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Evidence that Quasars and Related Active Galaxies are Good

Radio Standard Candles and that they are Likely to be a Lot

Closer than their Redshifts Imply

M.B. Bell1

ABSTRACT

For many years some astronomers have continued to argue, using redshift periodicities andquasar-galaxy associations, that quasars may be closer than their redshifts imply. Here, for thefirst time using raw radio data, I re-examine this question and find new evidence that supportsthis argument. Using VLBA flux densities and angular motions in jets, I show that the centralengine of quasars and BL Lac objects appears to be a good radio standard candle. Using thisinformation, relative distances are calculated and absolute radio distances are then obtained byreferencing to a source whose true distance has been obtained using Cepheid variables. Theresults reveal that in this model most of the strong radio sources found in early surveys arenearer than 100 Mpc. For such nearby sources the measured redshifts must be almost entirelyintrinsic, density evolution is unlikely and, if they are standard candles, their radio luminositycannot vary significantly with intrinsic redshift, which should result in flat flux density vs redshiftplots. LogN-logS plots must have a slope of -3/2, and this is expected to be true even over narrowintrinsic redshift ranges. Source number counts must also increase with distance as the cube. Allof these requirements are shown to be met in the local model, confirming that it is a viable one.On the other hand, if the redshifts are assumed to be cosmological, none are met except the logN-logS slope of -3/2 which, because of evolution, is then not expected. When the data are fittedto the cosmological redshift (CR) model, the luminosity is found to increase while the spatialdensity decreases with redshift. However, the luminosity and density evolutions found turn outto be just those that would be created by the assumption that the redshifts are cosmological, when

they are actually intrinsic. Thus the independent discovery here, using ejection velocities, thatthese sources are good radio standard candles, has led to the realization that the raw data fit thelocal model perfectly, and that the good logN-logS slopes likely occur because of this. The datacan be fitted to the CR model, but not without making many additional, arbitrary assumptions.It is concluded that the flux density, and not the redshift, is likely to give the best indication ofthe distance to these objects. If so, they must then be a lot closer than previously thought.

Subject headings: galaxies: active - galaxies: distances and redshifts - galaxies: quasars: general

1. Introduction

After Schmidt (1963) and Greenstein andMatthews (1963) determined the redshift of 3C273and 3C48 respectively, the redshifts of many morequasars were soon obtained. Most were quitelarge, and because these objects did not appear to

1Herzberg Institute of Astrophysics, National Research

Council of Canada, 100 Sussex Drive, Ottawa, ON, Canada

K1A 0R6; morley.bell@nrc.gc.ca

be optical standard candles, generally becomingmore luminous as their redshift increased (Bur-bidge and Burbidge 1967), the question of the ori-gin of their redshift immediately arose. However,since there appeared to be no way of explainingvery large redshifts (z > 0.62) (Bondi 1964; Buch-dahl 1959, 1966) other than by the expansion ofthe Universe, most astronomers soon concludedthat the redshifts must be purely cosmological.Since that time most of the work done on quasars

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has attempted to show that the data supportedthat assumption and most quasar papers haveassumed from the outset that the redshifts arecosmological.

However, a few astronomers have clung to thepossibility that some, as yet unknown, mecha-nism might be responsible for at least a por-tion of the observed redshifts of these objects,and this belief has continued to be supportedby evidence of possible periodicities in the red-shift distributions (Karlsson 1971, 1977; Burbidgeand Napier 2001; Bell 2004), and by the appar-ent associations between high-redshift quasars andlow-redshift galaxies (Arp 1997, 1998, 1999; Bell2002a,b,c, 2004; Burbidge 1995, 1996, 1997a; Bur-bidge and Burbidge 1997b; Burbidge 1999; Chuet al. 1998; Galianni et al. 2005; Lopez-Corredoiraand Gutierrez 2002). Unfortunately, because ofthe almost immediate acceptance by most as-tronomers that quasar redshifts were cosmologi-cal, the normal course of scientific research has notbeen followed, and both sides of this issue have notbeen fairly examined.

In models where intrinsic redshifts are pro-posed, the current picture is that galaxies are bornas QSOs that are ejected from the nuclei of activegalaxies. At birth their redshifts contain a largeintrinsic component of unknown nature, that grad-ually decreases. Their luminosity simultaneouslyincreases and, after ∼ 108 yrs, they mature intonormal galaxies. Although the intrinsic compo-nent is very small in mature galaxies (similar tothe peculiar velocity of the galaxy) it may neverdisappear completely, since small intrinsic compo-nents have also been found in the redshifts of ma-ture spiral galaxies (Tifft 1996, 1997; Bell et al.2004). Since in this model the intrinsic redshiftcomponent continuously decreases, it has been re-ferred to previously as the decreasing intrinsic red-shift (DIR) model. A natural consequence of adecreasing, or age dependent, redshift componentis that some radio galaxies will be more maturethan others. Here I will refer to these as mature

radio galaxies and young, active radio galaxies. Itis assumed that the latter can have a significantintrinsic redshift component while this componentin the former is almost negligible.

In the DIR model, as the objects age their opti-cal luminosity increases, as their associated galac-tic component grows, and eventually they become

mature galaxies that are bright enough to be de-tected to much larger distances. The small intrin-sic redshift components found in galaxies have alsobeen found to be superimposed on top of their dis-tance, or cosmological, redshift component (Bell etal. 2004, and references therein). In this model ithas not been necessary to give up the Big Bang,and this is one of the main ways that the DIRmodel differs from the decreasing intrinsic redshiftmodel proposed by Narlikar and Arp (1993).

It is suggested here that the evidence is nowstrong enough to warrant a re-examination of thequestion of intrinsic redshifts using a new ap-proach. Here, for the first time, I use accurateradio data to examine this question. For this pur-pose I use the raw data found in radio surveysof quasars and active radio galaxies (angular mo-tions, radio flux densities, source number counts,etc). The term raw data is defined here, as inKellermann et al. (2004), as those observablesthat are uncontaminated by modeling. Because itis important not to influence the results by makingunwarranted assumptions, the importance of usingraw data cannot be emphasized strongly enough ifa fair appraisal is to be obtained.

I first present evidence, in Section 2, indicat-ing that flat spectrum quasars may be good ra-dio standard candles and, as such, can be usedas an independent check of quasar distances. Itwill be shown that, plotted on logarithmic scales,the upper envelope of the angular motions seen inflat-spectrum, superluminal quasars and BL Lacobjects increases with increasing 15 GHz flux den-sity with the slope expected for a simple ejectionmodel in which all ejection velocities are reason-ably similar but are non-relativistic. A clearly de-fined upper envelope can be obtained only if thesources are good radio standard candles. For stan-dard candles, relative distances can be calculatedusing the flux density, and converted to absolutevalues by referencing to a source whose distance isknown by some other means. It will be shown thatthis leads to distances less than 100 Mpc for thesesources, and that they therefore occupy Euclideanspace in this model.

Second, in Section 3, I examine two indepen-dent samples of extragalactic jetted radio sources.In the CR model the observations can only be ex-plained if the radio luminosities of both the coreand giant radio lobe components of these objects

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increase significantly with increasing redshift. Theresults also require that the luminosity increase beremarkably similar in both the core and lobe com-ponents.

Finally, in Section 4, having presented evidencein Section 2 that these sources are standard can-dles in Euclidean space, I examine logN-logS plotsfor four samples of quasars and active radio galax-ies, and obtain slopes of -3/2 in all cases, confirm-ing that, if the above is true, the sources mustalso be uniformly distributed. In the local model,where redshifts must be almost entirely intrinsic,when the source S vs z distribution is subdividedinto several smaller intrinsic redshift ranges, goodlogN-logS slopes near -3/2 are still expected to beobtained for the sources in each narrow redshiftrange.

It is also demonstrated that the luminosity anddensity evolutions found in the CR model are ex-actly those predicted to be introduced by assum-ing incorrectly that the intrinsic redshift is cosmo-logical.

Hereafter radio standard candles will be re-ferred to simply as standard candles and opticalstandard candles will be referred to as optical stan-dard candles. Note also that the term local model

refers here to the fact that the sources being dis-cussed are local in that model. They are nearbyonly because they were found in early radio sur-veys where the sensitivity was poor. It does notmean to imply that all sources in the local, or DIR,model are local. Finally, although the CR modelis referred to here in general terms, because it hasbeen discussed in detail by many others over thelast 40 years it will not be discussed in detail here.

2. Radio Distance

In the CR model, anomalies were soon foundrelated to rapid variability in extragalactic radiosources (Sholomitskii 1965; Dent 1965; Pauliny-Toth and Kellermann 1966), and later, to appar-ent superluminal ejection velocities (Cohen et al.1977). In simple ejection models, if source dis-tances are known, changes in the angular posi-tions of blobs associated with their jets can beconverted into linear ejection velocity componentsperpendicular to the line-of-sight. However, it hasbeen known since the 1970s that this simple in-terpretation leads, in many cases, to apparent ve-

locities vapp = βappc, where βapp is greater than1 and c is the speed of light. The velocity thusappears to exceed the speed of light and has beenreferred to as superluminal. Although this appar-ent anomaly can be readily explained if the objectsare really much closer than their redshifts imply,models involving relativistic expansion were devel-oped to explain the rapid variabilty (Woltjer 1966;Rees 1966, 1967), so astronomers did not haveto give up their belief that redshifts are reliabledistance indicators. Relativistic beaming modelsalso nicely explained the apparent superluminalejection velocities. However, although relativis-tic motions in the ejected blobs can explain theapparent anomaly, even after forty years there islittle convincing observational evidence that thisis the correct interpretation. Although evidencehas been claimed this usually raises more ques-tions than it answers. There may well be rela-tivistic effects in the cores of active galaxies, andthis is not being questioned here. What is beingquestioned is whether or not the ejection veloci-ties of the discrete radio blobs are relativistic. Itis important to keep in mind that the apparentanomalies mentioned above also have a commonfactor: they both involve the assumption that theredshifts of these objects are a good indication oftheir distance.

2.1. Angular motions in radio jets

The results of a 10-year VLBA program tostudy motions in radio jets at 15 GHz has recentlybeen reported (Kellermann et al. 2004) and theseexcellent measurements can now be used to re-examine some of the characteristics of these activeradio sources. As noted above, I differentiate herebetween mature radio galaxies and young, activeradio galaxies. The latter, since they are youngerand may more closely resemble quasars, are stillexpected in the DIR model to contain a signifi-cant intrinsic redshift.

Once a model is specified, there are several welldefined relations that can be predicted. If quasarsare radio standard candles, their apparent radiopower, or flux density, is also expected to fall offinversely as the square of their distance. Whenthe flux density is plotted versus distance on loga-rithmic scales a slope of -2 will then be obtained.

In simple ejection models, if active radio galax-ies and quasars are ejecting material at reasonably

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Fig. 1.— Angular motion µ(1+z) (mas yr−1) plot-ted versus radio flux density at 15 GHz for 109quasars and BLLac objects from Table 2 of Keller-mann et al. (2004). The solid line has a slope of1/2 and indicates that the flux density varies di-rectly as the square of µ(1+z), which is inverselyrelated to distance in simple, non-relativistic ejec-tion models. Thirteen quasars with less accuratemotions plotted as open circles.

Fig. 2.— Same as Fig 1 with error bars. Thirteenquasars with less accurate motions have not beenincluded. See text for a discussion of the opensquares and dotted line.

similar but non-relativistic velocities, the apparentangular motion of these blobs per unit time willfall off linearly with distance, and it will also de-pend on the ejection angle relative to an observer.When plotted on logarithmic scales, the maximumvalue, or upper envelope, of these angular motionswill fall off inversely with distance with a slope of-1. The angular motion then becomes a direct in-dication of distance, or a standard yardstick. Inthis simple model, the maximum velocity is onlyseen for those ejections in the plane of the sky,and ejections closer to the l-o-s will fall below thisupper envelope.

In Fig 1 the maximum angular motion per unittime in the source reference frame, µ(1+z), ob-served for 109 superluminal quasars and BL Lacobjects from Kellermann et al. (2004) is plottedversus the 15 GHz VLBA flux density on logarith-mic scales. Here µ is the angular motion in masyr−1 and z is the relevant measured redshift. Al-though only 79 of 92 quasars were included in theprevious analysis (Kellermann et al. 2004), here91 of the 92 quasars are included. Thirteen werepreviously left out because their motions were lessaccurately determined. So that it may be clearlyseen that the 13 quasars left out of the earlier workdo not affect the results found here, they have beenplotted in Fig 1 as open circles. Because six of theBL Lac objects have no redshifts, only 18 BL Lacobjects can be included.

The 15 GHz flux density (SV LBI) is the totalflux density taken from the VLBA images (Keller-mann et al. 2004). Most is assumed here to beassociated with the central engine. In Fig 1, theupper envelope of the angular motion for thesesources increases with the 15 GHz flux densitywith a slope of 1/2. In a simple ejection modelµ(1+z) is a measure of the relative distance to theobject and the flux density then falls off as thesquare of the distance. This is what is expected ina simple model, if the sources are standard candlesand the ejection velocities are non − relativistic

and reasonably similar in all sources. The mea-sured angular motion is then due to geometryalone, with no time contraction, and with thelargest angular motion corresponding to ejectionsin the plane of the sky. It seems unlikely that thisupper envelope, with the correct slope, could beobtained by chance and this is discussed in moredetail in Appendix A. It would also seem to be

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difficult to explain this result in the cosmologi-cal model, where relativistic ejection velocities arerequired and a simple geometrical explanation isruled out.

Although it has been assumed here that the fac-tor (1+z) is needed to adjust the angular motionsto the source reference frame, since the nature ofthe intrinsic redshift proposed here is unknownthere is no way of knowing whether this assump-tion is correct. If removing the (1 + z) factor de-stroyed the upper envelope it might be consideredas a test of whether or not the intrinsic redshiftbehaves in a manner similar to other known red-shifts. Unfortunately, the same slope is obtainedif this factor is not included, and it is therefore nota meaningful test. Since this is a plot of angularmotion vs flux density, with the high- and low-redshift sources scattered at random throughoutthe plot, it is therefore no surprise that the factor(1+z) does not affect the result. This conclusionis also relevant to other small corrections that area function of redshift, such as the K-correction.The K-correction is assumed here to be small sincethese sources were selected because they had flatspectra. These data, without the 13 quasars withlarge uncertainties, are re-plotted in Fig 2 with er-ror bars and they show the same upper-envelopeslope. Note that the plotted errors are equal to thelisted errors in µ multiplied by the factor (1+z).

In Figs 1 and 2, the tight fit of the upper en-velope to the line is a measure of how good astandard candle the source is. In this model onlythe sources near the upper boundary, which rep-resents sources ejected in the plane of the sky, willhave significance. In order to obtain a value forthe slope of the upper envelope the following ap-proach was taken. Three sources were chosen thatwere felt to best define the upper envelope. Thesesources (0736+017, 1219+096, 2200+420) were se-lected because, a) they lie along the upper enve-lope, b) they cover a wide range of Flux Densi-ties (0.6 to 5.67 Jy), and, c) for sources at theupper boundary their angular motions (µ) havethe smallest uncertainties. When the logarithmsof the fluxes densities and the angular motions ofthese objects are plotted using linear co-ordinatesa slope of 1/2 is expected. Three cases were ex-amined: 1) A linear regression was carried out as-suming uniform errors on µ(1+z). For this casethe slope m obtained was m = 0.48 with a std er-

ror of 0.033. 2) A linear regression was carried outthat was weighted according to the uncertaintiesin µ(1+z). Here the slope obtained was m = 0.473with one std error of 0.03. 3) A linear regressionwas also carried out which included the errors inµ, but did not include the factor (1+z). In thiscase the slope obtained was m = 0.478 with onestd error of 0.018. Inclusion of the factor (1+z)here makes little difference because the redshift ofthese objects is small.

Assuming that the sources are standard can-dles, using the flux density their relative distanceswere calculated. These are easily converted to ab-solute distances by fitting the calculated distanceof a reference source to its distance established bysome other means. In this case Virgo A was usedas the distance standard and a value DV irgo = 18Mpc was assumed. In Fig 3 the maximum angularmotions per unit time in the source frame, µ(1+z),are plotted versus the radio distances on logarith-mic scales. The upper envelope falls off with theslope of -1, and these strong, jetted sources foundin early radio surveys can be seen to be closer than100 Mpc, and therefore the space they occupy cansafely be assumed to be Euclidean.

Changing the distance assumed for Virgo shiftsthe entire distribution in Fig 3 to higher or lowerdistances but does not alter the overall shape ofthe distribution, which is set by the relative valuesof the 15 GHz flux density. In Fig 3, where DV irgo

= 18 Mpc is assumed, the upper envelope of thesuperluminal sources (solid line) is displaced toa slightly higher distance than is found for theupper envelope of several radio galaxies (dottedline) whose distances are also thought to be accu-rately known and are plotted here as open circles.This may imply that the correct value of DV irgo isslightly less than 18 Mpc. In fact, excellent agree-ment is obtained between the upper envelopes ofthese radio galaxies and the quasars and BL Lacobjects when the Cepheid distance to the Virgocluster is assumed (DV irgo = 14.6 Mpc) (Freed-man et al. 2001). Finally, when new βapp val-ues are calculated using the distances determinedhere, they give ejection velocities for most sourcesthat are now not even mildly relativistic. How-ever, it is also important to keep in mind that theabsolute distances calculated here are tied to the15 GHz flux density of one source, and much morework is required before it can be concluded that

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Virgo is the best reference source to use to ob-tain absolute distances. The distances calculatedhere have not been included in a table becausethey are still subject to changes. However, majordepartures from the calculated distances are notanticipated.

2.2. Selection Effects in the Data

There are several selection effects likely to bepresent in the data. One is due to a radio detec-tion limit, which is visible in the SV LBI 15 GHzdata but is due to the 1 Jy radio limit set by the5 GHz survey (Stickel et al. 1994) from which thissample of sources was selected. Another is theplate limit set by early optical work at apparentmagnitude value mv ∼ 19±0.5 mag. The approx-imate radio detection limit is indicated in Fig 4where the flux density data have been plotted ver-sus redshift. Note that this limit cannot be respon-sible for the upper envelope seen in Fig 1 since itonly affects those sources that lie along the left-most edge of that plot. In Fig 4, if the sourcesare good radio standard candles, then distance in-creases downward as indicated. Also, apparentoptical brightness increases to lower redshifts, asshown by the apparent magnitudes included be-side several of the sources. This is true regardlessof whether one assumes the cosmological model(where redshift is interpreted as distance), or thelocal model (where most of the redshift is inter-preted as intrinsic and related to the age of theobject).

Also visible at the high redshift end of Fig 4 isan abrupt cut-off indicated by the dashed line. Itis suggested here that this cut-off may be relatedto the optical plate cut-off mentioned above. In or-der to prove this it will be necessary a) to examinethe magnitude distribution of the quasars and BLLac objects in the Stickel et al. (1994) sample tosee if the distribution shows evidence of a cut-offat the early plate limit and b) to examine the opti-cal magnitudes of the objects defining the cut-offin Fig 4. Fig 5 shows the distribution of mag-nitudes in the Stickel et al. (1994) sample whichcontains 262 quasars and BL Lac objects. The his-togram was obtained simply by counting the num-ber of sources present in each half-magnitude-widebin, and clearly shows that the sample of sourcesfrom which the present sample was selected has anabrupt magnitude cut-off at mv ∼ 19.5 mag. The

Fig. 3.— Angular motion µ(1+z) plotted versusdistance for quasars and BLLac objects, where dis-tance has been determined by assuming that thesources are good radio standard candle and thedistance to Virgo is 18 Mpc. The upper envelopefalls off with the expected slope of -1, as shown bythe solid line. Open circles represent radio galaxiesand have an upper envelope shown by the dottedline. A Hubble constant of Ho = 58 is assumed.

Fig. 4.— Radio flux density at 15 GHz plottedversus redshift for quasars, BLLac objects and ra-dio galaxies with measured redshifts and angularmotions from Table 2 of Kellermann et al. (2004).The dotted line indicates the approximate radiodetection limit, and the dashed line indicates a sec-ond clear cut-off at high redshifts. The numbersbeside sources indicate their apparent magnitude.

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Fig. 5.— Distribution of optical apparent magni-tudes for all quasars and BL Lac objects with mea-sured redshifts in the Stickel et al. (1994) sample.

Fig. 6.— Same as Fig 4, only on an expandedscale. Sources defining the cut-off at the dashedline are indicated by open circles and their param-eters are listed in Table 1. No redshift corrections(ie K-corrections, etc) have been applied to thedata.

visual magnitudes of the 14 objects located alongthe dashed line in Fig 4, from Kellermann et al.(1998), are listed in Table 1 where it is clear thatthey all have magnitudes that correspond closelyto the early plate cut-off. These results stronglysuggest that the cut-off in Fig 4 is indeed relatedto the plate cut-off (see also Section 4.5).

The 14 sources that lie along the cut-off in Fig 4are plotted as open circles in Fig 6 where the slopeof the dashed line must now be explained. Recall-ing that if the sources are good standard candlesthe distance increases downwards, how can themore distant sources lying along the dashed linehave the same apparent magnitude as the closerones? Obviously this can only happen if the moredistant ones are more luminous. In the DIR modelsources become more luminous as they age andtheir intrinsic redshift decreases. The DIR modelthus predicts that the dashed line in Figs 4 and 6will have a positive slope as seen, if it is producedby the plate cut-off as suggested here.

In fact, it is possible to use the slope of thedashed line to determine how the quasar opticalluminosity varies with intrinsic redshift (see be-low), at least for the intrinsic redshift range fromz = ∼ 0.8 to ∼ 4. It is also worth noting thatthe upper envelope cut-off in Fig 1 is in no wayrelated to the cut-off defined by the dashed linein Fig 4 because the sources that define these twocut-offs are completely different. Also, it is im-portant to note again that this cut-off is definedsolely by high-redshift quasars. If the sources arestandard candles as suggested here, these high red-shift sources are expected to be the most reliabledistance indicators. It is also worth noting that,unlike in Fig 1, here the measurement uncertain-ties in redshift and flux density are much too smallto affect the results.

Also apparent in Figs 4 and 6 is the fact thatone source falls above the cut-off. This source(0153+744) has an apparent magnitude of 16m

and therefore would have been easily seen in earlysurveys. Although it has a measured redshift ofz = 2.34, its intrinsic component must be muchsmaller for the source to be this luminous. Itsmeasured redshift must then contain a much largercosmological component than most other sourcesin this sample. The possibility that there mightbe other sources in this sample that fall into thissame category cannot be ruled out.

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2.3. Variation of Optical Luminosity with

Intrinsic Redshift

Although born sub-luminous by several magni-tudes, as a galaxy matures, and its intrinsic red-shift decreases in the DIR model, its optical lumi-nosity steadily increases as the surrounding hostgalaxy matures. If the central engine is a radiostandard candle, and the 15 GHz radio flux densityis then a measure of relative distance as claimedhere, as the distance increases along the dashedline (downward) in Figs 4 and 6, the source lu-minosity must then increase by the same amountthat the apparent brightness would normally beexpected to decrease, if the optical apparent mag-nitude is to remain constant. Since, in the DIRmodel an increase in optical luminosity is accom-panied by a decrease in intrinsic redshift, as notedabove the slope of the cut-off in Fig 6 must bepositive, exactly as found.

For an increase of a factor of ten in distance,the apparent magnitude mv must increase (sourcegets fainter) by 5 magnitudes. The luminositymust then increase by 5 magnitudes if the appar-ent magnitude is to remain constant. From Fig4, a factor of 10 increase in distance (a factor of100 in flux density) is also associated with a factorof ∼ 10 decrease in the intrinsic redshift. Thus adecrease of a factor of ∼ 10 in intrinsic redshift im-plies an increase in luminosity of 5 magnitudes forthe intrinsic redshift range between z = 1 and 3.Although no redshift corrections (ie K-corrections,etc.) have been applied to the data, this is notexpected to affect the result because the range ofredshifts covered is small (z = 1 to 2.5). Note thathere z is assumed to be almost entirely intrinsic.

It is also of interest to compare this result toprevious results obtained for the QSOs near NGC1068. Four years ago a close examination of the 14QSOs lying within 50′of the nearby Seyfert galaxyNGC 1068 found that 12 of these objects appearedto have been ejected from NGC 1068 in four sim-ilarly structured triplets, (Bell 2002a,b,c). Thispicture allowed Doppler ejection components tobe estimated, and since the cosmological redshiftof NGC 1068 is known, for the first time accuratevalues for the intrinsic, or non-Doppler, compo-nents could be determined. When these resultswere combined with results obtained earlier byBurbidge and Hewitt (1990), this led to a well

defined intrinsic redshift model that can now betested. The relation defining the intrinsic red-shifts in this model is given in Bell and Comeau(2003a) and Bell (2004). Fig 7 is a plot of datataken from Table 1 of Bell (2002b) and shows thatthe optical luminosity was previously found to in-crease by 4 magnitudes when the intrinsic redshiftdecreased by a factor of 10, which is in reason-ably good agreement with the value of 5 magni-tudes found here. Again, no redshift corrections(k-corrections, etc.) have been applied, since thedata cover a range of only two magnitudes. Al-though the results show good agreement, they areadmittedly approximate and are for comparisonpurposes only.

Several other questions concerning the relationsfound using the data from Kellermann et al. (2004)are examined in Appendix A.

2.4. On the source distribution in Fig 1

If the blobs are ejected in completely randomdirections at similar velocities the distribution ofsources in Fig 1 would be expected to be muchmore concentrated near the upper cut-off than isfound. The dotted line in Fig 2 indicates the lineabove which 50 percent of the sources should fallif the distribution is random. Clearly this is notthe case. However, this discrepancy is easily ex-plained, at least in the DIR model, requiring onlythat the radiation from the central engine be di-rective, with the observed flux density increasingfrom edge-on to face-on as the region inside thehole in the torus becomes visible. This meansthat the flux density is only a measure of relativedistance for a given inclination angle. However,this will not affect the slope of the upper envelopesince these sources all have the same edge-on ori-entation. The sources in the bottom half of Fig 2are nearer to face-on, thus if their measured fluxdensity contains an extra component of radiationcompared to the edge-on sources, the componentattributable to their distance will be smaller thanassumed here, and they will have moved into Fig 2from the left by an amount equal to the additionalcontribution. In fact, the lower sources should beplotted much further to the left when their lumi-nosity is normalized to the edge-on value and theycannot then be included in determining the sourcedistribution with inclination. This is examined inmore detail in Appendix B, and in Bell and McDi-

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Fig. 7.— Optical magnitude change with intrin-sic redshift obtained for sources near NGC 1068,taken from Table 1 of Bell (2002b). Filled circlesare mean triplet values and open circles are meanpair values. Note that these are approximate val-ues for comparison purposes only.

Fig. 8.— Flux density vs redshift plot showingarea where radio sources are located. See Section2 for an explanation of the slope of the upper red-shift limit set by the plate limit. See text for anexplanation of the two vertical dashed lines.

armid (2006), where it is demonstrated that whenthis effect is taken into account the source num-ber distribution as a function of inclination angleclosely resembles that expected for a random dis-tribution of orientations. Since the distance com-ponent of the fluxes for the low-µ sources in Fig2 will be lower, the distances for these sources inFig 3 will be slightly greater. Although the fluxdensity can vary with inclination angle, the totalradiated output of these objects is still assumed tobe a good radio standard candle and none of theconclusions reported here will be affected.

3. Radio Characteristics of Source Sam-

ples in the CR and Local Models

Here I look at two samples of extragalactic radiosources with jets, examining them in both the CRand DIR models.

3.1. Radio Characteristics Expected in

the CR and DIR Models

Fig 8 shows, qualitatively, the area where mostsource flux densities are located when plotted ver-sus redshift. In the CR model distance increasesto the right. In the local model distance increasesdownward.

In the DIR model, although sources are borncontinuously throughout the age of the Universe,and objects with a complete range of intrinsic red-shifts are expected to be present in all volumes ofspace (Bell 2004), the active radio galaxies andquasars being examined here (that were detectedin early radio surveys) are relatively nearby. Theircosmological redshift components will then all besmall compared to the intrinsic component. Aslight decrease in the mean flux density at highintrinsic redshifts might be expected, but therecan be no strong flux density fall-off with intrinsicredshift if the sources are standard candles. Fora uniform space density, the sources with strongflux densities are expected to be few in number,simply because they are nearest, and the volumeof space being sampled is small. This rapid de-crease in the number of sources with decreasingspace volume can be predicted to result in a rela-tively abrupt upper limit to the source distributionin Fig 8. Note also that in the DIR model, moredistant radio sources will be found by improvingthe sensitivity of the radio finding survey.

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Fig. 9.— Radio power in the cores of 125 jettedsources assuming cosmological redshifts. Data arefrom Bridle and Perley (1984).

Fig. 10.— Total radio luminosity assumed to bemainly from radio lobes, assuming cosmologicalredshifts, plotted versus z. Data are from Bridleand Perley (1984).

3.2. Radio Power in the Core

In Fig 4 the total flux densities in the core andinner jets of 123 quasars, BL Lacs and radio galax-ies measured at 15 GHz using the VLBA(on milli-arcsec scales) are plotted vs redshift. This is araw data plot, where the data have been takenfrom Kellermann et al. (2004), and it was shownin Section 2 above that these objects appear tobe good radio standard candles. There is littleevidence that the average flux density at high red-shifts is any smaller than at low redshift. In theCR model this requires that the source luminosityincrease significantly with redshift, which in turnmeans that there is luminosity evolution. Theremust also be a wide range of luminosities at eachredshift.

A second sample of radio sources with jets isalso available in the literature. The 125 radiosources known in 1983 to have jets are listed in Ta-ble 1 of Bridle and Perley (1984), where columns 3and 4 list the core and total monochromatic pow-ers respectively, after correcting for distance as-suming the cosmological redshift model. The corepower uses 5 GHz data and the total power uses1.4 GHz data. In the latter, the total flux densitiesalso include the contribution from the radio lobes.Only 10 of these jetted sources are common to the123 sources plotted in Fig 4. If the sources aregood standard candles, and the redshift is a mea-sure of distance, plotting these radio luminositiesversus redshift should result in a source distribu-tion that is flat in the CR model. On the otherhand, by converting the flux densities to radio lu-minosities by assuming that the intrinsic redshiftsare related to distance when they are not (as is thecase if the DIR model is correct), will produce asource distribution that has a steep positive slope.

In Fig 9 the radio power in the core of quasarsand radio galaxies from Bridle and Perley (1984) isplotted versus the logarithm of the redshift. Notethat this plot involves processed data, unlike theraw data plot in Fig 4. In the CR model the ra-dio luminosity can be seen to increase steeply withincreasing redshift, with an upper envelope slopeclose to that of the solid line. A similar result hasbeen obtained by others (Hutchings et al. 1988;Neff et al. 1989; Neff and Hutchings 1990), al-though the redshift range these investigators cov-ered was much smaller, covering only the top half

10

of the plot in Fig 9. In Fig 9 the solid line definesthe approximate radio detection limit. In additionto the radio luminosity increase with redshift, sev-eral other conclusions can be drawn from this plot.Since the solid line in Fig 9 would have had a slopeof zero before the conversion to luminosity wasmade, and the upper envelope of the source dis-tribution is roughly parallel to this, it would alsohave had a slope near zero, and the source distri-bution would then have had the same appearanceas in Fig 4. Furthermore, in Fig 9 there is no indi-cation of where the active radio galaxies stop andthe quasars begin. The plot is continuous, withno evidence of a discontinuity or a change in slopebetween quasars and active radio galaxies. In theCR model the radio luminosity of both the activeradio galaxies and quasars must therefore increasesteadily with increasing redshift with exactly the

same slope. This argues strongly that if quasarredshifts are mainly intrinsic, so must be a large

portion of the redshifts of most of the active galax-

ies in this plot.

Although these sources are defined only asgalaxies and quasars, some of the objects withredshifts near 0.1 are likely to be BL Lac objects.

In the DIR model, Fig 9 is exactly what wouldbe predicted if the core flux densities are convertedto luminosities assuming, incorrectly, that the red-shifts are an indication of distance. In other words,the luminosity evolution that appears in the CRmodel is just that created by assuming that theintrinsic redshifts are cosmological.

3.3. Radio Power in the Lobes

The total radio luminosity (in the lobes, core,and jets) for the 125 sources in Bridle and Per-ley (1984), is plotted versus the logarithm of theredshift in Fig 10. The mean total power is a fac-tor of 40 stronger than that from the core alone.Since the jet component is assumed to be a rel-atively small fraction of this, I assume here thatthe total power is made up mainly of power fromthe lobes. However, since the core and total radioluminosities use data from 5 and 1.4 GHz respec-tively, some of this difference may be a spectralindex effect. In Fig 10, as in Fig 9, the same largeincrease in radio luminosity with increasing red-shift is seen in the CR model. The fact that theupper envelope is not as clearly defined in this plotmay indicate that the radio lobes may be a poorer

standard candle. However, the fact that the up-per edge of both plots has a similar slope indi-cates that the luminosity increase with redshift inthe core and lobes is quite similar. This suggestsagain that this is not a real increase in luminosityat all, but has instead been simply created by theassumption that the redshift is cosmological whenit is not. Figs 9 and 10 resemble closely whatwould be expected if the local model is correct.

When the largest angular separation (LAS) be-tween the two giant radio lobes of jetted sourcesis plotted vs redshift, the upper envelope of thesource distribution is known to decrease as the red-shift increases (Legg 1970; Miley 1971). In theCR model this decrease is mainly due to the in-creasing distance of the sources. However, even inthose very early days, Miley (1971) reported thatthe upper envelope appeared to fall off slightlymore steeply than expected. Since the luminosityof both the core and lobes increases with redshiftin the CR model, if anything, one might expectthe linear separation to increase with increasingredshift. The density of the intergalactic mediummay play a role, however (Miley 1971). Fig 11shows some more recent LAS values plotted vs red-shift, using sources taken from Bridle et al. (1994)and Goodlet et al. (2003). Only sources that haveclear evidence for a core and two lobes have beenincluded to rule out doubles that might representa core and one lobe. The dashed line representsthe 1/z slope for Euclidean space taken from Mi-ley (1971), and shows that the previous limit hasbeen exceeded in many cases. There now appearsto be even more evidence that the slope is steeperthan expected, especially at high redshifts.

In the DIR model the increase in LAS with de-

creasing intrinsic redshift is interpreted as a linearincrease in the lobe separation as the source agesover a period of 107 to 108 yrs. In both models theLAS values that fall below the upper envelope areassumed to represent lobes that have been ejectedcloser to the line-of-sight. There is no problem ex-plaining a steeper slope in the DIR model. Evena steepening at high redshifts, if real, could be ex-plained by a less rapid initial decrease in intrinsicredshift.

3.4. Intrinsic Redshifts in Radio Galaxies

It has been argued (Burbidge 2004) that al-though there is significant evidence for intrinsic

11

redshifts in quasars, the redshifts of low-redshift,genuine, radio galaxies are almost certainly purelycosmological. This question is important because,if it is true, the presence of apparent superluminal

motion in the jets of some of these low-redshiftradio galaxies can be used to rule out the exis-tence of all intrinsic redshifts. However, it has al-ready been demonstrated that very small intrinsicredshift components are present in spiral galaxies(Tifft 1996, 1997; Bell 2002d; Bell and Comeau2003a,b; Bell et al. 2004; Russell 2005a,b) and anyadditional links between the large intrinsic com-ponents in quasars and the very small ones seenin mature spiral galaxies would be significant in-formation in the intrinsic redshift controversy.

From Section 2 of this paper, a natural con-sequence of the sources being standard candles isthat their radio distances (DS) can be calculated.When these are known the intrinsic componentcan be obtained immediately, and it is quickly seenthat some of these objects do contain a significantintrinsic component (see discussion on 3C120 be-low). Also, as discussed above, there is furtherconfirmation of this in Fig 9, where the activeradio galaxies and quasars are plotted using thesame symbol it is clear that the upper envelope ofthe distribution is continuous over the entire red-shift range for both the active radio galaxies andquasars. As noted in the introduction, the intrin-sic component in young, active radio galaxies isexpected to be larger than that in mature radiogalaxies, where a normal Hubble slope is seen (seealso Section 4.5 below). The term genuine radiogalaxy as discussed by Burbidge (2004), is thus as-sumed to apply to mature radio galaxies, and notthe younger, active radio galaxies examined here.The easiest way to determine if a radio galaxy isyoung (still has a significant intrinsic component)is to determine its cosmological redshift compo-nent from its radio distance, and compare this toits measured redshift. An example of an activeradio galaxy where superluminal motion has beenclaimed is 3C120, which has a redshift of z = 0.03and βapp = 4.6. If the distance to Virgo is 14.6Mpc (Freedman et al. 2001), the radio distancefound here for 3C120 is zc = 0.0023 giving an in-trinsic component of zi = 0.027 and βapp ∼ 0.35.

Fig. 11.— Largest angular separation of dou-ble radio lobes plotted versus z on logarithmicscales. (filled circle) from Bridle et al. (1994);(open squares) from Goodlet et al. (2003); (dashedline)upper limit reported by Miley (1971); (dottedline) current upper envelope.

Fig. 12.— LogN-logS plot for sources with fluxdensity S > 2Jy, from Kellermann et al. (2004).The slope of the line is -1.4.

12

Fig. 13.— LogN-logS plot for sources from(square) Wills and Lynds (1978), (open circle)Wall and Peacock (1985), and (filled circle) Stickelet al. (1994). The solid line has a slope of -3/2.The dashed line indicates the approx. detectionlimit of the Wills and Lynds (1978) sample.

4. Plots Involving Source Counts

LogN-logS plots, that merely count the numberof sources, N, to increasingly lower flux densitylevels, S, use raw data. No assumptions about thedistance are involved. If the sources are locatedin Euclidean space, as is indicated by Fig 3, andno evolution is involved (i.e. they are uniformlydistributed standard candles) the logN-logS plotmust then have a slope of -3/2. It is well knownthat for this slope to be obtained the objects donot have to be standard candles. Any luminos-ity distribution will produce the same slope solong as there is no evolution involved (Longair1966). However, the evidence presented in Sec-tion 2 indicates that in this case the objects are

standard candles and are also located relativelynearby. Since no density evolution is likely withina 100 Mpc radius, a slope of -3/2 is predicted ifthe findings in Section 2 are correct. LogN-logSplots are then a test of the local model and this isexamined below for four different source samples.

For standard candles, the relative distances, Ds,of the sources can also be obtained from the fluxdensities. For a uniform distribution in Euclideanspace, logN-logDs plots must have a slope of +3.

4.1. Data Samples for Source Count Plots

The four quasar and active radio galaxy sam-ples examined here are from Wills and Lynds(1978); Wall and Peacock (1985); Stickel et al.(1994); Kellermann et al. (2004). As discussedabove, the Kellermann et al. (2004) sample con-tains 123, VLBA core flux densities measured at15 GHz, and these values may represent the mostaccurate standard candles. However, it is assumedthat the sources in the other samples will alsobe reasonably good standard radio candles, givingdistances in the local model that are still muchmore accurate than the redshift distances. TheWills and Lynds (1978) sample contains flux den-sities for 160 quasars measured either at 178 MHz,2700 MHz, or both. The Wall and Peacock (1985)all sky catalogue contains the 233 brightest ra-dio sources at 2.7 GHz and is complete to 2 Jyover 9.81 sr of sky. The Stickel et al. (1994) sam-ple contains approximately 400 sources whose fluxdensities are measured at 5 GHz and exceed thedetection limit of 1 Jy. Each sample has a clearradio detection limit visible, however, this is only

13

a sharp limit in the Stickel et al. (1994) and Walland Peacock (1985) samples since the other twosamples are less complete and, in some cases, in-volve flux densities obtained at a frequency otherthan that of the finding survey.

4.2. LogN-logS plots

Fig 12 is a logN-logS plot using the data in Fig4. The solid line has a slope of -1.4, which is veryclose to that expected for a uniform source dis-tribution if the sources are good standard candlesin Euclidean space. Fig 13 is a similar plot ofthe data from the other three source samples. Allplots again show good agreement with the slopeof -3/2. It is also worth noting that the mostcomplete samples (Wall and Peacock 1985; Stickelet al. 1994) give the best fits. This result allowsus to conclude that the sources are uniformly dis-tributed in the local model, as would be expected ifthe sources are nearby. In fact this result is quiteremarkable, because it supports the local modelwithout requiring any arbitrary assumptions. Thisappears not to have been notice before, since pre-vious investigations have only attempted to inter-pret the logN-logS slope in the CR model. In fact,finding it here is a direct result of the evidencefound above that the sources are good standardcandles. Although this slope of -3/2 can be ex-plained in the CR model, it is unexpected because(a), there is luminosity evolution present, (b) thereis a possibility that the space is not Euclidean,and (c), as will be demonstrated below, there isalso evidence for strong density evolution in thismodel.

4.3. LogN-logDs plots in the Local Model

For standard candles, it is possible to use theflux densities to calculate the relative source dis-tances, Ds, in the local model. When logN-logDs

is plotted using these calculated distances, a slopeof +3 is expected for a uniform distribution of ra-dio standard candles in Euclidean space. This plotis shown in Fig 14 for the Wills and Lynds (1978)sample. The solid line has a slope of +3. Similarplots were obtained for the other source samplesand, as for the logN-logS plots, the best fits are ob-tained for the most complete samples. In the localmodel this slope is exactly what is predicted andhas resulted because the sources are uniformly dis-tributed in this model. It is important to realize

here that the uniform source distribution foundcomes from the raw data itself without requiring

any additional assumptions.

4.4. LogN-logDz plots in the CR model

In the cosmological redshift model it is possibleto use the redshift to calculate an approximateredshift distance, Dz , and this has been calculatedhere from the relation Dz (Mpc) = (c/Ho)[(z+1)2-1]/[(z+1)2+1],

where c is the speed of light and Ho is the Hub-ble constant. The value used for Ho changes thedistance obtained for all sources by the same fac-tor and therefore cannot affect the slope. Fig 15shows logN-logDz plots using redshift distances forthe Wall and Peacock (1985) and Stickel et al.(1994) samples. The dashed line gives the numbervs redshift-distance slope, which is close to 0.8,and much less than the value of +3 that wouldbe expected if the redshifts were a good measureof distance and the sources were uniformly dis-tributed standard candles in Euclidean space. Theradio luminosity was found to increase with red-shift (Fig 9), and Fig 15 indicates that the sourcedensity must decrease significantly with increasingredshift. This is discussed in more detail in Sec-tions 4.5 and 4.6 below where the reasons for thisdecrease are investigated. Similar results were ob-tained for the Kellermann et al. (2004) and Willsand Lynds (1978) samples.

4.5. LogS vs Distance Plots in the CR

model and the Generation of LogN-

LogS plots

In the CR model the source density was foundabove to decrease with increasing redshift fasterthan expected for a uniform distribution and thereason for this is now examined. Previously it hasbeen assumed that this is due to the fact that moreand more sources fall below the radio detectionlimit as the redshift increases (the Malmquist biaseffect).

LogS-Dz plots are shown in Figs 16, 17 18, and19 for the four data samples. The radio detectionlimit is clearly visible in each figure. In the Willsand Lynds (1978) plot a few additional sourceshave been included by these authors, that havemuch lower flux densities. These sources are re-sponsible for the change in slope in Figs 13 and

14

Fig. 14.— LogN-logDs plot for 160 sources fromWills and Lynds (1978). Ds is the relative distancecalculated assuming that the sources are good ra-dio standard candles. The line has the expectedslope of +3.

Fig. 15.— LogN-logDz plots for (filled circles) 231sources from Wall and Peacock (1985), and (opencircles) 393 sources from Stickel et al. (1994). Thedashed line has a slope of +0.77.

14 and do not indicate a real slope change. Stickelet al. (1994) give a larger sample of flux densi-ties at 5 GHz down to a limiting value of 1 Jy.The sample includes quasars, BL Lac objects andradio galaxies. It also includes many radio galax-ies with redshifts above z = 0.3 that are not inthe Wall and Peacock (1985) sample. The red-shifts of these radio galaxies are expected to con-tain much larger cosmological components thanthe other radio galaxies in the samples being con-sidered here, and these galaxies represent exam-ples of the mature radio galaxies discussed above.It is clear from the logz-mv plot of these objects(Stickel et al. 1994, see Fig 7) that the high red-shift radio galaxies follow the expected Hubbleslope, indicating that the largest component oftheir redshifts above z = 0.3 is cosmological. Inthe local model the source optical luminosity in-creases with age and therefore these older, moreluminous, radio galaxies can be observed to muchlarger distances. They therefore cannot be con-sidered to occupy the same volume of space as thesub-luminous (young) quasars, and hence cannotbe part of the same sample of quasars, BL Lacs,and nearby active radio galaxies, which all havean intrinsic redshift component that is similar to,or larger than their cosmological component. Fig19 includes all quasars and BL Lac objects withmeasured redshifts, but only those radio galaxieswith redshifts below z = 0.3.

It is also of interest to note that the cut-off seenin the Kellermann sample at the high redshift end(Fig 16), and attributed to the presence of theearly plate limit (see Section 2 above), is also vis-ible in the source samples in Figs 17 and 18. Itis less obvious in the Stickel sample (Fig 19) be-cause an extra effort was made to obtain redshiftsfor sources whose apparent magnitudes were below(fainter than) the early plate cut-off. This is fur-ther proof that this cut-off is caused by the platelimit, since it disappears when the plate limit isremoved. In the Wills and Lynds (1978) samplethis high-redshift cutoff is visible down to a fluxdensity level of S2.7GHz = 0.1 Jy.

The plots in Figs 16, 17, 18, and 19 all resemblewhat is predicted in the local model (Fig 8) closely,with little evidence that the upper envelope fallsoff with increasing intrinsic redshift. Thus, in theCR model, the possibility that many more sourcesare lost at high redshift than at low redshift, be-

15

cause they have fallen below the radio detectionlimit (the Malmquist bias effect), can be ruled out.If sources are not lost because they fall below thedetection limit, why is the slope of the logN-logDz

plots in Fig 15 (0.8) so low? Also visible in thenumber vs distance plots in Figs 16, 17, 18 and19, is the fact that none of them show the ex-pected increase in the source number density withincreasing redshift. This is then the main reasonwhy the slope is 0.8 in Fig 15, instead of 3, and itmeans that a real decrease in spatial density withincreasing redshift distance is required in the CRmodel. On the other hand there is an obvious in-crease in source density downwards in these figuresin spite of the fact that the scale is logarithmic andexpands downward. In order to be able to bettercompare the density change with distance in thetwo models, the logS scale has been converted toa linear distance scale in Fig 20. Here it is read-ily apparent by counting sources between dashedlines with equal separations, that the source den-sity increases roughly as the cube when countingdownwards, but remains relatively constant whencounting to the right. This constant density withredshift (producing a slope near 1 in Fig 15) is ex-actly what is expected in the local model, wherethe redshifts are intrinsic, if the source density isuniformly distributed over the entire range of in-trinsic redshifts.

In the local model, if the redshift in the logS-Dz plots (Figs 16 to 19) is divided into severalnarrow intrinsic redshift ranges (such as betweenthe vertical dashed lines in Fig 8), the data in eachis expected to produce a logN-logS slope close to-3/2. In Fig 21, logN-logS plots are shown forsources that lie within different redshift-distanceranges for the Stickel et al. (1994) sample. InFig 21, (a) represents all sources with redshift dis-tance between 0 and 1000 Mpc, (b) all sourcesbetween 2000 and 3000 Mpc, (c) between 3000and 4000 Mpc and, (d) between 4000 and 5000Mpc. These raw data plots show that there isgood agreement with the expected logN-logS slopefor uniformly distributed standard candles in eachdifferent redshift range. The variation in flux den-sity in each narrow redshift range can be explainedby a decrease in apparent radio brightness due toincreasing source distance, and this change mustbe present if the local model is correct. In the CRmodel this decrease in flux density is assumed to

Fig. 16.— LogS plotted vs distance calculatedfrom redshift from Kellermann et al. (2004).

Fig. 17.— LogS plotted versus redshift distancefor 142 sources with measured flux densities fromWills and Lynds (1978). There is no evidence foran increase in source number density with increas-ing redshift.

16

Fig. 18.— LogS5GHz plotted versus redshift Dis-tance Dz for 231 sources from Wall and Peacock(1985).

Fig. 19.— LogS5GHz plotted versus redshift dis-tance, Dz, for 393 sources from Stickel et al.(1994).

Fig. 20.— Relative Radio Distance plotted versusredshift Distance Dz for 231 sources fromWall andPeacock (1985). Distance increases downwards.See text for a description of the dashed lines.

Fig. 21.— LogN-logS plots for sources in differentdistance ranges in Fig 19, where (a) 0-1000 Mpc,(b) 2000-3000 Mpc, (c) 3000-4000 Mpc, (d) 4000-5000 Mpc. Data from Stickel et al. (1994).

17

be due to a decrease in radio luminosity, whichwould then have to mimic the variation producedby the inverse square fall-off with distance seenin the local model. That this would happen bychance in the CR model seems rather unlikely.

5. Interpretation of the Luminosity and

Density Evolution Seen in the CR

Model

Although the luminosity and density evolutionsrequired to fit the data in the CR model are arbi-trary and without explanation in that model, thelocal DIR model predicts both exactly as found.In the local model the sources are uniformly dis-tributed standard candles in Euclidean space and,because they are so close, their redshifts must bealmost entirely intrinsic. If they are good stan-dard candles, as found in Section 2, their luminos-ity cannot vary significantly with intrinsic redshift.This allows us to predict that the S vs redshift-distance distributions seen in Figs 16 to 19 will beflat, exactly as found. If it is assumed, incorrectly,that the intrinsic component is cosmological, thecalculated radio luminosity will increase exactlyas found in Fig 9. If sources are uniformly dis-tributed with intrinsic redshift in the local model,the spatial density in the CR model will decreaseas the cube of the distance, resulting in a slopeclose to 1 in the logN-logDz plot (Fig 15). Thatthe slope found (0.8) is slightly different from thepredicted slope of 1 is easily explained if either,or both of, the luminosity and spatial density areweak functions of intrinsic redshift. The evolu-tions in luminosity and density in the CR modelare thus predicted to be exactly as found, if thelocal model is correct.

6. Discussion

It has been demonstrated that the raw data fitthe local DIR model perfectly, requiring neither lu-minosity nor spatial density evolution. When thedata are fitted to the CR model, both luminos-ity and density evolution are required. These aredifficult to interpret in the CR model because theluminosity increases with redshift while the den-sity simultaneously decreases. However, as shownabove, these evolutions in the CR model are pre-dicted to be produced as found if intrinsic redshiftsin the local model are assumed, incorrectly, to be

cosmological. They are thus created solely by theprocessing carried out in an attempt to fit the datato the CR model. Although the data can be fittedto the CR model if enough assumptions are made,there is no real evidence from any of the raw dataplots examined here that they support that model.However, when the logN-logS plots were first beingexamined 40 years ago, neither the DIR model, northe fact that the sources could be radio standardcandles, were known. This is no longer the case,however, and in Table 2 a comparison is made be-tween the local and CR models using some of theevidence found here. The fact that the logN-logSplot is independent of distance is unfortunate. Itis possible that astronomers may have been mis-led by these impressive plots, simply because theycould still be explained in the CR model, eventhough the evidence presented here suggests thatthey are generated because the sources are uni-formly distributed radio standard candles locatedin the very local universe.

As noted above, a few astronomers have con-tinued to argue that high-redshift QSOs appearto have been ejected from nearby active galaxies,requiring that a large portion of their redshifts beunrelated to the Hubble expansion. And a signifi-cant amount of evidence has been reported claim-ing quasi-periodic quantization in the redshift dis-tributions of quasars extending to normal galaxies.Until now, these two arguments have been the twomain ones supporting intrinsic redshifts. When allthe evidence presented here is considered togetherit strongly suggests that these objects are likelyto be uniformly distributed standard radio can-dles in Euclidean space, and that they are muchcloser than their redshifts imply. These resultsthen represent a third independent set of evidencesupporting the claims that QSOs are born out ofthe nuclei of active galaxies, and that they initiallyhave large non-Doppler redshift components thatdecrease with age.

7. Conclusions

Because new evidence of possible galaxy-quasarassociations, and periodicities in redshift distri-butions, has continued to appear, the questionof quasar distances has remained somewhat con-troversial for many years, and this question hasbeen re-examined here using completely indepen-

18

dent radio data. It was found, using angular mo-tions in jetted sources and VLBA flux densities,that quasars and related active galaxies appear tobe good radio standard candles. This is an im-portant new result which leads to the conclusionthat these objects are closer than 100 Mpc. This,in turn, allows several different predictions to bemade, which can then be tested using radio datato see if this local model is internally consistent.No density evolution is expected for sources so lo-calized in space, and the redshift must be almostentirely intrinsic. For standard candles, no lumi-nosity evolution is expected with intrinsic redshift,which predicts that flux density vs redshift plotswill be flat. LogN-logD plots for complete samplesof these objects must have a slope of 3, and logN-logS plots must have a slope of -3/2. All thesepredictions are shown to be filled, confirming thatthis local model is completely viable. If redshiftis assumed to be a measure of distance, both theradio luminosity and space density of these ob-jects are found to evolve with redshift. However,these evolutions turn out to be just those predictedin the local model when intrinsic redshifts are as-sumed, incorrectly, to be a measure of distance.Because the local model provides an excellent fitin all instances to the simplest model, it is con-cluded that flux density, and not redshift, is likelyto be the best indication of the distance to theseobjects. If so they must be a lot closer than theirredshifts imply.

8. Acknowledgements

I thank Dr. D. McDiarmid for many helpfulcomments, and Simon Comeau for assistance withthe data preparation.

9. Appendix A

9.1. Can the upper envelope in Fig 1 have

occurred by chance?

To investigate the possibility that the upper en-velope in Fig 1 might have occurred by chanceseveral test datasets were generated. To keep thetest datasets as similar to the real one as possi-ble they were generated using the following pro-cedure. The two columns containing the sourceangular motions and 15 GHz flux densities werefirst placed side by side. A new dataset was gen-

erated by shifting one of the columns relative tothe other by one channel. Each additional shiftof one channel produced a new dataset. This wasfirst repeated for six one-channel shifts and finally,for a shift involving half of the data. None of thegenerated datasets produced plots with a clear up-per envelope, let alone one with the correct slope.It was concluded that it is extremely unlikely thatthe upper envelope seen in Fig 1 was produced bychance.

9.2. Are the VLBA flux densities good

standard candles?

Because of its importance to the results ob-tained here this question is now considered in moredetail. The 15 GHz flux densities used in this anal-ysis are described by Kellermann et al. (2004) asthe largest total flux density seen on any of theVLBA images at 15 GHz. The source sample in-cludes all known sources in the Stickel et al. (1994)catalogue that have a flat spectral index anywhereabove 500 MHz. This source sample is a flux den-sity limited sub-sample of the full 15 GHz VLBAsurvey, and was obtained by using the measuredVLBA flux densities as the main selection crite-rion. All flat spectrum sources that had a totalCLEAN VLBA flux density exceeding 1.5 Jy (2Jy for southern sources) at any epoch since 1994are included in this sub-sample. The flux densi-ties came from measurements made over extendedperiods up to 7 years in duration and many of thesources will have been variable over this period,with outbursts typically lasting the order of oneyear. Fractional flux density changes in variablesources range from a few percent to about 100 per-cent (Verschuur and Kellermann 1988, page 581).Because the slope is 1

2 in Fig 1, the flux densityvariations have to be twice as large to producethe same effect as the errors in angular motion.Clearly, even a few sources with flux densities inerror by a factor of two will not affect the slope inFig 1 where the total range in flux density coversmore than a factor of 50. It is therefore concludedthat although some of these sources are variablesthey can still be considered good standard candlesfor the purposes of this investigation. There mayalso be some evidence that the largest variationsoccur in radio galaxies which have not been in-cluded in Fig 1, and are not associated with thecut-off in Fig 4. Is there some reason to suspect

19

that the VLBA total flux density might be a gooddistance indicator? On the VLBA images (fig 2of Kellermann et al 1998) the core component,where the outbursts occur, dominates in almostall cases. Since the flux density used here is thelargest total flux seen on any of the images dur-ing the monitoring period, one might also specu-late that the outburst itself is a standard candle,resembling the standard candle characteristics ofSnIa peak luminosities. If so, the flux densitiesobtained in this investigation would represent aunique set of data. Perhaps the best evidence thatthe VLBA flux density is a good distance indica-tor is the sharpness of the upper envelope in Fig 1and of the cut-off in Figs 4 and 6. The 25 sourcesbest known as variables from early work (Keller-mann and Pauliny-Toth 1968, Table 1) are partof the present sample. However, none of these isamongst the 14 high-redshift quasars defining thecut-off in Figs 4 and 6.

Why has it not been noticed previously thatthese sources are good radio standard candles?Even using these VLBA flux densities, had theybeen previously available, it would not have beennoticed that they were a good measure of rela-tive distance because any attempt to detect thiswould have been carried out using the cosmologi-cal model, with the measured redshift as the dis-tance parameter. As can be seen from Fig 4, ifredshifts are assumed to be cosmological the fluxdensities do not show the expected decrease withincreasing redshift that would be expected if thesources were standard candles. In fact, this is agood example of the danger involved in not giv-ing fair consideration to all available evidence onboth sides of contentious issues before conclusionsare reached. This is especially true here, wherethe nature of the redshifts is a question that is asfundamental to astronomy as the Hubble constantitself.

9.3. Can the cut-off in Fig 4 be explained

in the cosmological redshift model?

The high-z cut-off in Fig 4 is clearly visible and,although it can easily be explained in the localmodel, the possibility that it might also be ex-plained in the cosmological model needs to be ex-amined. In a radio finding survey with a fixeddetection limit, the limit cannot depart from thisvalue as the redshift increases. However, since the

radio limit of 1 Jy was set in the 5 GHz survey, adeparture could occur when fluxes are measuredfor these same sources at a different frequency.However, this is unlikely to be the explanation forthe cut-off in Fig 4 since it would require an abruptand systematic change in spectral index between5 and 15 GHz, starting at z ∼ 1. It would alsorequire that the sources falling along the cut-off inFig 4 at 15 GHz be the same sources that fall alongthe 1 Jy cut-off at 5 GHz. This is easily checkedand it is found that the sources that lie along thecut-off in Fig 4 do not have flux densities of 1 Jyat 5 GHz. This indicates that some effect otherthan a systematic change in spectral index musthave produced the cut-off in Fig 4.

Another possibility that needs to be consideredis whether or not the early plate cut-off, which isclearly present in the 5 GHz data in Fig 5, couldalso explain the cut-off in Fig 4 in the CR model.Although the plate cut-off cannot affect the orig-inal radio limit, it presumably can affect the fi-nal source list, since the redshifts of these sourcescould not be measured until the sources were iden-tified on photographic plates. Furthermore thefew sources that fall above the plate cut-off in Fig5 would have had to have been observed to higheroptical sensitivity and perhaps should not even beconsidered with the main sample that may other-wise be complete to the early plate limit. However,in the DIR model the visibility of the plate cut-offcan be explained because a) the radio flux densityis a measure of distance and b) the source luminos-ity decreases with increasing intrinsic redshift. Inthe cosmological model the apparent magnitudesalso get fainter with increasing redshift, but thereis no evidence in this model that the radio fluxdensity is a standard candle. Without this, whenplotted as a function of the flux density there ap-pears to be no way that the plate cut-off could bealigned along the cut-off seen in Figs 4 and 6.

There thus appears to be no simple explana-tion for the cut-off in Fig 4 in the CR model. It isconceivable that complex flux related argumentsmight be offered to explain this relation since it isa function of the flux density, however, since thetotal flux is measured, and the un-beamed corecomponent appears to be the dominant compo-nent on the VLBA maps at all redshifts, argu-ments that involve selective Doppler boosting inthe jet at high redshifts are also unlikely to be

20

able to explain this result.

It is also worth noting that the cut-off in Fig4 has the same slope regardless of whether oneuses the total 15 GHz flux from Kellermann etal. (2004), the total 15 GHz flux from Kellermannet al. (1998), or the Jy/beam 15 GHz flux valuefrom Kellermann et al. (1998). This cut-off is alsoclearly visible in other source samples (see Figs17 and 18). It is not visible in the Stickel samplebecause a special effort was made to obtain red-shifts of sources in that sample that were beyond(fainter than) the old plate limit.

9.4. Can the upper envelope cut-off in Fig

1 be explained in the cosmological

model?

In the relativistic beaming model the sourceswith the fastest apparent motion will be those inwhich the jet is aligned most closely with the line-of-sight, with µ(1 + z) proportional to the blob

Lorentz factor γ. Although the flux density from ablob may be related to its γ, this flux is not relatedclosely to the total flux plotted in Fig 1. In Fig2 of Kellermann et al. (1998) where the maps ofthe individual sources are presented, the core fluxdensity dominates that from an individual blob byan enormous amount in all cases. Furthermore,the flux density from the core varies significantlywith no correlated variation seen in the jet, indi-cating that the flux density of a particular blob , oreven the entire jet, is unlikely to be significantlycorrelated with the total (core + inner jet) fluxdensity plotted in Fig 1. There appears to be noreason then that there should be any relation be-tween the total flux and the angular motion, letalone one with a slope of one-half. Although thereare many other corrections and assumptions thatneed to be taken into account in the cosmologicalmodel it is hard to believe that after making these,the tight angular motion vs flux density relationseen along the upper envelope in Fig 1 would beany more explainable. Furthermore, the resultsobtained after making many corrections and as-sumptions cannot approach the significance of re-sults obtained in raw data plots where none ofthese corrections are required. One has only tolook at a small fraction of the papers published inthis field to see that even with the enormous effortsthat have been made to date, there are still manyunanswered questions about superluminal sources

in the cosmological redshift model. Furthermore,even obtaining limited agreement with the data inthat model has only come at the price of makingthe interpretation much more complex.

10. Appendix B

On the Source Distribution in Figs 1 and 2.

If it is assumed that the blobs are all ejectedalong the rotation axis with reasonably similar ve-locities, the projected velocity vp, which is propor-tional to the angle between the ejection directionand the l-o-s, is also, therefore, proportional to theinclination angle i of the central torus. For simi-lar ejection speeds the projected ejection velocityvp, which is proportional to the angular motion µ

(mas yr−1) of the blobs in the inner jets, will bedependent on the ejection angle i. The observedprojected ejection velocity can then be convertedto the inclination angle of the central torus usingthe relation vp = vesini, where ve is the ejectionspeed.

By normalizing the µ of all sources to the samedistance using the flux density, the distribution ofsources versus inclination angle can be obtained.This has been plotted in Fig 22 after binning thesources into 3◦-wide bins. It can be seen thatthe observed distribution falls off almost exponen-tially with inclination angle. This is contrary tothe shape of the distribution expected for randomejections when no selection effects are present,which is represented by the dashed line and revealsthat for a random distribution of orientations, 50%of the sources are expected to be located above60◦. As noted above, the dotted line in Fig 2also represents the 50% line. This discrepancyneeds to be explained, regardless of which redshiftmodel (cosmological or intrinsic) is assumed. Inthe cosmological redshift model Doppler boostingis a possible explanation, although it is then dif-ficult to explain the upper envelope and slope of0.5 in Fig 2.

10.1. Source Detection as a Function of

Radio Flux Density

In the DIR model I claim here that the sourcesare radio standard candles for a given inclinationangle and the radio flux density is then also ameasure of source relative distance for sources atthat inclination angle. For a flux limited sample

21

an increase in radio luminosity, or a lowering ofthe detection limit, will translate into a large in-crease in the number of detected sources becausethe number of sources goes as the cube of the dis-tance. The increase in source density in Fig 22 asthe inclination angle, i, decreases towards face-on,which is counter to that expected if the sourcesare standard candles, can be explained by an in-crease in the radiated flux as the inclination angledecreases. In other words, the luminosity of allsources would be the same for any specified incli-nation angle but it would vary with that angle,becoming strongest when the object is viewed di-rectly into the central hole in the torus. In Fig 2,this means that the source luminosity increases asone moves downward from the solid line becausethe inclination angle is simultaneously decreasing.If the luminosity of each source was normalized tothat for i = 90◦, the location of any given sourcebelow the line in Fig 2 would move to the left hori-zontally, by an amount that depends on its presentdistance below the upper envelope.

What could be the origin of such a luminositydependence? One possibility is that the radiationcomes from an optically thick torus and there isa similar decrease in area of the torus from face-on to edge-on. In the DIR model a factor of 4decrease in flux density is equivalent to a factor2 increase in distance. For a flux limited sample,and since the number of sources increases as thecube of the distance, a factor of 4 decrease in fluxdensity (visible area of the torus), between face-onand edge-on, will translate into a factor of 8 de-crease in number for edge-on sources detected. Fig23 shows an example of an edge-on and a face-ontorus. The relative decrease in area from face-onto edge on will increase as the torus flattening in-creases and the dashed lines in Fig 23 move closertogether. This then is a selection effect that canexplain at least some of the decrease seen in thenumber of sources near the upper envelope in Fig1. However, large area changes will require sig-nificant flattening of the torus, presumably due torotation, and this method alone may not be ableto explain the large decrease seen with increasinginclinaton angle in Fig 22.

The overall shape of the number vs inclinationangle plot in Fig 22 suggests an additional expla-nation for the decrease in flux density betweenface-on and edge-on sources. Since the fall-off in

Fig. 22.— (solid line)Distribution of sources as afunction of the torus inclination angle after bin-ning into 3◦-wide bins. (dashed line) distributionexpected for a random orientations with no selec-tion effects.

Fig. 23.— Change in area between edge-on andface-on optically thick torus.

22

source number begins within a few degrees of theface-on position, there may be a component of theobserved flux density that is unrelated to radiationfrom the torus. It may be coming from inside thehole in the torus where the ejected blobs originate.In this case its strength would be entirely relatedto the visibility of this inner region which, in turn,would be controlled by the inclination angle of thetorus, as demonstrated in Fig 24. In fact, it maybe possible to obtain an estimate of the openingangle of this radiation emerging from the hole inthe torus using the number distribution vs incli-nation angle. In this scenario there is no problemproducing a large change in observed flux betweenface-on and edge-on inclinations.

In Fig 25 the observed distribution in Fig 22has been re-plotted assuming that negative rota-tion angles would result in a mirror image of whatis seen for positive rotations. This resulting distri-bution is remarkably similar to that of an antennaradiation pattern. However, it is unlikely that anypattern (including sidelobes) could be producedin the conventional manner. Emission may comefrom a combination of sources, including materialnear the central black hole, material throughoutthe hole in the torus, and material along the innercrescent on the inside edge of the torus as shownin Fig 26. However, after further examination ofFig 25 it is concluded, based on the shape of thebroad curve designated by a dashed line, that thiscomponent may be produced by a fat, opticallythick, torus as its orientation changes. This num-ber density variation near a factor of 5 can eas-ily be explained by the area change. It is furtherconcluded that the strong narrow feature within∼ 10◦ of face-on is produced by much stronger ra-diation emerging from the hole in the torus. Thisconclusion appears necessary since it appears tobe too strong to be explained by a change in area,and because a change in area could not explainthe sudden fall-off within a few degrees of face-on,although this fall-off is unlikely to be as steep as in-dicated in Fig 25 (see Bell and McDiarmid (2006)for a more complete discussion). The decrease insource density seen in Fig 25 can thus be explainedby a simultaneous decrease in flux density as theorientation changes from face-on (i = 0◦) to edge-on (i = 90◦).

As noted above, source flux at 90◦ is a mea-sure of distance in this model. Thus the number

Fig. 24.— Torus with two-sided jet viewed edge-on.

Fig. 25.— Change in observed source density withtorus rotation.

23

of sources will vary as S(90◦)2/3. If S is not depen-dent on i, the source number density as a functionof i will vary as sini. However, if S is i-dependent,we obtain another distribution, N(i), owing to thefact that the distance corresponding to S(90◦) isdifferent from that for S(i). The difference is pro-portional to (S(i)/S(90◦))3/2. This means that

S(i)/S(90◦) = [N(i)/sini]2/3 — (1)

The conversion of the solid line in Fig 25 toS(i)/S(90◦) is shown by the solid line in Fig27. This, however, is an approximation becausethe determination of the inclination angles signif-icantly below 90◦ is an approximation as is nowshown.

10.2. Correction of the Observed Flux

Density and Distance

Fig 27 shows that S(i)/S(90◦) peaks near i =0◦, which means that if the S values for all of thesources are normalized to S(90◦) to give us a uni-form measure of distance, the points below the linein Fig 2 will move to the left, especially those wellbelow the line whose inclination angle is small. Anew determination of the inclination angles basedon these new source positions will yield more ac-curate values. Because the movement to the leftresults in each point becoming closer to the lineabove, the inclination angles are increased. Theincrease is very small for sources whose i is near90◦ and zero for those with i = 90◦ (which meansthat the slope of the upper envelope will not beaffected). On the other hand, the increase is largefor those sources whose i ≪ 90◦ because they mustbe moved significantly to the left as indicated byFig 27. Consequently the width of the peak in Fig27 is actually larger than shown, as we will seebelow.

For clarity, I describe this analytical processagain. If the true flux density change with in-clination angle is known, it can be used to nor-malize all observed flux density values to one in-clination angle. Correcting the fluxes to edge-onby removing the intrinsic flux density componentwill move sources to the left in Fig 2, with theamount of movement proportional to their dis-tance below the upper envelope. Put another way,many of the sources that lie well below the up-per envelope in Fig 2 will have been plotted intheir present location simply because they con-

Fig. 26.— Change in radio flux density betweenedge-on and face-on orientations of optically thicktorus.

Fig. 27.— Change in flux density required withtorus rotation to produce density distribution inFig. 25. See text for a description of the dashedcurve.

24

tain a large intrinsic flux component. Not onlywill they have originated in a distant region wherethere are many more sources to choose from be-cause of the increased volume of space sampled,they are clearly not from the same space in whichthose near the upper envelope in Fig 1 are located,since these cannot have moved significantly. Theyshould then not be included in the same numberdistribution count.

In Fig 28 the solid curve in Fig 27 has beenused to normalize the intrinsic component of theflux at all inclinations to the edge-on value, so thatrelative distances can be compared. For distancesgreater than that corresponding to S ∼ 0.2 Jy thesource number density near edge-on will have beenreduced because of the detection limit, which isshown approximately by the dashed line. Becausethe inclination angle estimated for each source inFig 2 will be too small, the width of the peak nearface-on in Fig 27 will be too narrow. These under-estimated inclination angles will also have led toan over-correction in Fig 28. Thus Fig 28 is as-sumed to represent an upper limit to the adjust-ment required to move the sources to their originaldistances.

In Fig 29 the number density distribution hasbeen recalculated (solid line) using only thosesources above S = 0.2 Jy in Fig 28 to avoid the areawhere the number has been affected by the detec-tion limit. This curve is now a good fit to the ex-pected curve shown by the dashed line. When thedashed curve in Fig 27 was used to correct the fluxdensity, the number density distribution shown bythe bold dashed line in Fig 29 was obtained. Thedashed curve in Fig 27 was obtained simply byscaling down the values near the central peak bya factor of 2 in an attempt to correct for the un-derestimated inclination angles discussed above.

It is concluded from this analysis that thesource distribution in Fig 2 can be explained ifthere is a reasonable increase in radio luminositywhen the inclination angle of the central torus ap-proaches face-on. A more detailed discussion ofthis is presented in Bell and McDiarmid (2006)where an estimate of the opening angle of the holein the torus is also made.

Fig. 28.— Fig 1 after the flux densities were cor-rected using the solid curve in Fig 27. Dashed linerepresents the approximate detection limit.

Fig. 29.— Number distribution for sources withcorrected flux densities greater than S = 0.2 Jy asa function of inclination angle after binning into10◦ bins as described in the text.

25

REFERENCES

Arp, H. 1997, A&A, 319, 33

Arp, H. 1998, ApJ, 496, 661

Arp, H. 1999, ApJ, 525, 594

Bell, M.B. 2002a, ApJ, 566, 705

Bell, M.B. 2002b, ApJ, 567, 801

Bell, M.B. 2002c, astro-ph/0208320

Bell, M.B. 2002d, astro-ph/0211091

Bell, M.B., and Comeau, S.P. 2003a, astro-ph/0305060

Bell, M.B., and Comeau, S.P. 2003b, astro-ph/0305112

Bell, M.B. 2004, ApJ, 616, 738

Bell, M.B., Comeau, S.P., and Russell, D.G. 2004,astro-ph/0407591

Bell, M.B., and McDiarmid, D. 2006, The RadioDetectability of AGNs as a function of the In-clination Angle of the Central Torus. (in prepa-ration)

Bondi, H. 1964, Lectures on Relativity (BrandeisSummer Institute in Theoretical Physics), En-glewood Cliffs: Prentice-Hall

Bridle, A.H., and Perley, R.A. 1984, ARA&A, 22,319

Bridle, A.H., Hough, D.H., Lonsdale, C.J., Burns,J.O., and Laing, R.A. 1994, AJ, 108, 766

Buchdahl, H.A. 1959, Phys. Rev., 116, 1027

Buchdahl, H.A. 1966, ApJ, 146, 275

Burbidge, G., and Burbidge, E. 1967, Quasi-

stellar Objects, W.H. Freeman and Co. publ.

Burbidge, G. and Hewitt, A. 1990, ApJ, 359, L33

Burbidge, E.M. 1995, A&A, 298, L1

Burbidge, G. 1996, A&A, 309, 9

Burbidge, E.M., 1997a, ApJ, 484, L99

Burbidge, E.M., and Burbidge, G. 1997b, ApJ,477, L13

Burbidge, E.M. 1999, ApJ, 511, L9

Burbidge, G., and Napier, W. 2001, AJ, 121, 21

Burbidge, G. R. 2004, ApJ, 603, 28

Chu, Y. et al. 1998, ApJ, 500, 596

Cohen, M.H. et al. 1977, Nature, 268, 405

Dent, W.A. 1965, Science, 148, 1458

Freedman, W.L., et al. 2001, ApJ, 553, 47

Galianni, P., Burbidge, E.M., Arp, H., Junkkari-nen, V., Burbidge, G., and Zibetti, S. 2005,ApJ, 620, 88

Goodlet, J.A., Kaiser, C.R., Best, P.N., andDennett-Thorpe, J. 2004, MNRAS, 347, 508

Greenstein, J.L., and Matthews, T.A., 1963, Na-ture, 197, 1041

Hutchings, J.B., Price, R. and Gower, A.C. 1988,ApJ, 329, 122

Karlsson, K.G. 1971, A&A, 13, 333

Karlsson, K.G. 1977, A&A, 58, 237

Kellermann, K.I, and Pauliny-Toth, I.I.K. 1968,ARA&A, 6, 417

Kellermann, K.I., Vermeulen, R.C., Zenus, J.A.,and Cohen, M.H. 1998, AJ, 115, 1295

Kellermann, K.I. et al. 2004, ApJ, 609, 539

Legg, T.H. 1970, Nature, 226, 65

Longair, M.S. 1966, MNRAS, 133, 421

Lopez-Corredoira, M. & Gutierrez, C.M. 2002,A&A, 390, L15

Miley, G.K. 1971. MNRAS, 152, 477

Narlikar, J. and Arp, H, 1993, ApJ, 405, 51

Neff, S.G., Hutchings, J.B. and Gower, A.C. 1989,AJ, 97, 1291

Neff, S.G. and Hutchings, J.B. 1990, AJ, 100, 1441

Pauliny-Toth, I.I.K. and Kellermann, K.I. 1966,ApJ, 146, 634

Rees, M.J. 1966, Nature, 221, 468

26

Rees, M.J. 1967, MNRAS, 135, 345

Russell, D.G. 2005a, astro-ph/0503432, (Ap&SS,in press)

Russell, D.G. 2005b, astro-ph/0503440, (Ap&SS,in press)

Schmidt, M., 1963, Nature, 197, 1040

Sholomitskii, G.B. 1965, AZh, 42, 673; Soviet Ast.,9, 516

Stickel, M., Meisenheimer, K, and Huhr, H. 1994,A&AS, 105, 211

Tifft, W.G. 1996, ApJ, 468, 491

Tifft, W.G. 1997, ApJ, 485, 465

Verschuur, G.L., and Kellermann, K.I. 1988,Galactic and Extragalactic Radio Astronomy,

Springer-Verlag publ.

Wall, J.V., and Peacock, J.A. 1985, MNRAS, 216,173

Wills, D., and Lynds, R. 1978, ApJS, 36, 317

Woltjer, L. 1966, ApJ, 146, 597

This 2-column preprint was prepared with the AAS LATEX

macros v5.2.

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Table 1

Sources at the Plate Cut-off.

Source SV LBI z µ(mas yr−1) mv

0016+731 0.98 1.781 0.074 18.00035+413 0.53 1.353 0.1 19.10212+735 2.69 2.367 0.08 19.00458-020 2.33 2.286 0.1 18.40642+449 4.31 3.408 0.01 18.50707+476 0.63 1.292 0.11 18.20850+581 0.61 1.322 0.2 18.00917+449 1.43 2.18 0.07 19.01128+385 1.13 1.733 0.01 18.01532+016 0.76 1.42 0.21 18.71656+477 1.14 1.622 0.06 18.01758+388 1.75 2.092 0.002 18.02113+293 0.94 1.514 0.02 19.52136+141 2.75 2.472 0.02 18.5

Table 2

Comparison Between the Local and CR Models.

Local Model CR Model

1) Can the observations be explained without relativistic velocities? Yes No2) Does the logN-logD plot have the correct slope of three? Yes No3) Can the observations be explained without having to assume an arbitrary luminosity evolution? Yes No4) Can the observations be fitted without assuming an arbitrary density evolution? Yes No5) Is there corroborating evidence that the sources are standard candles? Yes No6) Is the logN-logS plot generated in the simplest manner predicted for the model? Yes No

28