of the Reciprocal System, the total redshift of a quasar consists of the normal recession, proportional to the spatial distance, which we will identify by attaching the subscript r to the standard symbol z, and an additional non-spatial increment amounting to 3.5 zr^½. This latter quantity, a result of the component of the speed that exceeds unity, was called excess z, or z^ex in Q&P, but for convenience we will hereafter designate it by the symbol q. We then have the general relation z = zr + q. Inasmuch as the distance is proportional to the speed, the redshift magnitudes, when expressed in suitable units, apply to both distance and speed.

It is evident that a direct correlation of luminosity with distance has little meaning in itself, as we cannot distinguish between a large fragment at a great distance and a small one that is comparatively near. However, the redshift gives us an independent measurement of the distance, and if we were dealing with ordinary astronomical objects, such as stars or galaxies, this would enable us to convert the observed luminosity directly to the true, or absolute, luminosity. In the case of the quasars another factor enters into the situation, as the route by which radiation travels back from the quasar depends on the location at which the galactic explosion occurred, and there are some further factors that also modify the distribution of the emitted radiation under certain circumstances.

If a fragment is ejected from our own galaxy (assuming this to be possible) at unit speed (the speed of light), its motion is coincident with the normal recession, and is reduced by gravitation in the same amount as the recession, so that at some later time the fragment which originated at zr = 0 will occupy a location at a spatial distance zr = x. Where the ejection speed is greater than unity, the excess speed causes change of position in time rather than in space, because of the inversion of the space-time relations at the unit level, but this temporal motion has a spatial equivalent of a scalar nature. The total outward motion of the quasars the motion indicated by its redshift, is then zr + q, as indicated earlier, and when zr =, the quasar is at a point q = a, where a = 3.5 x ½.

Radiation is emitted from the quasar at point a, and travels back along the line followed by the quasar in its outward motion. When this radiation has moved distance a in time (equivalent space) it has arrived at our galaxy, inasmuch as the distance x in space has been automatically eliminated by a reversal of the effect of the recession. The zr component of the explosion speed accomplished nothing in the outward direction, merely duplicating the recession, and consequently it does not have to be overcome on the return trip. For such a quasar, one which originated from our own galaxy (if our galaxy were large enough, which it is not) all travel, both of the quasar moving outward and the radiation coming back, is in time.

On the other hand, if an explosion ejects a quasar from a galaxy at some distant location zr - y, this location corresponds to a time location q = b, which is the point from which the normal temporal motion of the quasar begins. In this case, the distance b is simply the temporal counterpart of the spatial distance y that is, it represents travel in actual (not equivalent) space.

In either case, when q reaches 1.00 the quasar is at the boundary of the spatial reference system in one of the quasar dimensions, and this condition with q . 1.00 and zr - .08 constitutes a convenient natural datum to which the various measurements can be referred. At this time we are primarily concerned with luminosity, and the luminosity at q = 1.00 will be called the absolute luminosity of the quasar. In order to keep the numerical values within a convenient range, the observed luminosities employed in the following discussion, and in the tables, are the increments of magnitude above 15, converted to luminosity. Hence such a value represents the ratio of the luminosity in question to the luminosity corresponding to visual magnitude 15. For example, the value .200 indicates a luminosity one-fifth of the reference level. This is equivalent to magnitude 16.75.

When a radiating object is moving in space at a speed less than that of light its radiation is distributed over all three spatial dimensions, and the observed luminosity of such an object is therefore inversely proportional to the square of the intervening distance. As explained in Q&P, inasmuch as motion in space is limited to speeds below unity (the speed of light), the quasar motion beyond unit speed is a scalar addition to the spatial motion, and radiation from an object moving at such speeds is distributed two-dimensionally. In this case, the observed luminosity is inversely proportional to the first power of the distance. This conclusion from theory was verified as a general proposition in Q&P by a correlation between the observed optical magnitude and quasar distance for the quasars listed in the reference tabulation. For present purposes, however, we will need to go a step farther, and examine the manner in which the basic relationship is modified by the route that the radiation travels.

Because of the relation between the quasar motion and the motion of the normal recession, as indicated by their respective values, 3.5 zr, and zr, a quasar (time) dimension is equivalent to the square root of a recession (space) dimension, and the radiation received from a quasar through time, which is proportional to the first power of the quasar distance q, is also proportional to the square root of zr. The quasar radiation that is received through space is proportional to the first power of zr, and therefore also proportional to q². Inasmuch as the distances will be expressed in terms of q rather than zr in the discussion that follows, the relation of luminosity to distance will also be identified in terms of q and q².

Since the distance alone does not tell us whether a quasar has originated nearby, in which case the q relation applies, or has originated near its present location, in which case the q2 relation is applicable, the absolute luminosity cannot be positively determined from the observed luminosity and the distance. In the absence of further information, we can only establish the limits within which the absolute luminosity must lie. However, the special characteristics of the quasars at different stages of their evolutionary development enable us to arrive at some approximations of the true values that are adequate for present purposes.

As explained in the previous publications, the development of theory reveals that the quasars pass through three general evolutionary stages, two periods of strong radio emission separated by a radio-quiet stage. An early type Class I quasar, one which has just recently been ejected from the galaxy of origin, is in a high state of internal activity as a result of the energy imparted to it by the galactic explosion, and is radiating strongly at radio frequencies. As the quasar ages, the internal activity subsides. Consequently, the radio emission decreases, and in the late Class I stage it is relatively weak, ultimately dropping below the observable level. After a long radio-quiet period, the constituent stars of the quasar begin to reach their age limits, and disintegrate, releasing large amounts of energy. Radio emission then resumes, and the quasar enters the Class II stage, where it remains until it is either completely disintegrated or reaches the distance limit beyond which it is unobservable.

In the original presentation of the theory in Q&P the different evolutionary Stages were identified by a combination of the U-B color index and the intensity of the radio emission. Further study reported in TYL has shown that introduction of the B-V color index enables the evolutionary status of the quasars at distances less than q = 1.00 to be determined on the basis of color alone. No classification criteria are necessary beyond 1.00, as Class I quasars are not observable at such distances. However, the quasars beyond 1.00 do actually conform to the normal Class II colors until they approach the limiting distance, after which there are some changes that will be discussed later. The colors of the different classes of quasars at the shorter distances, where all are present, are as follows:

The more extensive and more accurate radio emission data now available reveal that the original distinction between Class II and late Class I set up in Q&P on the basis of the strength of the radio emission is not sharp enough. These data confirm the original finding that the Class II emission is generally high, whereas the late Class I emission is relatively low, but the additional information now shows that there is a greater range of values in each class than was indicated in the earlier data, and consequently there is a zone in which the two classes overlap if they are distinguished on this basis. On the other hand, the distinction on the basis of the B-V color index appears to be quite definite.

Identification of the evolutionary status of the quasars by color alone has a further advantage in that it enables utilizing the data with regard to the other observable features of the quasars to verify the theoretical conclusions as to the differences between the different classes, something that we could not do if these features entered into the criteria by which the various classes were identified. For example, we find from theory that Class I quasars have no absorption redshifts. If the absence of absorption redshifts is used as one of the criteria by which Class I quasars are recognized, then this absence would tell us nothing about the validity of the theoretical conclusion. But when the Class I objects are identified by color only, the absence of absorption redshifts in the spectra of the quasars thus identified serves to confirm the theoretical conclusion.

Inasmuch as the Class II stage is the last of the phases through which a quasar passes between its origin and its disappearance, a normal Class II quasar has been traveling outward for a very long time. It therefore follows that the absolute luminosity of such a quasar should approximate the value calculated on the basis of the first power of the quasar distance q. Table I gives the luminosity data thus calculated for the Class II quasars from the reference list that are nearer than q = 1.00. The symbols used as column headings are standard, and should need no explanation, beyond that already given, except for column 6, which gives the absolute radio power in

relative terms. The origin and significance of these radio data will be discussed later.

There is one exceptional case in the tabulation. This is the nearest of the Class II quasars, 3C 273. The special conditions applying to this quasar were discussed in Q&P. In this instance the point at which the galactic explosion occurred is so close that random motion in three-dimensional space which happened to be directed inward has almost canceled the small outward motion of the recession. As a result, the distance traveled since ejection is small, and the spatial (q2) relation applies, rather than the temporal (q) relation from which all of the other absolute luminosities in the table were calculated.

The maximum and minimum absolute luminosities listed in this tabulation are .369 and .017 respectively. Consideration of the maximum will be deferred until some values from other groups of quasars are available, but we can draw some conclusions from the minimum calculated value. Of course, this figure does not indicate what the

smallest possible luminosity of a quasar may be; it is instead an indication of the magnitude of the visibility limit, the least absolute luminosity that can be reached with the facilities available to the observers from whose measurements the tabulated values have been taken. Since this limit is a function of distance, a projection of the .017 absolute luminosity of the quasar 3C 2, at q = .962, to q = 1.00 would give us .018 as the corresponding value at the standard distance. On the assumption, however, that the lowest observed luminosity from the reference list is not quite the true minimum, we may take .017, and the corresponding visual magnitude 19.35, as the visibility limit from observation, expressed on the basis of the standard distance. The relation of the .017 value to the theoretical limit will be discussed after some further foundation is laid.

Inasmuch as the quasars beyond q = 1.00 are even older than those of the under 1.00 group, they, like the closer ones, approximate the situation wherein all travel has taken place in time. Here, too, then, the luminosity is proportional to the first power of the quasar distance q. Absolute luminosities for the distant quasars of the reference tabulation, calculated on the q basis, are given in Table II.

It is evident that, from a luminosity standpoint, this is a group of objects practically identical with the quasars of Table I. To demonstrate this point, the luminosities of the two groups arranged in order of magnitude, are compared in columns 1 and 4 of Table III. To avoid having unequal numbers of objects in the two groups, the point of division has been moved up to 1.09 for the purposes of this comparison, and the luminosities shown are those of the 22 quasars below 1.09 and the 22 above 1.09, respectively. The point of division has no special significance. What is being demonstrated here is that if we compare the luminosities of a random group of distant Class II quasars with those of a similar, but much closer, group, the luminosities of the corresponding members of the two groups deviate no more than can be expected on probability grounds.

This is a place where it will be helpful to take the more recent observations into account, and columns 2 and 5 extend the comparison to the first 22 quasars below and the first 22 above q = 1.00 that were added to the previous list in the compilation by Burbidge and O’Dell, Astrophysical Journal, Dec. 15, 1972. From an optical standpoint the 1967 and 1972 groups should be comparable, as the enlargement of the observational coverage during the intervening five years was due primarily to improvement of the radio facilities, and to further time applied to observation, and did not involve any significant extension of the range of optical magnitudes. In both cases the limiting magnitude was between 19 and 20.

The differences between columns 2 and 5, and between these columns and the values in columns 1 and 4, are no greater, except at the extreme upper limit, than the differences between columns 1 and 4. Within the degree of variability that can be attributed to chance, therefore, the corresponding values in the four columns, with the exception of some of those at the highest luminosities, are essentially the same. This agreement is brought out even more clearly in columns 3 and 6 by a comparison of the average values for the closer and more distant groups. We may say, then, that wherever we draw out a random sample of Class II objects we obtain practically the same luminosity mixture, just as we must necessarily obtain essentially the same mixture of sizes.

This does not mean that the ratio of luminosity to mass in the quasars of this class is constant it merely means that whatever variations there may be in this ratio occur throughout the Class II stage of quasar evolution. This agrees with the findings discussed in Q&P. As brought out there, the evidence from polarization and the magnitude of the radio emission indicates that there are periods in the life of the Class II quasars when the internal explosive activity is at a level much above normal, but that these active periods are not con_ fined to any one phase of the Class II existence, and may occur at any time. The optical emission naturally increases along with the greater radio emission, although not necessarily in the same degree.

The effect of the abnormal explosive activity on the optical emission supplies an explanation of the lack of uniformity in the highest values of the four columns of observational data in Table III. Because of the relative scarcity of quasars which are at a peak of activity, one group of 22 may by chance include one or two such objects, whereas they may be absent from another group. The probability of including an extremely active quasar is greater for the above 1.00 groups because the most violent activity takes place in quasars that are very old and are in the process of disintegration. The more distant of the observed Class II quasars are, on the average, older.

One of the signs of a high rate of explosive activity is the presence of absorption redshifts, and the luminosities of the quasars with absorption spectra therefore provide an indication of the magnitude of the increase in optical emission due to this cause. A comparison of the luminosities of the quasars with absorption redshifts in the Burbidge and O’Dell 1972 tabulation with the average of the four columns of Table III, which we may take as representing the normal luminosity distribution, including a small percentage of quasars with the enhanced luminosity, shows that in the lower third of the values there is no significant difference between the two groups. In the upper two thirds the luminosities of the absorption group average about 30 percent higher than those of the corresponding members of the reference group. This suggests that the increased activity which characterizes the Class II quasars at certain stages increases the ratio of luminosity to mass in the larger objects by an average of about 30 percent, but that in relatively small quasars the effect is minimal .

Summarizing the foregoing from the standpoint of the specific objective of the present study, the information developed thus far indicates that in the greater part of the range of luminosities of the Class II quasars, the ratio of luminosity to mass is near enough to being constant to enable taking the relative luminosities as representative of the relative sizes, with the exception that applying this normal Class II ratio to the most luminous quasars overstates their true relative mass by about 20 to 40 percent. In order to arrive at the actual, rather than merely the relative, quasar sizes it will be necessary to relate the Class II ratio to that of normal galaxies, but extension of the analysis to the Class I quasars will be necessary for this purpose.

Column 6 of Tables I and II gives the absolute radio emission recalculated from the data of Sandage, Astrophysical Journal, Nov. 15, 1972. Sandage’s original values are given in logarithmic terms, but for purposes of this analysis the relative emissions are more meaningful. These have been expressed on a basis which uses a value of 44.00 (in Sandage’s terms) as a reference datum.

It was noted in Q&P that the average radio emission from the Class II quasars should theoretically increase with distance, as the number of Stars arriving at their age limits increases with time, and it was shown that the radio data available at that time were consistent with this conclusion. Most of these data, however, were derived from observations of quasars in the lower and middle portions of the Class II distance range, and the additional information contained in the Sandage article now shows that the radiation received at radio frequencies reaches a peak somewhere in the neighborhood of q = 1.300, and decreases thereafter.

The decrease at the extreme distances is due to the same cause that is responsible for the decrease in the B-V color index in the same distance range. As pointed out in TYL, this index also reaches a peak at about 1.300 or 1.400, and declines thereafter. It was explained in that publication that the drop in the color index is connected with the changes that take place in the character of the quasar motion in the last stage of the existence of these objects, the changes which, among other things, are responsible for the existence of absorption redshifts. As the increase in the average speed of the constituent material of the quasar due to the release of energy from a growing number of disintegrating stars continues beyond q = 1.300, the speed of an increasing proportion of this material crosses another unit boundary into the region where, as shown in TYL, only 1/4096 of the results of the motion (in this case, the radio emission) is effective in the region below unity, the familiar three-dimensional region of ordinary space, where we observe it. This means that the radio emission from any matter moving at the higher speed is practically unobservable, and although the total emission is increasing throughout the range from 1.300 to 2.000, the observable emission is decreasing.

At q . 2.00 the speed of the quasar as a whole likewise crosses a unit boundary, and in the transition region beyond this point (that is, from z  2.326, which is equivalent to q = 2.00, up to the observational limit, now z = 3.53) the U-B color index undergoes the unit level inversion, and moves back from the negative values characteristic of the quasars toward the positive values of ordinary galaxies.

Before leaving the Class II quasars it should be mentioned that one of the significant results of the foregoing analysis of the luminosities of these objects is a further confirmation of the first power relation between luminosity and quasar distance (that is, a confirmation of the two-dimensional nature of the quasar radiation). The validity of this relationship was demonstrated in Q&P by a direct correlation between quasar distances and the average luminosities of small groups of quasars in which all group members are at approximately the same distance. Now the relation is verified in a different manner by showing that the distribution of luminosities calculated on this first power basis is, with the exception that has been noted, independent of the distance. Obviously, sample groups drawn from different sections of the range of distances, as in Table III, would not show the close approach to uniformity that is evident in the table unless the basis for reducing observed to absolute luminosity were correct.

The radio-quiet quasars constitute a transition group, and their properties vary all the way from those of late Class I to those of early Class II radio emitters. At the early end of this range the radio-quiet object is simply a former Class I quasar in which the primary radioactivity subsided relatively soon, while at the late end it is a prospective Class II quasar that is relatively slow in developing secondary radioactivity. Only a few of these objects are found in the 1967 reference list (although they are more prominent in the 1972 data), and for purposes of the analysis those in the Class II distance range have been included with the radio emitters.

Unlike the Class II quasars, which are old, because Class II is the last evolutionary stage, and have traveled mainly in time, so that their absolute luminosity approaches the value calculated on the time basis (inversely proportional to the quasar distance q), the much younger Class I quasars are more variable in this respect. The early type Class I objects are, by definition, still relatively close to their points of origin, and their distances represent mainly separation in space. In this case, therefore, the relation between the observed and absolute luminosities approximates the value calculated on the space basis (inversely proportional to the recession distance zr, or to q2). Late type Class I quasars may be just beyond the early stage, so that their radiation is still traveling mainly in space, or they may have originated nearby, so that most of the currently indicated distance represents movement in time, in which case their luminosity pattern approaches that of the Class II quasars. The uncertainty with respect to any individual late type quasar is therefore substantial. In general, however, the relation of the luminosities calculated on the two different bases to the applicable visibility limits gives a good indication of the point of origin.

Most of those quasars whose luminosities, calculated on the q2 basis, are above the q2 limits (the higher of the two limiting values applicable to each quasar) have probably originated at distant locations, and have true absolute luminosities in the neighborhood of the values calculated on that basis. Conversely, where the luminosity on the q basis is only slightly above the corresponding limit (the lower of the two limiting values) the quasar has probably originated nearby and has traveled mostly in time. In those cases where the luminosity calculated on the q basis is substantially above the q limit, but the quasar does not qualify as visible on the q2 basis, the absolute luminosity is somewhere between the q and q2 values, and its true magnitude cannot be determined from the information now available.

Luminosity data for the late type Class I quasars of the 1967 list are given in Table IV. The basis (either q2 or q) on which each of the absolute luminosities in the last column was calculated is indicated by the column in which the corresponding visibility limit is shown, and the probable deviation of the true luminosity from the value given in the table should in each case be judged on the basis of the factors discussed in the preceding paragraph.

In applying the spatial (q2) relation, to which the majority of the late type Class I quasars conform, we must take into account the fact that two-dimensional radiation originating in a three-dimensional region of the universe is divided between a plane passing through a given point and a plane perpendicular thereto. Consequently, the distribution of the radiation in distance is related to half of the absolute luminosity rather than to the total, and in order to obtain the absolute value it is necessary to multiply the observed luminosity by 2q². The relations between observed (l) and absolute (L) luminosities for the two different paths of travel can thus be stated as follows:

            Time basis        L = lq
            Space basis      L = 21q²

A rather striking feature of Table IV is the relatively large number of these late type Class I quasars. Inasmuch as the three classes of quasars that have been identified in the analysis are merely stages in the evolutionary course of quasars in general, the total number of each class present in the universe as a whole at any given time is proportional to the length of time spent in each of the evolutionary stages. The duration of the Class I stage is by far the shortest of the three, and the total number of Class I quasars is therefore relatively small. Yet almost 40 percent of the quasars in the reference list are Class I objects.

On first consideration it might be suspected that this is an effect of proximity; that because the Class I quasars are, on the average, much closer than those of the other groups we see more of the small ones. But this is not the case. The visibility limit on the time basis, characteristic of Class II and the radio-quiet class, is actually lower than that on the space basis, which most of the Class I quasars approximate. The true reason for the large number of visible Class I quasars is that all of these objects which are within the unit boundary and large enough to exceed the visibility limit can be seen on the space basis because of the manner in which

the radiation is distributed. Radiation originating on the time side of the unit level has no inherent spatial direction, and is therefore distributed randomly over all spatial directions when it travels in space. But for travel in time, the direction is determined at the time of emission and there is no occasion for any change. Consequently, this radiation is visible only if we happen to be in the plane of the two-dimensional propagation.

Another conspicuous feature of Table IV is the limitation of the Class I quasars to the shorter distances, although there are absolute luminosities in the table that are high even by Class II standards.

No late type Class I quasars are present in the reference list beyond q = . 646. This early cutoff is a result of the steep rise of the

visibility limit on the q2 basis applying to the spatial travel. Quasars originating nearby and moving out to a greater distance have

passed out of the Class I stage before traveling this far, whereas most of those originating beyond .500 are cut off by the rapidly rising visibility limit, which is up to .116 at this point. The most

distant late type Class I quasar in the list, 3C 57, is a relatively large fragment, with absolute luminosity .230, just above the .194

visibility limit corresponding to its distance.

The visibility limits depend, in the first instance, on the capabilities of the observational facilities that are being utilized. As previously indicated, the numerical values quoted earlier in this work are predicated on a limiting visual magnitude of 19.35, which is approximately the level reached by the observations from which the data in Tables I and II were compiled. We can establish the corresponding visibility limit for ordinary galaxies by noting the luminosity of some particular galaxy at a known distance, and applying the inverse square relation. The galaxy M 87, for instance, at distance .0031, has a magnitude of 9.3, equivalent to a luminosity of 190,5 on the 15 magnitude basis that is being used in this work. A 9.3 magnitude object is 10470 times as luminous as one of 19.35 magnitude. The corresponding distance ratio is 102.3. It follows that when the available facilities are able to reach out to the 19.35 magnitude, the visibility limit for an object of luminosity 190.5 is 317 .

In the initial presentation of the Reciprocal System of theory in The Structure of the Physical Universe, published in 1959, it was pointed out that the recession does not start from zero distance, but from the gravitational limit, the distance at which the outward motion due to the progression of space-time is equal to the inward motion due to gravitation. Inasmuch as the gravitational limit of our Milky Way galaxy, as evaluated in that same publication, is only about one million light years, the difference between this and zero can be ignored in dealing with the recession phenomenon itself, but this difference has an important bearing on the quasar visibility question. The gravitational limit is the point at which all scalar motion, the quasar motion as well as the recession, begins, and up to this point there is only one path by which radiation can travel. The gravitational limit therefore constitutes a datum level at which the visibility limits for the recession distance and the quasar distance are equal.

On the basis of the calculations carried out in the initial publication, a distance of one million light years is equivalent to zr = .00011. At this distance, the limiting luminosity 190.5, corresponding to distance zr = .317, reduces to 2.29 x 10-5. This, then, is also the visibility limit for a galaxy at the equivalent quasar distance .0367. In order to project this limit to the standard distance q = 1.00, we divide by the square of .0367, which gives us .017. This is the visibility limit that would exist if a quasar were able to emit radiation in three dimensions, in the manner of a normal galaxy. Of course, a quasar cannot do this, but at a level of 1.00 (in natural units) dimensional differences disappear, and consequently this value .017 is also the visibility limit at 1.00 for radiation emitted in two dimensions. This is the theoretical value corresponding to the .017 minimum of the observed absolute luminosities.

If we combine the foregoing calculations, we find that there is a direct relation between the gravitational limit and the visibility limit at the standard quasar distance. On the basis of a limiting magnitude of 19.35, the theoretical visibility limit at q = 1.00, expressed in the units utilized in this work, is 154.75 times the gravitational limit, expressed in natural units. The agreement between the theoretical limit thus calculated, .017, and the lowest absolute luminosity actually observed is therefore a confirmation of the theory, and of the previous calculation of the gravitational limit. It should be noted, however, that the correlation between the calculated and observed values is actually closer than we are entitled to expect. No more than an approximate agreement could have been anticipated, as the gravitational limit is a function of the mass of our galaxy, which is not known with precision. The fact that the .017 limit derived by calculation is identical with the lowest observed value is therefore somewhat fortuitous.

On the basis of the two-dimensional distribution of the quasar radiation, the .017 visibility limit at q = 1.00 becomes .0367 x .017 = .000624 at the gravitational limit q = .0367. Inasmuch as this is the initial point for all motion of the recession type (scalar motion) irrespective of whether it involves travel through space or through time, the .000624 visibility limit applies to both modes of travel, but since travel through space involves distribution of the radiation over an additional dimension, the visibility limits diverge at distances beyond the gravitational limit. The limit on the space basis, which is proportional to q2, rises much more rapidly. Its numerical value at any point q is .000624 (q/.0367)2. At q z 1.00 the limit is .4632, which is 27.25 times the .017 limit applying to travel through time. This is equivalent to 3.6 magnitudes, and it means that when the existing facilities are able to reach the 19.35 magnitude in dealing with radiation traveling through time, their theoretical limit in observing quasar radiation traveling by way of the space route is the 15.75 magnitude.

The explanation of this difference in the limiting magnitudes is that the ability of the instruments to detect radiation is a function of the intensity of the radiation rather than of the total amount received during a specified period of time. This is somewhat analogous to the photoelectric effect, which does not occur at all, irrespective of the total amount of radiation involved, unless the frequency of the radiation exceeds a certain limiting value. When the plane of propagation of a two-dimensional radiation is fixed, as it is for travel in time, the intensity is constant, just as in the case of three-dimensional radiation. The 19.35 limiting magnitude is a measure of the ability of the observational facilities to receive radiation of this nature which is continuously at full intensity.

But if the two-dimensional radiation is distributed over three dimensions of space by the operation of the probability principles, as it is when the quasar radiation travels through space, the intensity of the radiation in any one plane is reduced accordingly, and a greater total amount of radiation is required to produce the same intensity. The 15.75 magnitude is the theoretical total radiation that will produce the same radiation intensity as a 19.35 magnitude radiation confined to one plane.

The full theoretical effect on the visibility limit is never attained, however, because, as previously mentioned, only half of the total radiation from the quasar can reach any given point by way of the space route. The ineffective half of the radiation is part of the theoretical difference between the full amount of radiation and the portion that is effective in any one plane. The reduction by half therefore affects only the total radiation received, and not the intensity. It thus results in a reduction in the total luminosity required to produce the equivalent of a 19.35 magnitude intensity. A factor of 2 is equivalent to 0.75 magnitude, and with this reduction the limiting magnitude for quasar radiation traveling in space becomes 16.50. A similar modification of the theoretical limit is applicable to the early type Class I quasars, and will be discussed later.

This is another of the places where the development of theory from the basic postulates of the Reciprocal System -- the process of defining the principles and relations that exist in a universe composed entirely of motion -- leads to conclusions that are widely at variance with conventional thought. But the greater the deviation from orthodoxy, the greater the significance of agreement between theory and observation. Where a theory predicts only a slight deviation from the results that would be obtained on the basis of conventional ideas, observational uncertainties make a decision between the two alternatives very difficult, but where the predicted results are widely divergent, as in this matter of the visibility limits, and in so many of the other results of the same theoretical development, agreement between theory and observation is a definite confirmation of the theory.

The existence of the 16.50 magnitude limit is clearly demonstrated in Table IV. Eight of the quasars in this table have a high enough luminosity to make it probable that their radiation is traveling through space, and all of these are at the 16.50 level or lower (that is, more luminous). The most distant of these quasars, 3C 57, is a 16.40 magnitude object at q ~ .646. Its absolute luminosity is .230, which is relatively high, but not high enough to be unusual. If it were possible to reach the 19.35 magnitude, a late type Class I

quasar as luminous as 3C 57 could be seen at a distance almost four times as great; all the way out to the ultimate quasar distance limit. The sharp cutoff at distance .646 is therefore a confirmation of the theoretical conclusion that the visibility of quasars of this kind, when observed with facilities comparable to those available up to 1972, is subject to a limit at magnitude 16. 50.  As will be seen when we begin consideration of the early type Class I quasars the existence of a limiting magnitude numerically less than 19.35 is even more obvious there, as the early quasars constitute a very distinct group, and none of them has moved very far from the point of origin, so all of their radiation travels in space.

The radio-quiet quasars within the Class I distance range are also a distinctive and quite homogeneous group, and some consideration of their place in the general picture is appropriate, but only two of them appear in the 1967 reference tabulation. In order to have a Sample of adequate size, all Or the quasars of this class that are listed in the 1972 publication have therefore been included in Table V. As would be expected on theoretical grounds, these are small objects, their average luminosity being only .021, whereas the average of those of the late type Class I quasars of Table IV that are in the same distance range is .064. The reason is that smaller quasars nave less energy to start with, being products of less violent explosions, and they dissipate it more rapidly because of their greater ratio of surface area to mass. They consequently pass through the various stages of evolution in less time, and some of them reach the radio-quiet stage while the larger Class I quasars of the same age are still radio emitters.

Unlike those of the late type, the absolute luminosities of the early type Class I quasars are clearly defined, inasmuch as the criterion on which this classification is based excludes those objects which have undergone any substantial change of spatial position since their origin. For purposes of this present analysis, this unequivocal identification is very helpful, as these early type quasars have some unique characteristics, according to the theory, and the reliability of the values obtained from the calculations makes it possible to arrive at a clear picture of the situation; one that gives us a definite verification of the theoretical conclusions.

A significant feature of the early Class I stage is that this is the only evolutionary period in which a quasar has a net explosion speed above q = 2.00, the outer boundary of the first double unit of quasar motion. If a quasar originates at distance zr, its explosion speed arrives at an equilibrium with the oppositely directed gravitational motion at a quasar distance 3.5 zr² ½,  and a net outward speed below 2.00, but a finite time is required for the quasar to move out to this equilibrium distance, and in the meantime the quasar is traveling at a very high speed, starting with the full explosion speed, well above 2.00, and gradually slowing down as the equilibrium distance is approached. Ordinarily an object with a net speed above 2.00 will move off into time and become unobservable, but the retarding effect of gravitation begins to take hold immediately, and this, together with the low value of the recession, zr, keeps the quasar within the observable limits until it drops below 2.00 net speed and loses the special features of the early type quasars.

As brought out in Q&P, and discussed in further detail in TYL, only 1/8 of any motion beyond the double unit level (q = 2.00) is effective in the region of three-dimensional space. It follows that only 1/8 of the optical radiation from an early type Class I quasar is observable from our location, and in calculating the absolute luminosity from the observed magnitude the factor 8 must be substituted for the factor 2 which applies to the radiation from those of the late type Class I quasars whose radiation reaches us through space. The factor 8 also applies to the radiation at radio frequencies, but the radio emission takes place mainly from matter which is moving at ultra-high speeds within the quasar, and all of the radio values are therefore determined on the factor 8 basis. Inasmuch as we are interested only in relative values of the radio emission in this work, the constant factor can be absorbed into the units in which the radiation is expressed. Table VI gives the optical and radio data for

the early type Class I quasars of the reference tabulation, calculated on the basis explained in the foregoing discussion.

Since the early Class I quasars are products of recent extremely violent explosions, the emission can be expected to be relatively high both at optical and at radio frequencies. A comparison of the values of Table VI with those of Table IV shows that this expectation is fully realized. The maximum absolute radio power in the early group is sometimes the corresponding late group maximum. The ratio of the optical maxima is about the same, and the average optical emission of the early quasars is four times the average of the late group.

One of the effects of the enhanced luminosity is to increase the number of visible quasars of this class above that which could be expected on the basis of the comparatively short duration of the early Class I stage. A still more effective contributor to the greater numbers of visible early type objects is the extension   of the visibility limit by reason of the change in the