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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
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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
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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,
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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
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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
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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
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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
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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
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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
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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
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3 - 1 5
values of 60 of
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3-16
Fi .3.4 Restrictions on to and y from velocity cut-off
(schematic)
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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
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>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
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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
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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
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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 (
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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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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