Evolution Extragalactic Radio Sources [5th piece]

8/8/2019 Evolution Extragalactic Radio Sources [5th piece]

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CHAPTER SIX

COSMOLOGICAL EVOLUTION OF EXTRAGALACTIC RADIO SOURCES

6.0 Evolution of a typical (extended) extragalactic(double) radio source was treated in Cha pters 2-4. Anotherinterconnected aspect of the evolution of extragalactic radiosources is the change in the gross p roperties of populationsof such sources with cosmic e poch, assuming some (generally,a uniform relativistic) world model. One simple property isthe number density of sources at different cosmological dis-tances (


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out in space and time was completely belied since effects ofradio source evolution dominate any such studies

Although the source count test re quires the bare mini-mum information, viz, the flux density of each source, it isimportant to have a large number of sources to determine thelog n - log S relation reliably. Another test, which givesan idea of the uniformity of the radio source distribution inspace (or with cosmic epoch), but can be done with a muchsmaller number of sources from a flux density limited sampleis the V/Vm or luminosity-volume test (Schmidt 1968, Rowan-Robinson 1971). This test, however, reauires a knowledge ofthe redshifts and spectral indices of the sources in the sample.

In general, the V/Vm test is related to the sourcecount test via the underlying world model and the range of red-shifts in which the sources lie. For flat s p ace, the value ofs directly determined by the slo pe of the sourcecount (i.e., the slope of the log n - log S relation), without

the need for any redshift information. (See Longair &Scheuer 1970 for details).

A source of flux density S >S o , the limiting value forthe flux density limited survey, can be seen out to a redshiftat which its flux density dro p s to S. The volume upto the

redshift of the source (in a given world model) divided bythe volume upto the limiting redshift gives a quantity, called


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V/Vm , which ranges from 0 to 1. For a uniform space distri-

bution of sources, V/Vm has a uniform distribution on [0,1],so that the mean is 1/2 and the standard deviation 1/ 12. Con-versely, a nonuniform V/Vm distribution (e.g., with a meandifferent from 1/2)implies a nonuniform distribution of sources.A value >1/2means more sources farther away or at earlier epochs.The values found for steer,- and flat-spectrum sources for theFriedmann (i.e., uniform relativistic) world models are 0.7and 0.6 respectively. Thus, both the source count and V/Vmtests show that extragalactic radio sources evolve stronglywith epoch, as already mentioned above. Moreover, the compactflat-spectrum sources evolve less than the extended stee p -spectrum ones in uniform relativistic world models.

6.1 THE V/Vm TEST IN HN GRAVITY However, in certain noncon-ventional world models it is possible to reconcile theory withthe observations without invoking the evolution of the density/luminosity of radio sources with cosmic epoch. These modelsnecessarily have a nonmonotonic behaviour of flux density Sywith redshift z for a source of given monochromatic luminosityL . That is, the flux density decreases down to a certainminimum as one takes the source to greater and greater distances.It then increases and may have further maxima, minima and/orpoles. An example is the Lemaitre world models (Longair &Scheuer 1970). Another one is the world model given by Hoyle-Narlikar conformal gravity (Hoyle & Narlikar 1972, Canuto &


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tO9 Z

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Flo. 601 Sp(z) relation in Hoyle- Nar[1kar conForrnalgravity. Sv(z) and h(z) are retakedby Lvi SI(z)=-47-i(c/H0)Vh(z).


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Table 6 .1V/ Vn , F O R W I L L S A N D L Y N D S S A M P L E S

N o . O FS OUR C ES `(V/V,)

LI M I TS, =3.5 No Cutoff36(2) 0 .57 0 .0 48 0 .53 0 .0 46 Sc, =1.95 Jy at 178 MHz5(1) 0 .47 + 0 .0 80 0 .46 + 0 .0 84 log (So) o p , = -30.34 mag at

2500 A emitted wavelength41(3) 0.550.040 0.52 0 .04260(5) 0 .58 + 0 .0 31 0 .54 + 0 .0 33 So = 2.95 Jy at 178 MHz16(1) 0 .47 0 .0 62 0 .46 0 .0 62 log ( S 0 ) opt = - 30.34 mag at

2500 A emitted wavelength76(6) 0 .55 0 .0 28 0.52 0 .03015(3) 0.56 +0.068 0.55 0 .069 Sc, = 0.345 Jy at 2700 MHz45(3) 0.56 0 .040 0.58 0.041 log (So) O / A= 30.34 mag at2500 A emitted wavelength60(6) 0.56 + 0 .034 0.58 + 0 .035

T A B L E N o . aSAMPLEb11 > 0 .5a < 0.5

All sources12 a> 0.5a.5

All sources13 > 0 .5

a < 0.5All sources

a This refers to the Table number of Wills and Lynds 1978.bS, defines a, the radio spectral index.The number in parentheses is the number of sources not having measured redshift. These sources have been assignedvalues of V/ V, evenly between 0 and 1.


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Narlikar 1980). In spite of such a com p licated Sv (z) rela-tion, it can be shown that the V/Vm test is still applicablewith the same criterion for a naturally (re)defined V/Vm(Longair & Scheuer 1970, see also section 6.2 below). TheS(z) relation for the Hoyle-Narlikar model is shown inFig. 6.1 for several cases covering a (the spectral index) 1. It has a minimum at z 0 = 2/(1-a) for

a 1. We have performed the V/Vm testin Hoyle-Narlikar cosmology for the samp les listed in Tables11, 12 and 13 of Wills and Lynds (1978). Referring the readerto Kulkarni & Banhatti (1983) for details of the calculations,we present the results in Table 6.1, and discuss their impli-cations. The sources of Tables 11 and 12 (of Wills & Lynds(1978)) were selected at the low frequency 178 MHz from the4C survey and have predominantly steep spectra, while thoseof Table 13 were selected at the high frequency of 2700 MHzfrom the Parkes survey and have predominantly flat spectra.For each sample, we have given in Table 6.1 values of for two cases, one with a redshift cutoff of 3.5 and the otherwithout a redshift cutoff (more precisely, with z c = 1020).It is seen that the values for each sample are not significantlydifferent from the value 1/2 expected fora uniform distributionof sources in comoving volume. Thus the values are


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consistent with the hypothesis of uniform distribution ofsources in space.

In any world model where Sv decreases monotonicallywith z (for given luminosity Lv and soectral index a ) wehave a one-to-one correspondence between x_7_V/Vm and z. Infact, if p(x) denotes the probability density of x, it canbe easily shown that the number n(z) of sources of redshift zper unit comoving volume is (see section 6.2, equation 6.4below):

n(z) a p (v (z) /v (z) ) for 0 z zt m, . (6.1)

where zm is the limiting redshift corresponding to V m , andv(z) is the dimensionless volume defined by V(z) = (47/3)(c/H 0 3) v(z), V(z) being the actual volume. Thus Vm V(z).(The method of equation 6.1 is, of course, not practical forfinding n(z) since zm is different for different L \ ) ,a , andthere is no standard candle.)

On the other hand, if S v (z) has a minimum at z 0 (forgiven Lv and a, a given value of x generally corresponds totwo values of z, one less than z 0 and the other greater thanz 0 . Hence it is not possible, from a knowledge of p(x) (evenfor sources of the same L v and a) , to derive unambiguously

the comoving volume density of sources as a function of z.

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Generalizing to sources of all L v and a, though an


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exact relation like (6.1) is not p ossible, one can still saythat for S y monotonically decreasing with z, a predominanceof high values of x in p(x) imp lies a higher n(z) at higherz-values. If Sy (z) has any minima, maxima, or p oles, evensuch a statement is not possible. However, z o = 2/(1-a) forthe Hoyle-Narlikar model (thus, z 0 is 2, 4, 10 for a = 0, 0.5,0.8), and the redshift z is very rarely > z 0 for sources inthe samples we have used. Hence the effects of the nonmono-tonicity of S (z) are almost absent.

As noted above, the < V/Vm > values are not significantlydifferent from 1/2 and hence are consistent with the hypothesisof uniform distribution of sources in space in the frameworkof Hoyle-Narlikar conformal gravity. In addition, in view ofthe remarks made above and the fact that the distributions ofV/Vm for the various samp les do not show a bias toward eitherlow or high values, we conclude that they indicate a uniformdistribution in comoving volume of both steep- and flat-spectrumsources in Hoyle-Narlikar conformal gravity. On the otherhand, the values of of 0.74 and 0.60 for the samesamples in the Friedmann world models for steep- and flat-spectrum sources respectively (Wills & Lynds 1978) indicate astrong cosmological evolution of the source pooulations.

6.2 THE V/Vm TEST FOR NONMONOTONIC S y ( z) We show that thedistribution of x V/Vm for sources of given L, a is uniformfor a uniform volume distribution of sources, even if S v (z) is


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S(z)

Fig. 6.2 S (z) relation withone minimum


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nonmonotonic and has any minima, maxima, and/or poles. In-stead of considering the general case, we consider the simplecase when Sv (z) has just one minimum z 0 (Fig. 6.2). Afterwe are through with the calculations for this simple case, itwill be evident how the general case can be treated. Thecurve is drawn for given values of L , a. S 0 is the limitingflux density, and defines two limiting redshifts z ml and z m2which may coincide at z 0 . In addition to the radio surveylimit S 0' there may be a limiting optical/infrared/X-raymagnitude, which gives rise to a limiting redshift zu,chosenas the smallest of the various limiting redshifts. (It isassumed that the S(z) relation which goes into determiningthese latter limiting redshifts is monotonic decreasing. Butthis does not reduce the generality of what follows.)

We use below the dimensionless volume v(z) defined byV(z) = (47/3)(c/B 0 3) v(z) , and the abbreviations v s for v(z s )where s is a subscri pt. If z u is in the region where S v ( z )is decreasing, we have a monotonic decreasing behaviour in the

range of interest [0,z u ]. For such behaviour, we have x = v/v uand a given x-value corres ponds to a single v-value and hencea single z-value (since v(z) is monotonic). However, ifz u >zm2' the z-ranges of interest are [0, z ml ] and [zm2' z u ]:S v (z) is monotonic decreasing in the first region and monotonic

v(z) must not only be monotonic but monotonic increasing forany world model, since no part of s pace can have negative volume.


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increasing in the second. The quantity x is defined diffe-

rently for the two regions:

x = v/v, for z in [0, x = (vu-v)/(vu-v2)

for z in [zm2' z u1 ... (6.2)Note that x varies from 0 to 1 as z increases from 0 to z mlin the first range or decreases from z u to z m2 in the secondrange. Hence a given x-value arises from two z-values: onein [0, z ml ]nd the other in [zm2' z uI.hus there areessentially two cases to be considered in counting the numberof sources in the x-domain on the one hand and the correspondingz-domain on the other. We prove below that, for a uniformvolume distribution of sources, the p robability density p(x)of x is p(x) = 1 for both these cases.

CASE 1. For N sources in a survey covering solid angle0 of the sky, denoting by n(z) the number of sources in thewhole sky per unit volume at redshift z,

(47N/Q) p(x)1dx1 = n(z)IdV(z)1;

.% p(x) = (Q/3N) (c/ H 0 ) 3 n(z) vu= n (z) / (3N/Q) (H /c ) 3 (1/v u)u

using x = v/vu (so that dv/dx = v u ). The average T is


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6-13z uz= f n(z) dV(z) / f dV(z)0 0

= ( 4 7 N / S 2 ) / ( 4 - r r / 3 ) ( c / H 0 ) 3 v u= (3N/Q)(H 0 3c) (liv ) ;

:.p(x) = n(z(xv u ))/1i,(6.3)where z(v) is the single-valued inv erse of the monoto nicincreasing function v(z). For a uniform distribution ofsources, we hav e n(z) = n 0 = n (natu rally) so that equation(6.3) reduc es to p(x) = 1. Note that equation (6.3) canalso be written as

n(z) np(v(z)fivu) for 0 z ^ z u , (6.4)

which is the same as equation 6.1 abov e (section 6.1) .

CASE 2. x is given by equation s 6.2 for the tworanges. Two v alues, say z and z'(>z), o f the redshift giv erise to the same x-value. There are two correspondingvalues of the volume: v E v (z) and v' Ev(z'). Note thatz belongs to [0, z mi ] and z' belongs to [z m2 ,z u ]. Equa-rions 6.2 then giv e

x = v/v 1 = ( v u -v')/(vu-v2),dv/dx = v 1 , and dv '/dx = -(v u -v 2 ) .

Again co unting sou rces in the z-domain and the correspon dingx -domain,


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(4nN/Q)p(x) Idx1 = n(z)IdV(z)I + n( z') IdV(z')I

p(x) (Q/3N) (c/H0 ) 3 (nldv/dx1-4-n'IdvI/dx1)

= (Q/3N)(c/H 03) [nv 1 + n' (v u - v 2 )] ,

using the derivatives just found and with obvious abbrevia-tions, the average n is

n = (3N/Q)(H0 3/c) (1/v m '- vm = v 1 + v u - v2''rip(x) = n(z(x v i ))v i /v m + n(z(vu-x(vu-v2)))

- ( v u -v 2 )/v m'which for n(z) = n 0 = n reduces to p(x) = 1.

It is clear that such calculations can be extendedto models in which S y (z) has several minima, maxima and/orpoles - e.g., the Lemaitre models (Longair & Scheuer 1970).A properly defined x can then be shown to be uniformly

distributed on [0,1] for n(z) = n0.


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CONCLUSIONS

The evolution of extragalactic radio sources has two inter-connected as p ects. One is the origin and evolution of suchan object, and the other is the change in the gross proper-ties of populations of such sources at different epochs ofthe universe, assuming some (generally, a uniform relativi-stic) world model. We have considered both these aspectsin this thesis, the first one in much more detail.

(1) Most extragalactic radio sources have a double structurewith two outer components and a galaxy or quasar (the parentobject) roughly midway. If the process of production of thetwo outer components in these double radio sources is intrin-sically symmetric, the observed asymmetry among them can beattributed to projection effects. We have attempted toremove these projection effects from the brightness structureof two-statistically well-defined samples of extended extra-galactic double radio sources and have arrived at two intrin-

sic parameters related to component generation and evolution.(la) We find that the average s p eed of advance of the hot-spots, assuming intrinsic symmetry, must be about 0.15c ifwe are to explain the asymmetry in the positions of the twohotspots. and that

(lb) the radio luminosity of the components must decrease as


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fast as the inverse cube of the intrinsic component-age toexplain the asymmetry in the strengths of the components.

If part of the asymmetry is either intrinsic to the genera-tion mechanism or is produced later due to an uneven distri-bution of the intergalactic medium on the two sides of theparent object, the average speed and the rate of evolutionof the component-luminosity would come down.

(lc) The observed asymmetry can be accounted for if theintergalactic medium is clumpy on the scale of tens of kpc,about one-twentieth to one-tenth of the typical size ofextended extragalactic radio sources.

(2) Various types of structures other than the simple doublesource also occur among extragalactic radio sources. Insome sources, an S or Z symmetry exists around the parentobject from about an arcsec to tens or hundreds of arcsec.Clearly, the central engine, which gives rise to the bifur-cated double structure, sometimes p recesses. A surprisinglywide variety of structures can arise from twin precessingrelativistic jets of plasma (evolving in some way) projectedonto the plane of the sky.

(2a) In this scheme, we have attempted to model the high-redshift (z=1.595) quasar 1857+566. This source has a 'warm-spot' on one side and a jet with two sharp bends and no


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features and that for about two-thirds of the sources whichhave steep spectra these features are hotspots or steep-spectrum kiloparsec cores while the remainder contain flat-spectrum compact components.

(4) We have also observed with IPS at 91.8 cm another un-biased sample of 90 radio sources stronger than 0.75 Jy atthat wavelength selected from the Ooty lunar occulation sur-vey.

On an average, 30 percent of the emission from thesources comes from a region of angular size of about 0.3 arc-sec.

The sources cover a range in flux density from 0.75 to 4.5 Jyand the angular sizes go upto 500 arcsec.

Dividing the 90 sources into three flux density ranges,we confirm the low flux density end of the correlation foundbetween the fraction of scintillating flux density Ti (whichis thus a compactness parameter) and the flux density S ofextragalactic radio sources. The new points for the smallestS are in accordance with the levelling off of the 0-S rela-tion toward small S found by previous workers. The u-S rela-tion has bearing on the (cosmological) evolution of compactfeatures in extragalactic radio sources with epoch.

(4c) Another result from the IPS survey of 90 sources is


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that the scintillating size D is correlated with the largestangular size (LAS)of these sources. The median values oflog p plotted against the median values of log LASshow aroughly linear relation with a slope much less than 1. Themedian log p and log LASvaluess for the sample of 30 few-arcsec sources are in accord with this relation.

Asimilar relation is found between the median log I) vs

log LAS values of the brighter sam p le consisting of 128 identi-fied extended double radio sources usin g 81.5 ilHz IPS data frollliterature.

The slope of this relation is about twice that for thefaint Ooty sample and there is also an offset between thetwo relations. The different slopes are mainly due to themuch larger redshift-range of sources in the bright 3CRsample compared to the faint Ooty sample, whereas the offsetbetween. the two relations is mainly and about equally due totwo differences in the two samples: the different totalangular sizes (LAS)and the different ways of determiningthe scintillating angular sizes.

If the scintillating structure is inter p reted as hotspotsin double radio sources, this small slope has implicationsfor the collimation of extragalactic jets.

(4f) However, 4.87 GHz VLA data on the most compact and/orintense hotspots from a sample of sources chosen to minimize


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projection effects show that the hotspot size tp Hsnd thedistance 0 of the hotspot from the core are related. Aplot of log ( 1 ) H S vs log 0 shows a slope close to one.

(4g) The small slopes obtained from the IPS data are pro-bably due to projection effects and because the IPS techni-que averages over all the compact structure in the telescopebeam.

(5) The luminosity function of extragalactic radio sourcesgives the space density of the sources as a function ofluminosity and redshift (which determines the epoch) for agiven world model. It has been found that for uniform rela-tivistic world models, the luminosity function dependsstrongly on epoch, the high luminosity sources being abouttwo and a half orders of magnitude more numerous at a red-shift of about 2 than at present. This cosmological evolu-tion is stronger for the extended steep-spectrum source popu-lation than for the compact flat-spectrum sources. However,some world models do not require any evolution.

We have performed the luminosity-volume test withinthe world model given by Hoyle-Narlikar conformal gravityand find that no evolution is required for both steep- andflat-spectrum sources.

We also indicate the method for applying the luminosity-


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volume test to nonstandard world models with a nonmonotonicflux density vs redshift relation by treating the simplecase of one minimum in detail.


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Abbreviations for Journals and Series

Xv

A&AA&A SupAJPAJP Ap SupAnn Rev AAAp & Sp ScApJApJ SupAp LettBASIIAU SymnJAAMemASIMem RaSMNNatPASPPhys RevProc Roy Soc

Astronomy and AstrophysicsA & A SupplementAustralian Journal of PhysicsAJP Astrophysical SupplementAnnual Reviews of Astronomy and AstrophysicsAstrophysics and Space ScienceAstrophysical JournalAstrophysical Journal Sup p lementary SeriesAstro physical LettersBulletin of the Astronomical Society of IndiaProceedings of the International AstronomicalUnion SymposiumJournal of Astrophysics and AstronomyMemoirs of the Astronomical Society of IndiaMemoirs of the Royal Astronomical SocietyMonthly Notices of the Ro y al Astronomical SocietyNatureProceedings of the Astronomical Society of thePacificPhysical ReviewProceedings of the Royal Society


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XVIii

Acknowledgements

I thank Prof Govind Swarup for initiating me into the waysand means of radioastronomy in p articular and research ingeneral. I also thank him for being very p atient andgiving me his time during his active and busy schedule.

I am grateful to Prof R P Singh, the lateProf B N Bhattacharya and Prof J S Murty for the interestthey showed in my work despite its being rather removed fromtheir research areas.

I express my sincere gratitude to Vijay Kapahi andD J Saikia for almost being my acting suoervisors and alwaysegging me on to com p lete the work.

Colleagues and friends in Bangalore, Ooty and Bombay,who have been helpful in small and big ways throughout thelong course of the work reported in this thesis are toonumerous to name individually. -

Finally, and most significantly, my sincere apprecia-tion goes to Mr. N.K. Unnikrishnan, who took it u p on himselfas a challenge to finish the substantial job of typing thematter in a record time. I also thank him for the excellentjob he has done.

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Evolution Extragalactic Radio Sources [5th piece]

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