Evolution Extragalactic Radio Sources [2nd piece]

8/8/2019 Evolution Extragalactic Radio Sources [2nd piece]

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CHAPTER TWO

THE ASYMMETRY IN EXTENDED EXTRAGALACTIC

DOUBLE RADIO SOURCES I

2.0 The class of archetypal extragalactic double radio

sources described in section 1.1 has a radio luminosity (i.e.,

radio power output) much higher (>2.10 25 WHz -1 Sr 1 )than the

other classes like the head-tails and is known as the narrow

edge-brightened double or Fanaroff-Riley (FR) class II

(Fanaroff & Riley 1974). (See Miley 1980 for nomenclature of

extended sources based on structure.) The low luminosity FR

class I sources are a mixed bag. These include sources having

bent double and head--tail structures, which are associated

with galaxies in clusters (Simon 1978). The opening angle of

the twin trails, and the optical magnitude and prominence of

the associated galaxy in its cluster increase with the radio

luminosity (Rudnick & Owen 1977, Valentijn 1979). Birkinshaw

et al. (1978) showed that the distance from the galaxy to the

first brightness peaks along the two trails also increases

with the radio luminosity. The bending of the double structure

is modelled to be predominantly due to the motion of the galaxy

in the gravitational field of the cluster for the head-tails

i m (or narrow angle-trails) (Miley et al. 1972, Jaffe & Perola

1973, Cowie & McKee 1975, Pacholczyk & Scott 1976, Jones &

Owen 1979). For the bent doubles (or wide angle-trails), the

2-1


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2-2

parent galaxy generally has a close companion or is a D, cD

or db galaxy (Patnaik, Banhatti & Subrahmanya 1984), often

the brightest in the cluster, so that galaxian motion in the

relaxed cluster field is inadequate to account for the

bending. A variety of other mechanisms have been suggested

(Burns 1981, 1983, Valentijn 1981) and the most promising

one is motion of the cD in the intracluster medium due to

subclustering in a dynamically young cluster (Patnaik,

Banhatti & Subrahmanya 1984, Leahy 1984).

We do not consider the low luminosity FR class I

radio sources in clusters any further in this thesis, but

focus on the high luminosity FR class II classical double

radio sources. The natural deduction from the structure of

these narrow edge-brightened double radio sources is that

the central object is the parent object, giving rise to the

two hotspots and the corresponding radio lobes by providing

on two sides regions containing relativistic charged par-

ticles and magnetic field which radiate to produce the

observed radio emission through the synchrotron mechanism.

Though the nature of the central engine which produces the

bifurcated structure does not directly concern us in this

thesis, we mention that the current consensus of opinion is

that it consists of a thick accretion disk around a massive

black hole. (See, e.g., Rees 1978, Thorne & Blandford 1982,

especially Thorne & Macdonald 1982, Macdonald & Thorne 1982.


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2-3

See also Chakrabarti 1985a, b, Dhurandhar & Dadhich 1984a, b.)

The accretion disk has the sha p e of a torus with a two-sided

funnel centred on the black hole. The radio-emitting

material ejected at (perhaps) relativistic speeds from this

funnel along the rotation axis of the disk gives rise to the

two components, forming a roughly symmetric double radio

source. These two radio components are generally not obser-

ved to be equally strong nor are they observed to be exactly

equidistant from the central radio component or optical

object, which does not always lie exactly on the line

joining the two hotspots (Foimalont 1969, Ingham & Morrison

1975). (This is in addition to the apparent asymmetries

caused by errors in the radio and optical positions.) This

observed inequality of the two arms of the doubles and also

the inequality of the two component strengths (Fomalont

1969, Mackay 1971) can largely be attributed to projection

effects, if the process of production of the components and

their environments are taken to be intrinsically symmetric.

Chapters 2 and 3 treat the angular and brightness asymmetry

of extended extragalactic double radio sources. We first

present (section 2.1) the detailed model used in this chapter

and the next (Chapter 3), and then our investigation into

the inequality of the lengths of the two arms of the doubles

from the nucleus (section 2.2). Section 2.3 presents the

simplest possible model distribution of (projected and actual)

linear sizes implied by the relativstic expansion model.


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LINE OF

s iGHT

F;3 2.1 Geometry and terminology of thereicktrvrseic expansion model

2-4


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2- 5

2.1 THE RELATIVISTIC EXPANSION MODEL In this section, we

Present the aeneral model based on Ryle & Longair's (1967)

treatment, used in our investigation of the asymmetry in the

two arms of the extended double radio sources, as well a s

in the strengths of their comnonents. Whenever re q uired in

later sections, we s p ecialize from this model.

As shown in Fig. 2 .1 , a distant observer at rest rela-tive to the p arent object 0 would see the receding (R) and

a pp roaching (A) hotspots at ages t R and t A , when the age of

the central object since ejection of (the first pair of)

p lasmons or twin beams is t o . If v R and ; A are the two hot-

snot s p eeds averaged over their ages, and R and'A are the

angles of the two directions of motion with the line of

sight, t R , t A and t o are related by

t R (1+v Ry R/ c ) = t A (1-; AyA/ c ) = t o . (2.1)

In this equation, the abbreviations y i 7 os (1),. (i = R,A)

have been used. The equation can be derived by considering

the light-travel t imes of the radiation which arrives simul-

taneously at the observer from the receding and app roaching

comp onents and tha / parent object (see Fig. 2.1). Note that

the receding com p onent is observed younger than the app roa-

ching one: t Rto tA. The ratio of the two arms of the

double (the arm ratio) in the sense receding-to- a pp roaching is

r = O R/O A = (v Rt R/v At A) (sin ysin c A), . (2.2)


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2-6

(see, e.g., Saikia 1984) where O R and O A are the angular

distances measured on the radio ma p or from a one-dimensional

profile. To calculate the flux ratio, the ratio of the flux

densities of the two hotsoots in the model, we must assume

some form for the variation of the hotspot-luminosity with

its age. Following Mackay (1973), we take P c c T - 6 , a power-

law in the intrinsic age (or rest-frame age or p ro p er age)

of the hotspot T, which is given by integrating

2 2 -1/2dT. = dt . /Y. ; Y.= (1-v. /c ) , (2.3)

in which vi

(i-R,A) are the instantaneous hotspot speeds.

The flux ratio s is then

s = S R/S A = (T R/T A) [ (Y

APY R ) (i-v Ay A/c)/ ( 1 - 4 - v/c) 3+ a

R-R

(2.4)

where ocis the s p ectral index (section 1.2), assumed same

for both the hotspots.

2.2 THE FRACTIONAL ARM DIFFERENCE x The arm ratio (equation

2.2) contains information on the hotspot s p eed. To extract

this information simply, we formally assume that the soeed

is v, a constant. The information which we get by such an

assumption will then be about an average s p eed. Replacing

v/c by v for ease of notation, equations 2.1 and 2.2 give

vy ( 0 A - 0 R ) / ( 8 A + O R ) E x, (2.5)


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2-7

Fig 2.2 L7m1ts of 7nLearrd r- ) de..Avl ecQ.2.6


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2-8

the fractional arm difference. We have assumed a collinear

source structure (y F L = y a m , i.e., cP = (1) - see Fig. 2.1) in

deriving equation 2.5, so that y = cos (/) now defines the

(single) source axis making angle (1) with the line of sight.

This is justified since departure from collinearity is

small for the powerful doubles (Ingham & Morrison 1975,

Macklin 1981). The range ocyl covers all orientations of

the source in the sky. Since the fractional arm difference

x is restricted to 0x ^ 1 by its definition, equation 2.5

restricts v to 0


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2 9

Differentiating twice,

1 p(v)g(x)=f dv and g'(x) = -p(x)/x,

x

where p rime denotes differentiation with res p ect to the argu-

ment. The last equation is equivalent to

o(v) = -vg'(v). (2.6)

This means that for a sam p le of double sources chosen without

any bias for the orientation of the source axis from the

line of sight, the distribution of the average hots p ot speed

(relative to the central p arent object) can be directly

found from the distribution of the fractional arm difference

x, which can be calculated from observations of double

sources as

0 - 0x =

> +e < '

where the shorter arm 0 is identified with the receding

component (0 = O R ) and the lon g er one with the approaching

(o > = e A ) see equation 2.5).2.2.1 Application to a strong source sample We have used

doubles from the 166 3CR sources (Jenkins et al. 1977) to find

the distribution of v in this way. The number of beamwidths

N within the angular se p aration of the two outer hotsoots is

used to select well-se p arated doubles. Data are taken mainly

from the Cambridge observations at 5GHz (Jenkins et al. 1977

and references therein). Selection of (i) o p tically identified


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2-10

Table 2.1 The sample of extended double radio sources used for deri-ving the distribution of separation speeds of the hotspots

Src,3C1

Op. Id .2

Str.13

N4

x#5

LAS/arc sec6

6. 1 G C D 12.7 0.020, 0 .107 25.813 G D 10.9 0 .005 28.014 G* D 4.1 0 .332 23.322 ** D 12.1 0.597 24 .533 G C M,E 50.6 0.113, 0 .114 251 .333.1 G E,M? 105.6 0 .241 215 .841 G* D 8.2 0.166 23.142 G D 11.5 0 .001 28.046 G E,M? 74.0 0 .132 155 .047 Q C E 22.2 0.057, 0 .104 68.755 G E 34.5 0.190 69.061.1 G E 93.1 0.091 186.679 G C E 41 .8 0.104, 0 . 1 4 5 86.598 G E 62.9 0.096 283.1

109 G C D 27.8 0.081, 0 .051 90.4

132 G E,M? 8.1 0 .037 20.3133 G C E 5.7 0.024, 0 . 0 3 8 11 .8171 G D 4.4 0 .133 8.9173.1 G E 28.1 0 .122 58.0175 Q C E 20.4 0.181, 0 . 1 3 7 48.5184.1 G C E,M 88.7 0.144, 0 .142 179.4192 G E,M? 81.7 0.093 185 .7200 G C E 5.1 0.357, 0 . 1 4 3 17.0204 Q C M 17.5 0.008, 0 . 0 3 6 35 .0205 Q C D 6. 9 0.088, 0 .095 16.0208 Q C D 5.5 0.063, 0 .177 11 .2217 G D 5.9 0 .557 12.1219 G C E 61.8 0.033, 0 . 0 2 8 149.2220 1 G C E,M? 14.9 0.022, 0.091 29.8223 G C D 81 .1 0.096, 0 .099 255 .9226 G D 9. 3 0 .111 30.7228 G C E?,M? 6. 8 0.064, 0 .009 44 .9234 G C E 51.5 0 .144 , 0 .153 110 .1244.1 G E 21.9 0.062 51 .0247 G D 6. 4 0.261 13.3249.1 Q C E,M? 11 .5 0 .313 , 0 .348 23.1

250 G D,E? 20.6 0 .531 49.1252 G E 27.7 0 .324 56.7254 Q D 6. 5 0 .765 13 .2263 Q C D,M? 21.9 0.283, 0 . 267 44 .4265 G M 37.9 0 .202 78.0267 G* D 18.5 0 . 0 2 7 37.6

contd..


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2-1 1

Table 2.1 contd. . .

2 6

268.1 G D 21.7 0 .235 43 .5268.4 **C D 4.2 0.208, 0.003 10.1272 Q E,M? 21.3 0.367 57.2274.1 G E 73.9 0.044 151 .8277.2 G D 23.8 0.472 53.7280.1 Q C E,M? 9. 2 0.267, 0 .229 19.3284 G E 86.4 0.178 175.6285 G C D ,E? 5.8 0.030, 0 .013 134.2300 G C M 36.2 0.382, 0.374 93.4303 G* D,E? 8.5 0.470 17.0321 G C E 110.9 0 .034, 0 .038 286.6324 G D 5.0 0.196 10.3325 Q* D 7. 7 0.281 15.8330 G D,E? 30.2 0 .137 61.5334 0 C E 18.0 0 .252 , 0 .255 44 .3336 Q E 7. 0 0 .230 21.9337 G D,M? 21.4 0.049 43.3338 G C E,odd shape 22.2 0 .030 , 0 .003 44 .6340 G M 22.4 0 .434 44 .8341 G E,M? 28.6 0.141 70.6349 G C E 34.5 0.033, 0 .037 82.8381 G E 25.5 0.072 69.1382 G C M,E 23.0 0.111, 0 .100 153 .2388 G C E,M? 14.9 0 .040 , 0 .046 30.9390.3 G C M,E 105.4 0 .173 , 0.174 212 .9401 G C M,E 8.4 0.247, 0 .180 18.7427.1 G D 11.3 0.161 23.1

432 Q D 5.2 0 .221 12 .9438 G D,E? 8.1 0.064 18.7452 G C E 127.0 0.014, 0 .016 256.6

G = galaxy, Q = quasar, * indicates probable galaxy or quasar, ** =faint object. The presence of central radio component is indicatedby a C after the op.id . code.

I The structure code is: D = double with almost all of the emission con-centrated in the hotspots, M = double having mult iple components and

E = double having bridges.# The first value is calculated with respect to position of the op.id . ,

the second is with respect to the central component position, whenpresent.


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Sample OP : a. = 3.90Sample C : a =6.53Sample of Lonaairet al }-a= 4.75

2-12

F1:1 Observed distributions and fitsfor the fractional arm clifftrente x for sa-mples of doubles listed in Table 2.1.


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2-13

doubles (ii) with N ^ 4 and (iii) at least one bright hotspot,

and exclusion of 4 sources because the peaks are too broad,

and one source for unreliable o p tical identification leaves

72 doubles (51 galaxies, 4 possible galaxies, 13 QSOs, one

possible QSO and 3 faint objects). Central radio components

have been detected in 32 of these. In this section, we p re-

sent results of the two samples, OPs72 o p tically identified

doubles and Cs32 doubles with detected central components.

Calculations were also made for the sam p le G of 51 radio gala-

xies. Various orooerties of the doubles are tabulated in

Table 2.1. Note that the shorter arm is identified with the

receding side and the longer arm with the approaching one

(cf equations 2.5 and 2.7).

Equation 2.6 reauires that (i) g(x) be a monotonically

decreasing function and (ii) g(1)=0. Several forms of g(x)

satisfying these conditions were tried. The form

g(x) = A(l-x) ex p (-ax); A = a2/[a-l+exo(-a)]

provides a good fit to the observed distributions. 'A' is

given in terms of 'a' b y normalization. The method of least

squares was used to determine the single p arameter 'a'. Equa-

tion 2.6 then gives

p(v) = Av[l+a(1-v)]exp(-av).

Fig. 2.3 shows the histograms of x and the corresponding


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0. 5

Fes. 2.4 Distributions of the hotspot separationspeeds v for samples of doubles listed T r) Table 2.1.

Sample OP : a = 3.90Sample C : a = 6.53Sample of ) a= 4.75

Lonsai r et al

---------


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2-15

least squares fits g(x) for sam p les OP and C. The derived

distributions p(v) are shown in Fig.2.4. For sam p le G, half

of the sources have average speeds between 0.075 and 0.30c.

The corresponding ranges for OP and C are 0.10 to 0.37c and

0.06 to 0.25c.

Since the two components are assumed to be intrinsically

symmetric, the values of the hots p ot speeds are, in a way,

upper limits. Any intrinsic asymmetry either in the powers

of the op p ositely directed beams or in the environment shows

up as an increase in x, the (fractional) arm difference. Hence

if it is assumed that part of the spread toward higher x-

values in Fig. 2.3 is due to intrinsic asymmetry, the value

of 'a' after eliminating this asymmetry would be higher and

consequently, p(v) in Fig. 2.4 would show a predominance of

smaller speeds. Eliminating both systematic and random

errors would also act in the same direction (section 2.2.2

below).

Within the assum p tion of intrinsic symmetry, the spread

of p(v) arises from (i) the intrinsic spread in p lasmon ejec-

tion speeds (for a plasmon model) or the spread in the rates

of feeding the beam (for a beam model) among the different

sources and (ii) the difference in ages among the sources in

the sample. Thus, a source of greater age would have a

smaller average hotspot s p eed since the instantaneous hotspot

speed is expected to decrease as the hotspot moves through the


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2-16

intergalactic medium. A specific form for the time variation

of the hots p ot speed must be assumed to se p arate the two

effects. Ty p ical radio source lifetimes are much smaller than

the Hubble time. Hence a uniform distribution between 0 and

a maximum value is reasonable for the source age, and the

Peak in the distribution of initial hots p ot s p eeds is expected

to occur at a value about twice the mode of p (v), which gives

0.30c (Fig. 2.4).

We note that numerical hydrodynamic calculations carried

out upto the ages and distances corresponding to the sizes of

extended radio sources (Siah & Wiita 1983) give hotspot speeds

in excellent agreement with our results from arm ratios.

2.2.2 Error analysis in brief In this section we briefly

examine the effect of p ositional errors on x and consequently

on the distributions of x and then of v.

From equation 2.5 (section 2.2) x=(0A-07z)/(0A+0a).

Most of the sources we have used belong to the Fanaroff-Riley

(1974) class II, i.e., the edge-bri g htened sources. If the

resolution is too coarse to correctly locate a peak (hotspot)

in such a source, the observed peak is closer to the optical

object/central com p onent than the actual, so that the observed

6R

and 0

Aare underestimates. If the true values are 0

R+ AO

Rand 0 A + AO A'

x actual = "A - R 4 - A eA -Ae R )/(e e R- 1 - A eA +AeR)*


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2-17

Since AO R ,A0 A (and these errors are inde p endent of o R and

0 A to a first approximation), x actual < x. Thus, the values

of x are systematic overestimates. We assume that the random

error on x is inde p endent of x and that it is equally likely

to be positive or negative. Considering the x-distribution

as a histogram, the number of sources going out of a bin is

then proportional to its population. Since the bins systema-

tically decrease in p opulation toward larger x, more x-values

will shift toward larger x at every x and the x-distribution

will consequently widen. Thus, both systematic and random

errors cause a widening of the actual distribution. This

widening of the x-distribution leads to a corres p onding wide-

ning of the v-distribution and a shift in its p eak to higher

v. Therefore, as noted in section 2.2, the values of hotspot

speeds derived from the asymmetry in the angular structure

(i.e., inequality of the two arms of the doubles) should be

taken as up p er limits on account of errors also.

2.3 PREDICTED LINEAR SIZE DISTRIBUTION Linear sizes of extra-

galactic radio sources can be derived from their largest

angular sizes (LASs) and redshifts given the world model and

the value of the Hubble p arameter. Since redshift is much

more difficult to determine (and hence available for only a

relatively small number of the brighter sources) than the

radio flux density S, Swaru p (1975) used S as a rough distance

indicator in investigations of large samples of bright and


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2-1 8

faint radio sources and found a correlation between LAS and

S. In interpreting this correlation, Ka p ahi (1975a,b) assumed

a triangular distribution for the intrinsic linear sizes, with

the smaller sizes more probable, and used it in his prediction

of the LAS-S correlation. A detailed kinematic model for the

separation of the hots p ots of double radio sources from the

parent object in the middle, however, im p lies a definite

distribution for the actual (and hence also the projected)

linear sizes. The p urpose of this section is to carry out

this calculation leading to the two distributions for a simple

kinematic model and examine its applicability.

For the constant hots p ot-speed model to which we s p ecia-

lized in section 2.2 from the general treatment of section 2.1,

it is possible to anal y tically derive the distribution of

actual and projected linear sizes, assuming further that the

speed is the same for all sources. We derive these distribu-

tions in what follows, and examine the ap p licability of the

resulting two- p arameter ex p ression to the observed distributionsfve

of projected linear sizesL subsamnles of the 3CR sample.

Measuring speed in units of c, equation 2.1 of section

2.1 becomes, for a collinear source (v f c y x .e., p T c p_A!,

and constant hotspot speed v,

tR

(l+vy) = t o (1-vy) = to

, (2.8)

where y E cos (1 specifies the orientation of the radio source


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2-19

axis in the sky. Two expressions for the difference

AtE

o - t R in the ages can be derived from equation 2.8:

At = y.v(t R+ t A) , and At = t o .2vy/(1-v2 y 2 ) .

v( t R+t A) can be identified with the actual linear size L (see

Fig. 2.1, section 2.1). Also, writing

w = 2vy/(1-v 2 y2

) ,

the two ex p ressions become

At = Ly, and

At = w to .

(2.9)

Equation 2.10 is similar to equation 2.5 (x = vy) of section

2.2, since L and y can be considered independent random vari-

ables, so that, analogous to equation 2.6 there, we have

f L(L) = -Lf 1At(L) , o


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2-20

source lifetime. It is convenient to express t o and At in

units of T L ; t o is then uniformly distributed on [0,1], and

L must be measured in units of cT L . Since w and to

are inde-

pendent random variables, equation 2.11 gives the distribution

fAt (At) of At (Papoulis 1965, p.205):

2v/(1-v2

)f

At

(At) = f 1 f (w dww wAt

and differentiation gives, using equation 2.13,

f (At) =1

( 11

At 3vAt

1+At2

) for 0


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2-21

16

25

.c L

0

2

14

1 2

I9

1 0

1 5

O

1 06

4

5

2

0 0 0 .5

Ei j 2.5 lit, vs

01 .0

for Plioc = 1.or T L Myr VS V

(See text fo


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2-22

in which L and n (which varies on [0,1]) are independent

random variables. Therefore (see, e.g. Kapahi 1975a, p.94):

f L ( L )f (k ) = Qf dL for 0

L L 2 -k 2

Using f L (L) from equation 2.14, we have

1 - ' 1 + z 21 o 1-(gh 2o

) + (1/z 2 )cos -1 (k/k 0 ) +f k" 2v zzu

+1/2(1-1/Q2

)(7/2+sin-1 21/Z 2 - 2 / k - 1 ) / (1 + 1 / k 2 ))] , for o


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3.

of

3-

1

2-23Mfc S

(

2CC 4-CC 6C0 co

.6 Model drstrTbuitrons of projectedand actual Unear sizes for 1,-= 0.i, 0.3,0. 5 & 0.7 and (a) l o m e c= 0,8


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F C3 2. 6 ... (b) k, m e, . . - -: 0.9


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12-25.,X103

IvIpc

Lkt, kt,0

UfAikr)

ZOO 400 600 SC O 1000

g krc,

F r3 . 2.6 (c) _L ir = 1 .0


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10-3 2-26

fupc.(1-kpc)

fitk r c krc)

1.

0.1

0.3

0.5

0.7

3.

2.00 400 600 800 1000 12.00

L krc, kpc

00

F i9 . 2 . 6 , . . ((I) 1 .2


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4. r-Xf0-3

2.-27

2,

6

rJ

0

tiriSC2-7CC205G740

200 4-00 600 X00 1000 1200

E 1 9 . .7 Observed cHstr-Nou,ei'ons of pro je ct-ect UnearSizes for four samples (a) 126 + - 4 FRU 3CR sources


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C )

ki)

a

3. -

570 0

2-28

t , t7, 2500

200 400 60C 800 4000).-

Fr9 . 2.7 WEIRers &NAIley's(1977)

85-t-- 2 3CR sources

00


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2-29

-3x40

3.

0 2001 I

400 600 0 0 G OO

kfC

057001

EI8 2.7 (c) Lor-)3a.ir ey 's (4979)65 -4-1 3C-4Z sources


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2-30

-3XI 0

2 .

I I I I

ZOG 400 600 SOO 106C 1200

EL 9 . 2.7 (d) 72 wetl-sepocrated douioles (3CR)

used r) section 2.2


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2-31

Table 2.2 Rough fits for the observed linear size distri-butions of Figures 2.7a-d. Curves for variousmodel p arameters are shown in Figures 2.6a-d.

Sample oMpc v Remarks

a 1 .2 >0.7

1 .0 0 .7 O K

0 .9 0 .7

0 .8 0 .6

b 1 . 2 0 .8

1 .0 0 .8 least-squares

0 .9 0 .7

0 .8 0 .7

1 .2 >0.71 .0 0 .7

0 .9 0 .7

0 .8 0 .6

d 1 .2 0 .7

1 .0 0 .5

0 .9 0.5 Better than both above0 .8 0.3


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2.-32(2-22

zoMpc = 0.8, 0.9, 1.0 and 1.2, with four curves for v=0.1,

0.3 , 0.5 and 0.7 for each 9, , oMoc -value. The curves are norma-lized to make the area under each unity. Note that as v

f (L) -+ 1, as i t should.

To examine the applicability of the model, we have

plotted the observed distributions ofMDC for four samples:

(a) the 126+4 FRII 3CR identified radio sources, (b) the 85+2

sources from Fig.la of Ekers & Miley (1977), (c) the 65+1

sources from Longair & Riley (1979) and (d) the 72 doubles

used in section 2.2 (Figs. 2.7a-d). Normalization is done to

make areas under the histograms unity. The few very large

sources in samples (a)-(c) have been ignored for this purpose,

though they are shown in the plots. Since only those doubles

which have at least 4 beamwidths across them were selected in

formulating the sample of well-separated 72 3CR doubles, the

Paucity of sources near QMipc = o for that sam p le (Fig. 2.7d)

is artificial. Table 2.2 shows the rough fits suggested by

comp aring Figs. 2.6 and 2.7. Since the values of v are too

high com p ared to those derived in sections 2.2.1 and 3.3 from

more detailed study, clearly the model is too simplified.

Models similar to those used in sections 2.2.1 and 3.3 need

to be worked out for the distribution of projected linear sizes

also.


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CHAPTER THREE

THE ASYMMETRY IN EXTENDED EXTRAGALACTIC DOUBLE

RADIO SOURCES II

3.0 The arm ratios of double radio sources give informa-

tion on the kinematic evolution of these sources. In

sections 2.2 and 2.2.1, we saw how this information can be

extracted under the assumption of intrinsic symmetry. The

ratio of the strengths of 'corresponding' features on the

two sides is affected, in addition, by the evolution of the

luminosity of these features. To get this information in an

intrinsically symmetric model, it is necessary to keep track

of which is the receding hotshot and which is the a?p roaching

one. This is done by assuming that the shorter arm of the

double corresponds to the receding hotshot and the longer one

to the approaching one ( O R 50 A in section 2.1). (0_ K50A

holds rigorously for a collinear (O R = O A )

ouble. But for

q )R OOA , there can be pathological cases where O R> 0 A - see

Saikia 1984). But before going into the model calculation

within the relativistic expansion model for the distributions

of the arm ratios r and the flux ratios s thus defined (see

section 2.1), we examine the distribution of the flux ratios

f, defined to be for sources covering a range of flux

densities of about 10 to 1. This is done by using double

sources from the bright 3CR survey and the faint Ooty lunar

3-1


34/57

3-2

occultation survey. \ 0

\"-Af:LNVThe Ooty survey covers the flux density range of about

0.3 to 6 Jy at 326.5 MHz. Lunar occultation observations have

been made so far for over 1200 sources, out of which 712 have

been catalogued in lists 1 to 9 (Ka p ahi, Joshi & Sarma 1974,

and references therein; Subrahmanya & Go p al-Krishna 1979,

Singal, Gopal-Krishna & Venugooal 1979, Venkatakrishna &

Swarup 1979, Joshi & Singal 1980). Of these, 158 sources have

been classified as definitely having a double structure. There

may be doubles among the remaining sources also, not recognized

as such from the lunar occultation p rofiles due to coarse

resolution (relative to the angular size), poor signal-to-

noise ratio or both.

An advantage in using f, rather than s, is that it can

be determined for a well-separated double, whether identified

(or having a central radio component) or not. The reliability

of the measured p arameters(viz., r, s,f) of a double source

can be indicated by the number of beamwidths N within the

angular se p aration of the two outermost peaks (as was done for

the p arameter x in section 2.2.1). From the 158 definite

doubles in Ooty lists 1 to 9, we have selected an unbiasedK

sample of 103 sources having N 4 and S 326.5 0.5 Jy. For 55

of these, N 8. Of the 103 double sources, 30 are identified.

Three of these have been excluded from the r, s - distribution

presented below and interpreted in section 3.3 since the

( . . . 3 - 7 )


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Table 3.1 Data for the Ooty double radio sources

(a) The optically identified sources

Source List* LAS/asec N f Op. Id .# r

0038+086 3 96.1 12.0 1 .000 EG 0 .352 1 .0000123+140 6 12.5 8.3 2.714 BG 0.942 2.7140213+178 7 14.4 4.6 1 .500 BG 0 .511 0.6670228+173 8 29.3 9. 1 3 .000 N SO 0 . 747 3.000

0635+191 9 30.0 7. 5 2 .000 BS O 0 .530 2.0000645+189 9 11.3 5.6 1 .400 RG? 0.168 0.7140648+263 3 16.5 7. 8 1.111 RG 0.364 1 .1110713+195 8 31.0 14.1 1.750 G 0.939 0.5710814+227 3 21.7 16.7 1 .429 BSO 0.831 0.7000832+143 8 30.6 9. 9 2 .300 RO 0.419 2 .3000848+181 3 16.0 12.3 1 .000 BS O 0 . 503 1 .0 000856+170 3 9. 3 7. 7 1 . 4 0 0 QS O 0 .855 0 .7140911+174 3 46.3 35.6 3 .000 BS O 0 .0 64 3 .0 000943+123 6 12.1 10.1 2 .500 BSO 0 .2 59 2 .5000946+076 9 69.3 22.4 1 .833 RG,C? 0 .519 1.833

1052+023 7 27.5 11 .9 1.375 N S O P 0.696 1.3751107+036 6 64.6 21.5 2.597 BG 0.944 0 .3 851150-044 7 23.8 10.8 2 .000 BG,C? 0 .286 2 .0001201-041 9 21.2 10.1 1 .000 RG,C 0.670 1 .0001220-059 9 151.5 25.3 1.799 G 0 .3 26 0 .5561356-176 4 10.4 5.0 1 .818 B S O ? 0 .752 1 .8181451-192 8 36.4 10.7 2.789 RS O 0.415 2.7891527-242 1 21.1 4.9 1 .300 RG 0.769 1 .3002020-211 5 85.8 10.7 1 .429 DG,C 0 .038 1 .4292 0 4-r-149 7 28.0 14.0 1 .000 RO 0.037 1 .0002059-135 7 299.7 15.0 1 .000 EG 0.934 1 .000

2059-127 8 9. 5 4.1 1.200 RG 0.192 0 .8332111-185 1 16.0 8.0 1 .0 00 BO 0 .428 1 .0002200-130 4 26.7 5.3 1.667 RG,C 0.756 0.6002225-055 7 49.4 6. 2 1.750 RG ? 0.614 1.750

The list number in the O oty lunar occultation survey (see text)

# E = el l ipt ical , G = galaxy, SO = stel lar object , 0 = object , B = blue,N = neutral, R = red, QSO = quasar, P = probable, D = double. A 'C'after the id. code denotes membership of a cluster.

B-3


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3-4

( b ) The unidentified sources

Source1

List*7

LAS/asec3

N4

0007+051 9 29.2 7 . 1 1.1670015+064 8 55.5 13.5 1.6160132+132 8 12.5 5.5 2.1980150+164 1 7.6 7.6 1.5000156+126 9 42.2 14.6 1.0000200+130 9 45.0 5. 8 1.2500220+172 8 24.1 8. 0 1.1250237+154 9 5. 2 4.7 2.0000246+219 5 8. 9 4.3 1.2000328+248 3 6.6 5.5 1.0000334+220 7 52.4 6.5 1.8590339+208 8 24.2 4.0 1.2720341+251 3 17.1 14.2 1.4000343+184 9 121.7 40.6 1.2850416+270 4 77.1 9.6 2.3980432+218 8 156.0 15.6 1.1670433+262 6 17.3 5.8 1.307

0435+217 8 83.8 27.0 2.2520516+224 8 275.9 64.2 1.0000532+281 5 17.0 4.3 1.4000536+284 6 78.2 7.8 1.0000557+221 8 25.3 12.1 4.1320604+266 4 59.9 27.2 1.5000609+276 5 11.7 5. 6 1.4290619+266 3 6.5 5.0 1.5000706+199 8 63.7 19.3 1.0910710+257 3 17.5 13.5 2.1970805+225 3 14.8 6.7 1.00o

0806+152 9 26.3 8.8 1.5000818+217 5 22.4 5. 6 1.1110822+151 8 22.7 18.9 1.3180852+124 9 12.7 6.0 1.2500909+165 5 13.0 10.0 1.6000958+113 3 6.0 7.5 1.0001007+062 9 29.7 14.1 2.6251023+078 3 10.1 4.6 1.0001039+029 7 5.7 4.8 2.3311142-002 4 28.5 23.8 3.3331150-036 9 34.2 5.5 1.7151216-069 6 53.6 26.8 1.3331257-113 6 49.8 12.4 2.2521422-150 9 150.5 18.1 2.0001505-200 8 12.1 6.7 1.715

contd...


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Table 3.1(b) contd...

1 2 3 4 5

1555-218 8 137.6 13.8 1.2501615-201 9 53.2 5.3 1.6261618-235 7 38.4 4.9 1.5381627-272 1 22.6 10.3 3.0001634-215 9 25.7 6.4 1.333

1657-203 9 43.0 6.9 1.6671700-204 9 5.1 4.7 1.2571701-232 8 60.7 28.9 1.7011709-281 5 14.8 12.3 1.3001726-225 8 8.4 7.0 3.9061749-224 8 14.3 6.5 1.8621800-278 5 43.1 19.6 1.8001826-271 6 33.2 16.6 1.0001833-192 9 27.8 6.8 1.1251912-269 4 46.8 9.4 2.5001932-189 8 5. 9 5.4 1.0001933-173 9 195.5 19.6 1.3331953-178 8 23.2 5.8 2.1652033-146 8 16.5 7.9 2.7252057-179 5 10.1 7.7 2.5972109-188 1 92.3 11.5 1.0002110-160 6 10.0 4.3 1.2502120-166 5 10.1 7.8 2.7002154-117 5 21.2 9.6 1.6002227-037 8 23.7 11.9 2.5972232-068 6 55.9 7.0 1.3332246-022 8 8.6 8.6 1.5462254-039 6 21.2 10.6 2.2522300-013 7 32.5 5.1 1.0002302-025 6 34.9 29.1 1.500

* The list number in the Ooty lunar occultationsurvey (see text).

3-5


38/57

1

8sa

10Em

z

- 25

1

1

1

I_1 1 _ . . . . . ....,...I.I!1--n," 01.8 2.6 3.4 4.2

f-_,....

R

Ocsty

5

3-6

4 0

CC

U

r o 0 . . . . . .8

saE 20m

z

10

F 3.1 The observed cltstrIbutton of flux ratios ffor the Ooty(326.5Kitidoubles and the 10 Braes brighter

SCR (5 GHz) doubles,


39/57

3-7

( 3 - 2 . . . )

identified optical object coincides with one of the two com-

ponents. Of the remaining 27 sources, 16 have N>8. Data

for the Ooty doubles are presented in Table 3.1.

The histogram of f for the 103 Ooty occultation sources

is shown by broken lines in Fig. 3.1. That for the 55 Ooty

sources with N>8, shown in the proportion 103/55 with short

bars, has nearly the same shape. Full lines show the histo-

gram for 97 doubles from the com p lete sam p le of 166 3CR

sources (Fig. 2a of Riley & Jenkins 1977). The median values

of f are 1.28 and 1.33 for the Ooty and 3CR samples. These

are close to the value 1.33 for Mackay's (1973) sam p le of 36

3CR sources, and also agree roughly with the median value of

about 1.5 determined earlier by Fomalont (1969) for about 100

sources from a large sample observed at 1425 MHz with a two-

element interferometer and by Mackay (1971) for 65 double

radio sources observed with the One Mile Cambridge synthesis

telescope with =- 1/3 arcmin resolution at 1407 MHz. The

flux density of Ooty doubles ranges between 5 326.5= 0.5 to

6 Jy, with a median value of 1.4 Jy. For a spectral index

(see section 1.2) 0.8, 3CR sources would have 5326.5 6 J y .

Thus, it is seen from Fig. 3.1 that the distribution of f is

independent of flux density over a range 10 to 1, and also

inde pendent of the observation frequency over a range 15 to 1.

Grueff & Vigotti (1975) p resent a distribution of f for a

sample of 66 B2 doubles stronger than 0.9 Jy at 408 MHz. This


40/57

3-8

also agrees very well with our distribution (Fig. 3.1).

3.1 THE FLUX RATIOS AND ARM RATIOS Within the intrinsically

symmetric model of section 2.1, the arm ratio r is defined

in the sense receding-to-a p p roaching (and so also the flux

ratio s). For collinear sources, osrl by definition. Obser-

vationally, then, the identifications receding a closer to

the optical object/central radio com p onent and ap proachingF.=.

farther from it can be made for collinear sources (see, how-

ever, Saikia 1984, who questions the assum p tion of collinearity

for quasars). The deviation from collinearity is not signi-

ficant for the 3CR sources since a majority of them are gala-

xies (Smith, Soinrad & Smith 1976 and later updates) and we

assume collinearity below (section 3.3 in applying the model

of section 2.1.

We would ideally like to calculate the flux ratio s

for only the hotsnots, but it is not easy to do that for all

the sources from the 6 cm ma p s (mainly from Jenkir,d, Pooley& Riley 1977 and references therein) that we have used for

the 3CR sources as well as for the lunar occultation profiles

for the Ooty sources. However, we have not considered any

contributions by an inward tail or bridge of low brightness

(say


41/57

rs

8

0 Ab 1 - ; AI,,4 ; /4 6

0\ A N Aa

t. N\ I \ .0

\ kl eI

0

0

0

0

\A

0

.8 6 4 .2 0 4 6

* 1 ,3CRstellar obj

A

3 CR 00TY

o GAL

A A QSO

LOg S --).-a21. The joint distribution of arm ratios r and {lux ratios s (on a 09 -[09 scale) for thefaint Ooty (326.5 MHz) doubles and the 10 Limes brighter 3CR (5GHz) doubles


42/57

3- 10

source is rather complex. For most sources, the flux density

of the outer components (including hotspots and radio lobes)

can be estimated to an accuracy of better than 20 Percent.

Macklin (1981) has carefully selected a sam p le of 76 doubles

from the com p lete sample of 3CR radio sources defined by

Jenkins, Pooley & Riley (1977) and analysed the arm ratiosh o t s p o t s , the flux ratios of

and flux ratios ofLthe whole com p onents and other symmetry

parameters. (See end of section 3.3 for a brief summar y of

Macklin's results.)

The arm ratios r were calculated using p ositions of

the peaks of the com p onents, and refer to the hotsoot posi-

tions since the resolution is generally fine enough to locate

the high-brightness hotspots accurately enough, but coarse

enough not to resolve them out.

Fig. 3.2 presents the joint distribution of log r and

log s for the 27 Ooty and 66 3CR identified double radio

sources. Of the Ooty sources, 17 are galaxies or red objects,

nine are auasars or blue/neural stellar objects and one is a

red stellar object. The 3CR sam p le consists of the 66

doubles listed by Longair & Rile y (1979) who restricted the

sample to those optically identified 3CR doubles for which

reliable r-values could be calculated from the 6 cm maps

(Jenkins, Pooley & Riley 1977 and references therein). Of

these there are 48 galaxies, two p ossible galaxies, 14 QSOs


43/57

3-11

Table 3 .2 D ata for the 3CR double radio sources

5rc,3C Op.Id. r s Src,3C Op.Id.

6 1 G 0.960 0.778 9 Q 0.615 0.2971 4 G* 0.501 1.947 1 9 G 0.979 0.7073 3 G 0.805 0.854 33.1 G 0.589 1.7144 1 G* 0.716 0.573 42 G 0.998 1.5174 6 G 0.767 1.200 47 Q 0.893 0.4755 5 G 0.681 1.789 79 G 0.811 1.4129 8 G 0.825 0.390 109 G 0.849 0.878

1 3 2 G 0.928 1.000 133 G 0.953 0.6381 5 3 G 0.573 1.068 171 G 0.765 1.229173.1 G 0.782 0.714 175 Q 0.694 1.2191 8 1 Q 0.956 0.538 184 G 0.855 1.067184.1 G 0.749 0.889 192 G 0.824 0.6671 9 6 Q 0.804 0.640 20 0 G 0.471 0.8892 0 4 Q 0.838 1.154 20 5 Q 0.838 0.3802 0 8 Q 0.882 0.263 212 Q 0.883 0.4322 1 7 G 0.284 1.294 219 G 0.936 0.989220.1 G 0.957 1.750 225B G 0.688 1.5152 2 6

G 0.800 0.875 228 G 0.879 0.7942 3 4 G 0.748 2.174 236 G 0.549 1.347244.1 G 0.884 0.690 249.1 Q 0.523 0.6402 5 0 G 0.306 0.636 25 2 G 0.510 0.7002 5 4 Q 0.133 1.075 263 Q 0.537 5.000263.1 G 0.977 0.587 265 G 0.812 1.4622 6 6 G 0.558 1.176 268.4 * * 0.656 0.193274.1 G 0.916 0.688 284 G 0.698 3.2502 9 5 G 0.917 0.806 300 G 0.421 5.1253 2 1 G 0.935 2.700 325 4* 0.561 1.9023 3 6 Q 0.625 0.490 340 G 0.325 2.267

3 4 1 G 0.753 1.105 349 G 0.936 0.9003 5 2 G 0.865 1.833 3 8 1 G 0.865 0.907390.3 G 0.728 1.353 401 G 0.604 0.978427.1 G 0.723 0.705 432 Q 0.638 1.2504 3 8 G 0.879 1.080 452 G 0.973 0.767


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3-12

(or quasars), one possible QSO and one stellar object. The

data for these sources are listed in Table 3.2. Mostly

the values of flux densities for the outermost components

are the same as listed by the Cambridge workers (Jenkins,

Pooley & Riley 1977 and references therein). In some cases,

where the listed values included contributions by extended

features, suitable corrections were made.

3.2 THE POSITIONAL OFFSET BETWEEN THE OPTICAL IDENTIFICATION

AND THE RADIO CENTROID If the optical identifications were

to coincide with the centroids of the double radio sources,

their r and s values would like on the line rs = 1. Fig. 3.2

shows that there is a considerable scatter among r and s

values, which is more than can be attributed to measurement

errors of about 0.1 in log r and log s. Sources with

log sl < 0.2 seem equally distributed around s = 1. Sources

with log sl > 0.2 seem to occur more often in the right half

of the diagram, im p lying that for these sources the stronger

comp onent is closer to the o p tical object. For sources with

large positive values of log s, the optical object lies between

the geometric centre (r=1) and the centroid (rs=1), as also

noted by Fomalont (1969) and Valtonen ( 1979). Structures of

the outer components of these sources do not differ appreciably

from those of the others.

Part of the scatter seen in Fig. 3.2 may be due to the

difficulty in determining the r and (especially) s values for


45/57

3-13

sources with a p preciable emission between the two outer com-

ponents. A majority of the 3CR sources in our sam p le, how-

ever, have most of their flux density in the outer components.

In fact, there is no clear physical reason why the radio

centroids should coincide with the positions of the ootical

objects. We show below that the observed scatter in Fig.3.2

is broadly in agreement with the known differences between

the radio centroids and o p tical positions as found from several

investigations based on accurate ontical identification of a

large number of radio sources.

For an identified double source with little emission

outside the two outermost components (excluding any central

flat-spectrum component), let us denote by 60 the intrinsic

difference between the radio centroid and the o p tical nosi-

tion. Then, by definition, s.60 = SROR sAeA; S = SR+SA,

where e iR 0A and se is measured positive toward the hotspot

closer to the o p tical object. Dividing by Se = S(O R+ OA ) and

expressing the right hand side in terms of r = 0 R /O A and

s = S R/S A'

= (rs-1)/[(1+r)(1+s)]. (3.1)

Extragalactic radio sources, in general, have their radio

centroids displaced from the optical identifications, consi-

stent with 160/0 1


46/57

3-14

10-

1 .5 2.0 1 .5200kpc

3.0 3.5log(t/kpc)

Ft c .S.3 Observed linear size cirstrthut-fon of CR.

doubles divided in-to two classe_s ,'' those, with38/6


47/57

3 - 1 5

values of 60 of


48/57

3-16

Fi .3.4 Restrictions on to and y from velocity cut-off

(schematic)


49/57


50/57

24

20

16a)

E 12

0 11I I

0 . 2 .4 .6 .8

L__

3CROoty

r

1

1

a)1

1

Vo=0.16c 0-1

V = 0.4C

3-18

r

F T9. 3.5 Observed distributions of arm ratios r or theFaint Ooty and bright 3CR doubles and, model fits to3CR data for v . 0.4c and vo=0.16c


51/57

>4-0

O

3-19

50

ti0-

0 16c 8 = 1

v=0.6c, = 3

20

I6 o

a)12-0

8

4

0

4

2

-.8 - 4 0 4

Log s

F9.3.6 Observed distributions of flux ratios s on a.

to9-seate for the faint Ooty and the bright 3CR. amblesand model fits to the 3CR data for v o = 0.6c, 6=3 and

vo= 0.18c , 8=1


52/57

log r

0 to .1

V=0.3c,P=3

----- V = 0.08c,/3=I,

//

/

rlr

r

/

/

/

,

1

1

,1

r

bins

I = Z Z Z I GAL

c=== Q S 0

.I to--2.. IIIIIP7----

.2 to--.3

--:3to .4

,IIIINIVIIII

__....---------7r-----

-4to.5IT-77-7-7.71

.5 to.6

.6to.7

1.7to---.8

1 . . 8 to .9

r---.-9 toIII IIII i I ' fi t!

40

32

24

1 6

84

04040

40404O40

4040

.5 0 .5 log s

Fie. 3.7 Joint distribution of Log r and Log s and model fits


53/57

3-21

(3-17...)

Fig. 3.6 shows the observed distribution of log s for

the Ooty and 3CR samples. The number of sources on the two

sides of s = 1 is about equal for both the samples. There

are, however, more sources, particularly radio galaxies, with

a high positive (>0.2) rather than hi g h negative value

( 1 only if 6>3.75. However, for models in which

velocity decreases with time, s can be greater than 1 even

for 61) starts dominating over the second factor (which is < 1) as

the source ages. With increasing age, r increases from

r o = (1-v o y/c)/(1+v o y/c) to nearly 1, and s fromr3.75-6 (being


54/57


55/57

3-23

brighter. In the relativistic expansion model (section 2.1

and also equations 3.3 and 3.5 above), this is possible only

if the component luminosity decreases fast enough. Teerikorpi

(1984) has recently noted that this type of asymmetry prevails

in double-lobed quasars with low luminosity, but in double-

1 1 1 lobed quasars with monochromatic radio luminosit y at 500 MHz

in the source frame > 10 27 W Hz -1 , the brighter com p onent is

farther from the parent object.

3.4 INHOMOGENEITIES IN THE IGM AS CAUSE OF THE ASYMMETRY

Multifrequency observations of radio galaxies have given esti-

mates of the lifetime of radio com p onents, assuming transverse

expansion at Alfven velocity (Willis & Strom 1978, Burch 1979).

These results indicate ap p reciably smaller values of the hotspot

separation velocity than derived in the last section (see also

section 2.2.1). Also, the lack of any marked correlation bet-

ween linear sizes and luminosities of radio sources does not

support a high value of 6(Baldwin 1982).

As shown below, the observed correlation between r and

s can alternatively be explained by considering different inter-

galactic densities p 1 and p 2 facing the two hotspots, whence

high values of hots p ot speeds and 6 are not required. If the

average s' of hotspot speed (in units of c) is small (


56/57

3-24

thermal gas are ejected in two opposite directions, it can be

shown from equations 5.82 - 5.85 and 5.95 of Pacholczyk (1977)

that r = (U 02 /U 01)2/3 (P2/P1)1/3 and s = (U 01 /U 02 )(p 2 /p 1

) - 3 / 4

where U0

is the initial energy of the plasmon. Thus, r1 for p i >p 2 . similar conclusion is supported by the

results of numerical hydrodynamic calculations by De Young

(1977) and Nepveu (1979).

For a simple beam model in which a beam of luminosity L

maintains a constant solid angle Q , ram p ressure balance

gives pV2 L/Q D2 c, where D is the distance of the hotspot

from the origin of the beam (core) and the velocit y v = dD/dt.

As shown by Scheuer (1974), Dz- (L/Qpc) 4 (2t) 2 . e assume that

the com p onent size h is proportional to S2 ZD (free expansion -

see section 5.4.4). For synchrotron emission, the radio lumi-

nosity P ccU7/4 V-3/4,

where U is the energy of the relativistic

00 particles and V = h3

is the volume of the component. For ram

pressure balance, U/V ' . p v 2 . Hence it can be shown that

r= D 1 /D 2 (1,102/L2Q1)1 / 4 and s = P 1 /P 2 (L1/L2)13/8 ( P 1 /0 2 )

1 /8,

on the assumptions Q i = Q 2 and t 1 = t 2 . Thus, if p 1 >0 2'

there is a weak tendency for rl, i.e., the closer

comp onent is brighter. The de p endence of r and s on p is

enhanced if the beam or the associated radio lobe is assumed

to diverge with D.

In contrast, if there are intrinsic variations, with


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3-25

the luminosity L of the relativistic beam or the energy U0

of the plasmon different in the two directions, say, we should

expect the brighter component to be farther away, i.e., s

Documents

Evolution Extragalactic Radio Sources [2nd piece]