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Now that we have identified the different classes of quasars, located them in the evolutionary course of development, and established criteria by which to distinguish one from another, it will be of interest to undertake what we may describe as a census, to get an idea as to the relative numbers of observable objects of the various classes, the factors that are responsible for the differences between these classes, and the effect of the evolutionary development on these various populations.

The list of known quasars is continually being extended, both by increasing the capability of the available instrumentation, and by more use of the existing equipment. A complete survey of the observable quasars is therefore impossible, as matters now stand. The best that we can do is to examine all those on which the necessary information was available up to some particular date. Under the circumstances there is no advantage to a very large sample. As the modern poll takers have demonstrated, a relatively small sample is adequate if it is actually representative. Rather than attempting to cover all of the quasars currently known, we will therefore review and update the results of a study made some years ago on the same group of quasars examined in the studies reported in the preceding chapter, those on which the relevant data were available in 1967.

The total number of quasars included in the 1967 tabulation by the Burbidges is 102, but color indexes were not available for 26 of these. The study was therefore confined to the other 76. Of these, 45, or sixty percent, were quasars of Class II. The spatial distribution of these objects is quite uniform out to a quasar distance of 1.00. On the two-dimensional basis that we have seen is applicable to the intermediate speed range, two independent distributions are possible in three-dimensional space. The existing quasars can be located either in the scalar dimension that is represented in the conventional spatial reference system, or in a dimension that is perpendicular to it. It follows that only half of the existing quasars are visible. There are 20 visible Class II quasars within a 1.00 radius (quasar distance) and 5 within 0.50. Both of these figures represent the same density: 20 quasars in a sphere of radius 1.00. We may therefore take this as the true density of Class II quasars observable in this distance range with the 3C instruments and procedures. The total number of these quasars in equivalent space is twice this number, or 40 per spherical unit. In the second quasar distance unit, from 1.00 to 2.0O, there is another division between two perpendicular dimensions, which again reduces the visibility by one half, cutting the visible number to one quarter of the total. This means that where the actual quasar population remains unchanged, only 10 Class II quasars per spherical unit are visible in the quasar distance range from 1.00 to 2.00.

The number of Class II quasars calculated on the foregoing basis for spheres of successively larger radius is compared with the observed number in Table XI. There are a number of factors that cause some deviations from the theoretical distribution at very short distances, but the number of quasars involved is so small that the effect on the distribution pattern is negligible. Except for the normal amount of random fluctuation, the theoretical distribution is maintained throughout the quasar distance range up to about 1.80. Beyond this point there is a slow decrease as the normal limit at 2.00 (total redshift 2.326) is approached, and an increasing number of quasars become unobservable because they cross the boundary into the cosmic sector.

The relation of the number of visible quasars to the distance has been a matter of much interest to the astronomers because of the bearing that it has, or may have, on the question as to whether the density of matter in the universe is decreasing, as required by the Big Bang cosmological theory. This has been a hotly contested subject, but the present consensus, as reported by H. L. Shipman, is that ”Quasars were far more abundant in the early universe than they are now.“ 256 But this conclusion is based on the assumption that the quasars are distributed three-dimensionally, and the data of Table XI that confirm the two-dimensional distribution, together with the corroborative evidence presented earlier, cut the ground out from under the astronomers' conclusions. From these data it is evident that there has been no change in the quasar density during the time interval represented by the quasar distance of 2.00.

The close correlation between the calculated and observed quasar distributions not only demonstrates the uniformity of the quasar density throughout space, but also confirms the validity of the theoretical principles on which the calculations were based. It should be emphasized that this is not merely a case of providing a viable alternative to the currently accepted view of the situation. The fact that uniformity of distribution on the two-dimensional basis has been demonstrated not only for the total number of radio-emitting quasars in a representative sample, but also individually for each of the three classes of objects included in this total puts the findings on a firm basis. The essential concept of the Big Bang theory is thus invalidated.

The data for the other two classes of radio-emitting quasars, early Class I and late Class I, are included in Table XI. Here the distribution is reproduced with space densities of 40 and 60 quasars per spherical unit respectively. We thus find that the predominance of Class II quasars in the observed list does not reflect the true situation. Instead of being a 40 percent minority, the Class I objects actually constitute about 70 percent of the total number of radioemitting quasars.

Class II
Number =20q²
Class I—Early
Number =20q²
  0.1   0   0   0.1   0   0
  0.2   1   1   0.2   1   0
  0.3   2   1   0.3   2   0
  0.4   3   5   0.4   3   2
  0.5   5   5   0.5   5   2
  0.6   7   5   0.6   7   7
  0.7   10   7   0.7   10   11
  0.8   13   8   0.8   13   14
  0.9   16   15   0.9   16   16
  1.0   20   20

Number = 10q² + 10
Class I—Late
Number = 30q²
  1.1   22   23
  1.2   24   25   0.1   0   0
  1.3   27   29   0.2   1   1
  1.4   30   31   0.3   3   3
  1.5   33   32   0.4   5   7
  1.6   36   34   0.5   8   9
  1.7   39   36   0.6   11   11
  1.8   42   41   0.7   15   14
  1.9   46   44
  2.0   50   45

The sample on which the study was conducted contains no quasars with quasar distances above 2.00, a fact which indicates that the asymmetric redshift factors, discussed in Chapter 23, that lead to redshifts exceeding the normal limit are relatively uncommon.

Although we know the quasars (and other astronomical objects as well) only as sources of radiation, the amount of information that can be extracted from this radiation is surprisingly large; so large, in fact, that much of it will not be needed for purposes of the kind of a general survey of the various quasar populations that we are now undertaking. The current status of the quasars as astronomy's greatest mystery is not due to a lack of sufficient information, but to the astronomers' inability, thus far, to construct the kind of a theoretical framework that would enable placing the many items of information that now seem irrelevant or contradictory in their proper places relative to each other, and to the astronomical universe as a whole. Availability of a purely deductive system of theory, in which all conclusions are derived by development of the consequences of the fundamental properties of space and time, now provides what is needed.

Our present undertaking is to examine the primary characteristics of the different classes of quasars and to show how they fit into the general picture. We will make use of the information developed in the preceding chapters, particularly that referring to the color indexes, the recession redshift (and distance), z, and the quasar distance (and redshift), q. The other magnitudes with which we will be mainly concerned are the optical luminosity, 1, its absolute value, L, and the radio emission or flux, for which we will use the customary symbol S.

The optical radiation as received is ordinarily expressed in terms of the astronomical magnitude scale. This system of measurement is presumably satisfactory to the astronomers, since they continue using it, but it is confusing to just about everyone else. Actually. it is a historical accident. The magnitudes were originally ordinal numbers—simply positions in a series. The brightest stars were designated as stars of the first magnitude, the next brightest as stars of the second magnitude, and so on. Later these magnitudes were adjusted to conform to a specific mathematical relation, so that they became a measurement scale. but in order to avoid major changes, the upside down ordinal sequence was retained. Thus the stars with the greatest numerical magnitude are not the brightest, but the faintest. For the same reason, the numerical scale, which for convenience is exponential, was constructed on an awkward basis in which 2.5 magnitudes are equivalent to a factor of 10. It has been necessary to refer to astronomical magnitudes to some extent in this work tin order to maintain contact with the astronomical literature. To facilitate translating these values into terms that are more familiar to most readers of this volume, the following table of equivalents may be helpful:

  2   0.75   10   2.50
  4   1.50   50   4;25
  5   1.75   100   5.00
  8   2.25   1000   7.50

The quantity that is being measured in terms of the magnitude scale is the luminosity of the object. For our present purposes we will want to deal with the actual luminosity, and we will therefore convert the magnitudes to luminosities. In order to keep the numerical values within a convenient range we will state the luminosity in terms of the increments of magnitude above 15, converted to the luminosity basis. Such values represent the ratio of the measured luminosity to the luminosity corresponding to visual magnitude 15. For example, the value 0.200 indicates a luminosity one fifth of the reference level. As indicated by the foregoing tabulation, reducing the luminosity by a factor of 5 adds 1.75 to the magnitude. The value 0.200 thus corresponds to magnitude 16.75. We will be concerned mainly with the absolute luminosity, the actual emission from the quasar, rather than with the observed value, which varies with the distance. For this purpose, we will establish a reference datum at the point where q is 1.00 and z is 0.08. The absolute luminosity will be expressed in terms of the measured value projected to this datum by the appropriate relation.

No doubt some exception will be taken to the use of an unorthodox measurement scale in the comparisons that follow, but in addition to generating values that are more convenient to handle, this different scale of measurement will help to avoid the confusion that might otherwise arise from the fact that the basis for projecting the observed luminosity to the absolute system is not the same in our calculations as in conventional practice, and the calculated absolute luminosities corresponding to the observed values will not usually agree.

The same considerations apply to the radio emission values. The values given in the tables are absolute emissions recalculated from the data of Sandage,257 and expressed on a relative basis similar to that used for the optical emission.

As we have seen in the preceding pages, the distinctive characteristics of the quasars and related astronomical objects are due to their greater-than-unit speeds. However, in undertaking to follow the course of development of these objects it will be necessary to recognize that the quasar is a complex object with many speeds, each of which may vary independently of the others. These include:

  1. Quasar speeds. The quasars are ejected with scalar speeds exceeding two units. During the interval in which it is restrained by gravitation, each quasar has a speed of z in space, due to the normal recession, and a net speed of 3.5 z½ in time (equivalent space) in the dimension of the spatial reference system. The observed quasar redshift is a measure of the scalar total of these two redshift components.
  2. Stellar speeds. The pre-explosion activity and the violent explosion raise the speeds of most of the constituent stars of the ejected galactic fragment (the quasar) above the unit level. It is this intermediate speed of the stars of the quasar, and the consequent expansion into time, that are responsible for the small apparent sizes of the quasars. They are galactic equivalents of the white dwarf stars.
  3. Stellar component speeds. The speeds of the individual atomic and molecular components of the stars (temperatures) are independent of the speeds of the stars. Like the stellar speeds, they are increased to levels in the intermediate range by the energy released during the explosion, but they are subject to radiation losses, while the speeds of the stars are not affected by radiation. Consequently. the speeds (temperatures) of the stellar components decrease relatively rapidly, and in most quasars they return to the speed range below unity at the end of the early Class I stage. The stellar speeds, on the contrary, remain in the intermediate range throughout the entire life of the quasar.
  4. Independent particle speeds. Dust and gas particles are accelerated to high speeds in the stellar and galactic explosions, and they retain these speeds (temperatures) longer than the atomic and molecular constituents of the stars because of the lower rate of radiation in the gaseous state. Radio emission therefore continues through both Class I stages.

As indicated in the foregoing paragraphs, the explosive forces impart the initial speeds of the quasar system. Prior to the explosion that produces the quasar the interior of the giant galaxy of origin is in a state of violent activity resulting from a multitude of supernova explosions. The products of these explosions are confined to this interior region by the overlying stellar aggregate, which, as pointed out earlier, has physical characteristics resembling those of a viscous liquid. The dust and gas particles in the agitated interior are moving with speeds greater than that of light. When the internal pressure finally becomes great enough to blow out a section of the overlying material as a quasar, a large quantity of this fast-moving material becomes part of the quasar aggregate. The violent readjustments resulting from the explosion accelerate a substantial proportion of the component stars of the quasar to these same intermediate speeds.

After the initial sharp decrease during the lacertae stage, the status of the quasar speeds at the beginning of the early Class I stage is as follows: The quasar as a whole is moving unidirectionally outward at ultra high (above two units) speed, but is subject to the gravitational effect of the galaxy of origin. This results in the net speed reflected in the observed redshift, z + 3.5z½ The constituent stars of the quasar are moving at intermediate (between one and two units) speeds, and are therefore expanding into time, causing the apparent spatial dimensions of the quasar to decrease. The atomic and molecular constituents of the stars are likewise moving at intermediate speeds, with similar results, putting the stars into the white dwarf condition. The gas and dust particles, which acquired upper range speeds prior to the explosion, undergo a relatively slow speed decrease. All matter accelerated to a higher speed level by the explosion is experiencing isotopic adjustments, and is therefore emitting strong radiation at radio wavelengths.

As the quasar ages and moves away from the galaxy of origin its net outward speed increases because of the continual reduction of the retarding gravitational force. All of the internal speeds decrease because the large initial energy content is supplied by the galactic explosion, and there is no active source of energy in the quasar itself, other than the normal stellar generation processes, which are wholly inadequate to maintain the high energy concentration that exists initially. The internal motions therefore lose energy in radiation and other interactions with the environment.

This decrease in the internal activity results in a corresponding decrease in the optical luminosity. In determining the true, or absolute, luminosity from the observed value, one of the factors that must be taken into consideration is the effect of the distribution to two perpendicular planes. This applies to the radiation as well as to our ability to see the quasars, and it means that only half of the radiation originating from the quasar components that are moving at speeds below unity is included in the observed luminosity. If the quasar components from which the radiation originates are moving at intermediate speeds, the distribution of the radiation is extended to the full eight units of the intermediate region. In calculating the absolute luminosity, the measured value is thus subject to an increase by a factor of 2 or 8. The limitation of the intermediate range speeds (temperatures) to the early Class I stage restricts the application of the ratio of 8 to l to this class. For all other classes of quasars the ratio is 2 to 1.

The other determinant of the relation between the observed and absolute luminosities is the distance. The magnitude of this effect depends on the route by which the radiation travels. The normal recession in space of a quasar elected from a nearby galaxy is small, and the quasar motion is therefore primarily in time from the very start. Consequently, the radiation from this object travels back to us through time. On the other hand, a quasar ejected from a distant galaxy is receding at a high speed in space at the time of the explosion, and a substantial period of time elapses before the motion in time in the explosion dimension reaches the recession level. In the meantime the radiation from this quasar travels back through space. Eventually, however, the continually increasing net explosion speed exceeds the speed of the recession, after which the travel of the radiation from this distant quasar, like that from the one nearby, takes place through time.

On this basis, the radiation from the lacertae, the quasars of early Class I, the youngest members of Late Class I, and a few small, rapidly evolving, members of the radio-quiet class, travels in space. That from the remainder of late Class I, most of the radio-quiet quasars, and the quasars of Class II, travels in time. Quasars that are very close, where random motion in space plays a significant role, may continue on the space travel basis beyond the normal transition point.

Because of the two-dimensional distribution of the quasar radiation originating in the intermediate speed range, the radiation received through space is proportional to the first power of the distance in space, z. Inasmuch as q = 3.5 z½ it is also proportional to q². The distribution of the radiation in time is likewise two-dimensional, and the quasar radiation received through time is proportional to the first power of the distance in time (equivalent space), q. In the discussion that follows all distances will be identified in terms of q (time) or q² (space).

Table XII gives the observational data for the early Class I quasars in the group under consideration, expressed in the terms that have been described, together with two calculated values, the quasar distance, q, and the visibility limit. This visibility limit is the approximate luminosity that a quasar of a given class and distance must have in order to be located by a survey with the equipment and techniques available to the observers whose results constitute the quasar sample that is being examined.

A purely theoretical determination of this limit would require a quantitative evaluation of the capabilities of the equipment in use at the time the observations were made, an undertaking that is not feasible as a part of the present investigation. The visibility limits for the quasars of the various classes have therefore been determined empirically from the minimum luminosities of the observed Class II quasars; that is, it is assumed for present purposes that the limiting luminosity actually observed approximates the true limit.

The faintest magnitudes reached in the results here being studied were 19.44 (3C 280.1), l9.35(3C 2), and 19.25(1116 + 12). The corresponding absolute luminosities are 0.025, 0.017, and 0.037. The quasar distance of 3C 2 is 0.962. If we assume that this quasar, which has the lowest luminosity of any Class II object in the sample group, is almost at the visibility limit, we can take a luminosity of 0.016 (magnitude 19.50) as the limit at q = 1.00. The corresponding limits, on the q basis, for 3C 280.1 and 1116+12 are then 0.020 and 0.029 respectively; that is. both of these quasars are close to the limit of visibility. This should be sufficient to justify using 0.016 for the visibility limit on the q basis for the purposes of our investigation.

Quasar Z q U-B B-V S m Limit L
1049-09 .344 .335 -.49 +.06 .17 16.79 .057 .172
3C 48 .367 .357 -.58 +.42 1.49 16.2 .065 .337
1327-21 .528 .507 -.54 +.10 .31 16.74 .132 .413
3C 279 .538 .516 -.56 +.26 .76 17.8 .136 .162
3C 147 .545 .523 -.59 +.35 2.79 16.9 .140 .381
3C 275.1 .557 .534 -.43 +.23 3.77 19.00 .146 .057
3C 345 .595 .569 -.50 +.29 .72 16.8 .166 .495
3C 261 .614 .586 -.56 +.24 .25 18.24 .176 .140
3C 263 .652 .621 -.56 +.18 .48 16.32 .197 .913
3C 207 .684 .650 -.42 +.43 .43 18.15 .216 .186
3C 380 .692 .637 -.59 +.24 2.61 16.81 .221 .653
1354+19 .720 .682 -.55 +.18 .42 16.02 .238 1.455
3C 254 .734 .695 -.49 +.15 .78 17.98 .247 .247
3C 138 .760 .718 -.38 +.23 1.33 17.9 .264 .285
3C 196 .871 .817 -.43 +.60 3.25 17.6 .342 .486
0922+14 .895 .838 -.52 +.54 .23 17.96 .360 .365

The objects that have been used for the evaluation of this limit are quasars of Class II, in which, as we have seen, the radiation travels through time (on the q basis). The radiation from most of the Class I quasars travels through space and this modifies the visibility limits. The principal factor that enters into this situation is that there is a difference between the brightness, or luminosity, of an astronomical object, and what we may call the intensity of the radiation, if the radiating matter is moving at a speed greater than unity (the speed of light). This difference arises because of the introduction of a second time component at the higher speed. At speeds less than unity the only time entering into the radiation process is the clock time. At higher speeds there are also changes in position in three-dimensional time (relative to the natural datum). Here it becomes necessary to> distinguish between the time of the progression of the natural reference system, the time that is registered on a clock, and the total time involved in the physical phenomenon under consideration. This total time is the sum of the clock time and the change in time location.

Ability to detect radiation with equipment of a given power is determined by the intensity of the radiation, the radiation per unit of time. Distribution of the radiation over additional units of time reduces the intensity. The luminosity, however, is measured as the amount of radiation received during the total time corresponding to a unit of clock time (one of the components of the total), and it is not affected by the number of units involved in this total.

If the radiation travels through time its magnitude is a scalar quantity in spatial terms. It therefore has no geometrical distribution, and is received at full strength. However, if radiation from an object in the intermediate speed range travels through space it is distributed in the spatial equivalent of time; that is, in equivalent space. As we saw in Chapter 23, the full distribution extends over 64 effective units. Only two of these are collinear with the scalar dimension of the spatial reference system. Thus the radiation received through space from an object in the intermediate region per unit of total time, the intensity of the radiation, is 1/32 of the total emission.

It follows that the visibility limit for travel in space corresponding to the 0.016 limit for travel in time is 32 x 0.016 = 0.512. This is the limit applying at quasar distance 1.00. For other distances, the limits are 0.016 q (time travel) and 0.512 q² (space travel). The limits shown in Table XII and the tables of the same nature that will follow have been calculated on this basis.

While this general distribution of the radiation over the full 64 units in time does not affect the luminosity, we have already found that there are other distributions in space that reduce the ratio of the observed radiation to the original emission by a factor of 8 for the early Class I quasars and a factor of 2 for all others. The ratio of intensity to luminosity for motion through space is then the ratio of intensity to emission, 1/32, divided by the ratio of luminosity to emission, 1/2 or 1/8. This gives us 1/4 for the early Class I quasars and 1/16 for the others.

The significance of these ratios is that they enable us to determine the visibility limits in terms of the observed magnitudes (luminosities) for those Class I quasars whose radiation travels through space. The 1/4 ratio tells us that quasar radiation originating in the intermediate speed range and received through space (q² basis) has only one quarter of the intensity that it would have if travel through time (q basis) were possible. This is equivalent to a difference of approximately 1.5 magnitudes. The q² limit corresponding to the 19.50 magnitude of the q limit applicable to the quasar sample under investigation is thus 18.00. While the equipment used in collecting the data included in this sample was capable of observing Class II quasars at 19.50 magnitude, early Class I quasars, whose radiation travels through space, had to be 1.5 magnitudes (4 times) brighter in order to be detected.

The reality of the 18.00 limit can be seen by inspection of the values in Table XII. Only one of the magnitudes in this list exceeds this limit by more than the amount that can be expected in view of the variability in the luminosity of these extremely active objects. The one exception, 3C 275.1, is a very strong radio emitter, with the largest radio output of any quasar in the sample under examination. It was probably located optically in an intensive search with powerful equipment.

The gradual decrease in the energy level of the quasars that we observe in the early Class I stage continues during the late Class I stage, as indicated in both the radio emission (Fig. 30) and the optical luminosity (Fig. 31). Since the spatial change of position is initially very slow, the travel of the radiation is still mainly in space (q² basis) at the start of the late stage, but by its end the radiation from many of the smaller objects (those below about 0.50 absolute luminosity) is reaching us through time (q basis). Coincidentally, the color indexes become less reliable as an indicator of quasar age, as the smaller aggregates evolve more rapidly.

These factors introduce some uncertainty into the determination of the absolute luminosity of objects of this class. Any individual late Class I quasar outside of the local region in which random motion is significant may be just beyond the early stage, so that its radiation is still traveling in space, or it may have originated nearby, so that the currently indicated distance represents travel in time. Usually, however, the relation of the luminosities calculated on the two different bases to the applicable visibility limits indicates the correct alternative. Most of the quasars whose absolute luminosities calculated on the q² basis are above the q² limits probably have true 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 quasar radiation probably travels through 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.

Time travel   1   1   1   19.50
Early Class I   1/32   1/8   1/4   18.00
Other space travel   1/32   1/2   1/16   16.50

Luminosity data for the late Class I quasars of the reference list are given in Table XIII. The basis (either q or q²) 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. For these quasars. whose luminosity to emission ratio is ½, the intensity to luminosity ratio becomes 1/16. This corresponds to a magnitude difference of 3.0, which puts the visibility limit for this quasar class at 16.50. The limiting magnitudes for the different classes of quasars are summarized in this tabulation:

Quasar Z q U-B B-V S m
q q
2135-14 .200 .197 -.83 +.10 15.53 .020 .048
1217+02 .240 .235 -.87 +.02 .06 16.53 .028 .027
PHL1093 .260 .255 -1.02 +.05 17.07 .004 .038
PHL1078 .308 .301 -.81 +.04 18.25 .005 .015
3C249.1 .311 .303 -.77 -.02 .22 15.72 .047 .095
3C277.1 .320 .312 -.78 -.17 .20 17.93 .005 .021
3C351 .371 .360 -.75 +.13 .33 15.28 .066 .200
3C 47 .425 .411 -.65 +.05 .58 18.1 .007 .024
PHL 658 .450 .435 -.70 +.11 16.40 .097 .104
3C 232 .534 .513 -.68 +.10 .18 15.78 .135 .257
3C 334 .555 .532 -.79 +.12 .35 16.41 .145 .155
MSH 03-19 .614 .586 -.65 +.11 .60 16.24 .176 .219
MSH 13-011 .626 .596 -.66 +.14 .48 17.68 .010 .051
3C 57 .68 .646 -.73 +.14 .01 16.40 .214 .230

The limitation of the Late Class I quasars to the shorter distances is a conspicuous feature of TableXIII, as there are absolute luminosities among this group of objects that are high even by the standards of the Class II quasars, which can be seen all the way out to the 2.00 sector limit. No quasars in TableXIII have a quasar distance beyond 0.646. This early cut-off is a result of the 16.50 limiting magnitude, together with the steep rise of the visibility limit on the q² basis applying to space 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 0.500 are cut off by the rapidly rising visibility limit, which is up to 0.128 at this point. The most distant late Class I quasar in the list, 3C 57. is a relatively large fragment, with absolute luminosity 0.230. just above the 0.214 visibility limit corresponding to this distance.

The existence of the l6.500 magnitude limit is clearly demonstrated in the table. Nine of the quasars in this list have a high enough luminosity in proportion to the visibility limit to make it probable that their radiation is transmitted through space, and none of these is appreciably above 16.50 magnitude (that is, less luminous).

A comparison of the values in Table XIII with those of Table XII shows the extent of the decrease in energy emission that takes place as the Class I quasars grow older. Because the early Class I quasars are products of extremely violent galactic explosions, their emission is very high, booth at optical and radio frequencies, much above that of any other quasar class. In the absence of any adequate source of replacement of the energy that is lost by radiation the internal activity gradually subsides, and the average emission in the late Class I stage is much lower. The maximum emission in the early class, both optical and radio, is six times the maximum of the late class. The average optical luminosity of the quasars of early Class I is four times the average of those of late Class I. The average radio emission in early Class I is also four times the average emission of those members of the late class for which radio data were available.

Since the radio and optical radiation are produced by different processes their decline as a result of the gradual decrease in the internal energy content of the quasars does not necessarily have to proceed at exactly the same rate, but the fact that the relative emissions of the two groups are the same for both types of radiation is a significant confirmation of the validity of the theoretical relations on which the calculations are based.

The Class I radio-quiet quasars are 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 sample under examination. In order to have an adequate sample, the quasars of this class listed in the 1972 compilation by Burbidge and O'Dell 251 have been added to those in the 1967 list. TableXIV gives the emission data for these quasars. As would be expected on theoretical grounds, these are small objects, their average luminosity being only 0.018, whereas the average of those of the late Class I radio-emitting quasars of Table XIII that are in the same distance range is 0.064. The reason for this difference is that the smaller quasars have less energy to start with, 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.

B 234
  .060   .060   .001   .006
B 264
  .095   .094   .002   .016
TON 256
  .131   .130   .009*   .015*
B 154
  .183   .180   .003   .007
B 340
  .l84   .181   .003   .030
  .l86   .183   .003   .006
B 114
  .221   .217   .003   .015
PHL 1186
  .270   .264   .004   .010
B 46
  .271   .265   .004   .020
PHL 1194
  .299   .292   .005   .029
RS 32
  .341   .332   .005   .009
PHL 1027
  .363   .353   .006   .054
PHL 1226
  .404   .391   .006   .020
B 312
  .450   .435   .007   .010
*q² basis

This more advanced evolutionary status is reflected in the mode of travel of the radiation. While the radiation from the majority of the late Class I radio-emitting quasars travels in space, all but one of the radio-quiet quasars in Table XIV has reached the stage where the travel of the radiation is in time. One of the factors that contributes to this result is that the visibility limit of these small objects on the q² basis is reached relatively soon. Only three of the 14 quasars listed in Table XIV have absolute luminosities over 0.020. The visibility limit on the q² basis corresponding to 0.020 luminosity is at a quasar distance of about 0.200. This means that a Class I radio-quiet quasar whose radiation travels in space is visible only within this relatively short distance.

As in the case of the Class I radio emitters, the limitation on the distance of the radio-quiet quasars whose radiation travels in time is a result of evolutionary development. By the time these objects have moved from their relatively near locations of origin out to a quasar distance of about 0.400 their optical emission has decreased to the point where it is not detectable with equipment of the kind used by the investigators whose results are reported in Table XIV. The most distant quasar of this group is at a quasar distance of 0.435. There are no radio-quiet objects between this distance and q = 1.136 in either of the two samples that we are examining. They reappear in the range beyond I .136. The factors that are responsible for this distribution pattern will be considered later in this chapter.

There is considerable doubt as to the true status of some of the small objects that have been classified as quasars. A recent (1982) news item reports that B 234, the closest object in TableXIV (z = 0.060) and B 272, another object that has been regarded as a nearby quasar (Z = 0.040), are H II galaxies, in which the radiation originates in large regions of ionized hydrogen 258. The members of this recently recognized class of galaxies appear to be in the size range of small spirals, and in approximately the same evolutionary stage, but they have not yet acquired the spiral structure. It is possible that more of the small nearby ”quasars“ are actually galaxies of this new class, but this should not change any of the conclusions reached herein, other than the estimate of the minimum quasar size, which might be increased slightly.

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 an object should approximate the value calculated on the q basis. Table XV gives the luminosity data thus calculated for the Class II quasars from the reference list that are nearer than q = 1.00. There is one exceptional case in this tabulation. As noted earlier. when a relatively large quasar is very close to the location from which we are observing it, the outward movement may be retarded long enough to enable the quasar to reach Class II status before the transition from radiation travel in space to travel in time. The quasar 3C 273 is in this condition.

Quasar Z q U-B B-V S m Limit L
3C 273 .158 .156 -.85 +.21 1.50 12.8 .012 .369
2251+11 .323 .315 -.84 +.20 .15 15.82 .005 .148
1510-08 .361 .351 -.74 +.17 .35 16.52 .006 .087
1229-02 .388 .376 -.66 +.48 .20 16.75 .006 .075
3C 215 .411 .398 -.66 +.21 .21 18.27 .006 .020
2344+09 .677 .643 -.60 +.25 .30 15.97 .010 .263
PHL 923 .717 .679 -.70 +.20 17.33 .011 .079
3C 286 .849 .797 -.82 +.22 2.21 17.30 .013 .096
3C 454.3 .859 .806 -.66 +.47 2.13 16.10 .013 .293
1252+11 .871 .817 -.75 +.35 .26 16.64 .013 .181
3C 309.1 .904 .846 -.77 +.46 1.33 16.78 .014 .164
0957+00 .906 .847 -.71 +.47 .23 17.57 .014 .080
3C 336 .927 .866 -.79 +.44 .69 17.47 .014 .089
MSH 14-121 .940 .877 -.76 +.44 .95 17.37 .014 .099
3C 288.1 .961 .895 -.82 +.39 .56 18.12 .014 .050
3C 245 1.029 .955 -.83 +.45 .68 17.25 .015 .120
CTA 102 1.037 .962 -.79 +.42 1.91 17.32 .015 .114
3C 2 1.037 .962 -.96 +.79 .83 19.35 .015 .017
3C 287 1.055 .977 -.65 +.63 1.24 17.67 .016 .084
3C 186 1.063 .984 -.71 +.45 .95 17.60 .016 .090

Table XVI is a similar presentation of the corresponding data for the Class II quasars at quasar distances greater than 1.00. The objective of separating the Class II objects into these two groups is to show that, from a luminosity standpoint, the two groups are practically identical. The range of values in each case is about the same, and the average luminosity for the group below 1.00 is 0.126, while that for the more distant group is 0.13X. In booth the average and the maximum luminosities there is a small increase at the tar end of the distance range, above' 1.70, due to the changes that take place as the sector limit at 2.00 is approached, changes that were previously discussed in connection with the redshifts (Chapter 23) and the color indexes (Chapter 24). Otherwise, wherever we draw out a random sample of Class II objects we obtain practically the same luminosity mixture.

Quasar Z q U-B B-V S m Limit L
3C 208 1.110 1.024 -1.00 +.34 .98 17.42 .016 .111
3C 204 1.112 1.026 -.99 +.55 .19 18.21 .016 .053
1127-14 1.187 1.090 -.70 +.27 1.51 16.90 .017 .190
BSO-1 1.241 1.136 -.78 +.31 16.98 .018 .183
1454-06 1.249 1.142 -.82 +.36 .45 18.0 .018 .072
3C 181 1.382 1.254 -1.02 +.43 1.02 18.92 .020 .034
3C 268.4 1.400 1.269 -.69 +.58 .73 18.42 .020 .055
3C 446 1.403 1.271 -.90 +.44 1.48 18.4 .020 .056
PHL 1377 1.436 1.298 -.89 +.15 16.46 .021 .339
3C 298 1.439 1.301 -.70 +.33 3.30 16.79 .021 .250
3C 270.1 1.519 1.367 -.61 +.19 1.03 18.61 .022 .049
3C 280.1 1.659 1.480 -.70 -.13 .80 19.44 .024 .025
3C 454 1.757 1.559 -.95 +.12 .82 18.40 .025 .069
3C 432 1.805 1.597 -.79 +.22 .93 17.96 .026 .104
PHL 3424 1.847 1.630 -.90 +.19 18.25 .026 .082
PHL 938 1.93 1.695 -.88 +.32 17.16 .027 .232
3C 191 1.953 1.713 -.84 +.25 1.18 18.4 .027 .075
0119-04 1.955 1.715 -.72 +.46 .39 16.88 .027 .304
1148-00 1.982 1.736 -.97 +.17 .84 17.60 .028 .158
PHL 1127 1.990 1.742 -.83 +.14 18.29 .028 .084
3C 9 2.012 1.759 -.76 +.23 .41 18.21 .028 .091
PHL 1305 2.064 1.800 -.82 +.07 16.96 .029 .295
0106+01 2.107 1.833 -.70 +.15 .56 18.39 .029 .081
1116+12 2.118 1.841 -.76 +.14 .90 19.25 .029 .037
0237-23 2.223 1.922 -.61 +.15 .74 16.63 .031 .429

This does not mean that the optical characteristics of all Class II quasars are identical; it merely means that whatever differences do exist are distributed throughout the Class II evolutionary stage. There are periods in the life of Class II quasars when the internal explosive activity is at a level above normal. but these active periods are not confined to any one phase of the Class II existence, and may occur at any time.

One of the significant results of the near identity between these two quasar groups at much different distances, when their absolute luminosities are calculated by means of the first power relation derived from theory, is to supply another confirmation of that relation; that is, to confirm the two-dimensional nature of the quasar radiation. The validity of this relationship was demonstrated in Quasars and Pulsars by a direct correlation between quasar distance 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 one exception that has been noted, independent of the distance. Obviously, sample groups from different sections of the range of distances would not show the close approach to uniformity that is evident in the tables unless the basis for reducing observed to absolute luminosity is correct. The identification of the Class II quasars above q = 1.00 is positive, as no other quasars have quasar distances in this range. It then follows that the agreement between the properties of the two groups of Class II quasars also validates the criteria by which the members of the group below 1.00 were differentiated from the Class I quasars that exist in the same distance range.

It is clear from the entries in Table XVI that the quasars do not thin out gradually with distance, as expected on the basis of conventional theory. On the contrary, there is evidently a sharp cut-off at some point just beyond the last object of the sample group (quasar distance 1.922). This is not due to decreased visibility, as the visibility limit at the 1.922 distance is 0.031, far below the 0.133 average luminosity of the Class II quasars. It must result from some other limiting factor that comes into operation at this distance. This is in full agreement with the theoretical conclusion that the quasars that retain the normal 3 ½--3½ distribution of the intermediate region units of motion convert to motion in time, and disappear from view. at quasar distance 2.00.

The radio-quiet quasars included in Table XVI are relatively large objects. their average absolute luminosity being 0.145, in sharp contrast to the Class I radio-quiet quasars of Table XIV, which average only 0.018. A substantial size is thus indicated as a requirement for attaining the Class II radio-quiet status. This is understandable when we consider the nature of the process that is responsible for the Class II activity. As we have seen, the Class II stage is initiated when a considerable number of the stars of the quasar reach their age limits and undergo supernova explosions. If some or all of the explosion products are confined within the interior of the structure, the quasar becomes a Class II radio emitter. If it is not big enough, or compact enough' to confine these products they are ejected as they are produced, or at intervals, and the quasar gradually disintegrates.

The luminosity data for the various classes of quasars are summarized in Table XVII. The most conspicuous feature of this tabulation is the high luminosity of the early Class I objects. However, when we consider the enormous disparity in size between the exploding galaxy that produced the early Class I quasar and the exploding fragment that constitutes the Class II quasar, the difference in luminosity between these two classes is easily accounted for. The relatively low emission of the late Class I objects is obviously a result of the energy losses during the time that has elapsed since the galactic explosion. At the end of the Class I stage, the quasars are in what we may call a condition of minimum internal activity.

    ..057   ..422   25
I-Late (under 0.76)
    ..024   ..155   11
I-Late (over 0.76)
    ..015   ..057   10
I-Radio Quiet
    ..006   ..017   .9
Il-Below 1.00
    ..017   ..126   22
II-Above 1.00
    ..025   ..138   17

Table XVII separates the 14 quasars of late Class I into two groups of 7 each, with the dividing line at U-B = 0.76. The ratio of maximum to minimum luminosity in these two sub-groups is practically identical, indicating that the decrease in internal activity continues throughout the late Class I stage, as would be expected from theoretical considerations, and that the difference between the tabulated values for the two groups reflects a decrease in the luminosity level because of the reduced activity, rather than a difference in the sizes of the quasars in the two groups. We may thus conclude that the absolute luminosity of a radio-emitting quasar of minimum size in a condition of minimum internal activity is about 0.015.

As indicated earlier, the radio-quiet quasars in the Class I distance range differ from the coexisting radio emitters mainly in size. Addition of this radio-quiet class brings the minimum size down to 0.006, or to make some allowance for the rather small sample, let us say 0.005. Some question may be raised as to why there should be a minimum size; that is, why the explosion does not produce debris of all sizes from sub-atomic particles up to some maximum size of fragment. The answer is that the quasar is the whole cloud of ultra high speed matter ejected by the explosion, including stars, star fragments, dust, and gas. We see the cloud as a discrete object because of the great distances that are involved.

The maximum luminosities vary considerably more than the minimum. This is evidently due to the fact that in the quasars, as well as in the pre-explosion galaxies, the internal activity can build up to a higher level in the larger aggregates before breaking through the overlying layers of material. The effect of this factor is shown by the ratios of maximum to minimum luminosities, which range from 17 to 25 in the active quasar classes, but average only about 10 in the relatively inactive late Class I groups. Since each of the larger quasars passes through all of the stages represented by the various radio-emitting classes, the range of sizes should be the same in each, if the sample is representative. The 0.155 maximum of the sub-group of late Class I in which the U-B index is over 0.76 should therefore be the maximum value comparable to the 0.015 minimum that we found to be applicable under the condition of minimum internal activity.

Since the sample is small, there may be some larger objects elsewhere, but the continuity of the maximum-minimum ratio throughout Class I indicates that the 0.155 value is at least close to the maximum. Furthermore, the quasar 3C 334, which has the 0.155 luminosity, may still have somewhat more than the minimum internal activity. These possibilities tend to counterbalance each other. It thus appears that a value of about 0.150 is acceptable as the maximum absolute quasar luminosity under conditions of minimum internal activity.

What we now want to consider is the meaning of these maximum and minimum values in terms of the masses of the quasars; that is, are they consistent with the theoretical conclusion that the quasar is a fragment of a giant spheroidal galaxy? The various factors that enter into this situation are not yet defined clearly enough to enable an accurate calculation, but an approximation is all that is needed in order to answer the question as stated. The most convenient way of obtaining this answer is to make a direct comparison between a quasar and the galaxy from which it was ejected, both of which are at the same spatial distance. The logical pair for this purpose is the one that we know the best, the quasar 3C 273 and its associate, the giant galaxy M 87.

The largest uncertainty in this evaluation is in the relative mass-to-light ratios of these two objects. It is known that there is a systematic increase in this ratio as the size of the galaxy increases, as would be expected from the theoretical information about the galactic structure developed in the preceding chapters. A recent review by Faber and Gallagher reported relative values for spiral galaxies ranging from 1.7 for the smaller class to 10 for the large so spirals.259 Information with respect to the giant spheroidal galaxies, the parent objects of the quasars, was reported to be scarce, but the available data indicated a substantially higher ratio, probably at least 20.

The increase in the mass-to-light ratio with the size of the galaxy is mainly due to the increasing amount of confined high density, high temperature, material in the galactic interiors. At the level of minimum internal activity the quasars contain much less of this dispersed material, without the confinement.

The stars are still moving at upper range speeds, and the star density remains high, but this does not affect the mass-to-light ratio, which is determined primarily by the extent to which upper range speeds exist in the constituents of the stars. As previously noted, these constituents return to temperatures below unity at the end of the early Class I stage. The mass-to-light ratios of the quasars in the minimum activity condition should therefore approximate those of the smaller spiral galaxies. An estimate of 2 should be reasonable. This means that the ratio of the masses of the minimum activity quasars to those of the galaxies of origin is less by a factor of about 10 than the ratios of the luminosities.

As indicated in Table XVII, the Class II quasars are about twice as luminous as the quasars in the stages of minimum internal activity. This brings the mass-to-light ratio of 3C 273 down to about ½0 of that applicable to M 87. The observed magnitudes of M 87 and 3C 273 are 9.3 and 12.8 respectively. The corresponding ratio of luminosities is 25. Applying the correction for the difference in the mass-to-light ratios, we arrive at the conclusion that M 87 is 500 times as massive as 3C 273.

From the data in the tables in this chapter it appears that 3C 273 is somewhere near the maximum quasar size. On this basis, then, only about 0.2 percent of the mass of a giant galaxy is ejected in the form of a quasar, even when the fragment is one of maximum size. This is only a very small portion of the galaxy, but the galaxy itself is so immense (about 1012 stars, according to current estimates) that 0.2 percent of its mass is a huge aggregate of matter. It is equivalent to about two billion stars, enough to constitute a small spiral galaxy. The smallest quasar, radio quiet by the time we observe it, represents only about 0.007 percent of the galactic mass—a mere chip, one might say—yet it, too, is a very large object by ordinary standards, as it contains approximately 70 million stars, the equivalent of about 100 large globular clusters, or a dwarf elliptical galaxy.

The data examined in this volume, and the two that preceded it, together with the interpretation of these data in terms of the quasar theory derived from the postulates of the Reciprocal System give us a picture of the quasars that is complete and wholly consistent. As this analysis shows, if a fragment of a giant galaxy, of a size consistent with the theory. has been ejected at a speed greater than that of light, as required by the theory, then the optical emission from the constituent stars of the fragment, occurring at a rate consistent with the normal emission from such stars, at the distance theoretically indicated by the redshift, and distributed in space and its equivalent in the manner required by the theory, will be received here on earth in just the quantities that are actually observed. There are no inconsistencies of the kind that are so conspicuous in the application of conventional theory to the quasars. All of the observations fit easily and naturally into the theoretical structure.

As brought out in the preceding pages, this is true not only of the general situation, but also of the minor details. The correlation between theory and observation provides individual confirmation of many of the special features of the theory, such as the first power relation between distance and luminosity, the changes in color and distribution of the radiation that take place when the speed exceeds one or another of the unit levels, the special characteristics of the early type quasars, the differences between the limiting magnitudes of the various quasar types, etc.

Furthermore, the theory from which all of these results have been obtained is not something that has been constructed to fit the observations. Each and every conclusion that has been reached is a necessary consequence of the basic assumptions as to the properties of space and time. The theoretical development shows that just because space and time have these postulated properties, quasars must exist, and they must have exactly the characteristics that are now revealed by observation.

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