Study for the physical properties of AGN jetsby radio imaging analyses of jet structurefrom the Schwarzschild-radius to galactic scales
Satomi Nakahara ISAS/JAXA
Nakahara et al. (2020), AJ, 159, 14
Nakahara et al. (2019), ApJ, 878, 61
Nakahara et al. (2018), ApJ, 854, 148
A. Doi, Y. Murata (ISAS/JAXA)
K. Hada (NAOJ)
M. Nakamura, K. Asada (ASIAA)
S. Sawada-satoh (Yamaguchi-U.)
S. Kameno (Joint ALMA observatory)

Introduction

N images showing rich jet structure on scales of 100 mas or more (left-hand panel and middle panel)√

ulent Cygnus region. The contours are plotted at increasing powers of 2. The restoring beam isconstructed total intensity ridgeline is shown by red. The 1.4 GHz VLBA contour images of 122
e in the online journal.

disch image parameters. Columns are as follows: (1) B1950 name; (2) other name; (3)am (milliarcseconds); (5) I peak of image (Jy per beam); (6) rms noise level of imageel (mJy per beam). This table is available in its entirety in the online journal. A portionm and content.

Epochyy/mm/dd)
(3)

Beam
(mas)
(4)

10/11/05
10/11/05
10/06/18
10/07/29
10/08/23
10/09/23
10/05/21
11/08/18
10/03/07

14.4
8.7
13.5
9.5
13.4
11.6
12.1
9.5
10.2

Ipeak
(Jy beam−1 )
(5)
1.983
BH
0.314
0.218
0.682
1.445
0.209
1.102
1.127
0.542

rms
(mJy beam−1 )
(6)

Ibase
(mJy beam−1 )
(7)

0.48
0.11
0.13
0.18
0.36
0.09
0.22
0.29
0.16

1.90
0.44
0.50
0.73
1.44
0.35
0.88
1.16
0.63

Downloaded from https://academic.oup.com/mnras/article-abstract/468/4/4992/3573854 by guest on 17 September 2018

The measurement of AGN jet structure profile
W(r) ∝ r a

jet width

Distance from the black hole

Distance from the BH r

parabolic a~0.5-1

conical a~14996 2018
A. B. Pushkarev et al.
ref:pushkarev2017, Kovalev



VLBAf15/1.4 GHz



(mas)

VLBAf15 GHn

Figure 4. Transverse jet width versus a distance along ridge line for BL

we show the combined data sets and corresponding fits. Typically,
the truncated 1.4 GHz data at larger scales follow the trend of the
15 GHz measurements quite well, without any essential break inthe slope. The BL Lac object 0716+714 (Fig. 7, left-hand panel)

We tested the robustness of the obtained results by progressively
cutting the ridgeline length r down to 1 mas from the core and repeating the analysis with the sub-data sets. The corresponding median
k-index values remain constant until the ridgeline is up to 10 mas
long, while for shorter ridgelines the median gradually increases,
peaking up to 1.0 at r = 1.2 mas. We explain this by a non-uniform
degree of completeness of jet cross-section that can decrease beyond a certain distance from the VLBI core. This is because thesource brightness distribution is stacked over a limited time intervalthat might be not long enough for jet features emergent at different
position angles to propagate all the way down to distances where
jet emission is detected in the stacked image. At the same time,the difference between the accelerated and non-accelerated sources
also holds for all the data subsets. An observational bias that canalso affect the k-index measurements to some degree is that there
is a maximum angular scale to which the VLBA is sensitive. It
is about 0.5λ/Bmin , where λ is the wavelength of observation and
Bmin ≈ 236 km is the minimum baseline length (between the antennas Los Alamos and Pie Town, New Mexico). This corresponds tothe scale of about 9 mas at 2 cm, while about 75 per cent of sourcesin our sample manifest jet structure on smaller scales, making thisbias weak.

The jet structures were measured
by radio observation in narrow
range of r in most cases.

3.2.1 Larger scales at 1.4 GHz

Downloaded from https://academic.oup.com/mnr

W(r) (mas)dge line for the BL Lac object 0716+714 (left-hand panel) and radio galaxy M87 (right-handLacpanel)
at scales probed by the MOJAVE observations at 15 GHz. The thickblue line
cales probed by the observations at 15 (filled black dots) and 1.4 GHz (open red circles). The
solidis the best fit of an assumed power-law dependence d ∝ rk . Thekplots for other sources are available in the online journal.
nce d ∝ r . The plots for other sources are available in the online journal.

asurements apGHz data sets toby the 15 GHz
ect is negligible

W(r) jet widthIntroduction

Theoretical model
The external pressure of the surrounding medium"#$% ∝ & '(( r : Distance from the BH)

Jet width ) & ∝ &

*
+

(
/

(- = )
Komissarov+ 2009; Nakamura+ 2008

power-law index power-law index Structureof the externalof the jet apressure N
4

1

2~4

0.5

<2

< 0.5

conicalExample for the external pressure profile

à conical
1

parabolicà parabolicà over-collimation
cylindrical (over-collimation)

Komissarov et al. 2009

Introduction

VLBA data at 15 and 5 GHz (green and blue triangles), and our EVN(-i, ii, iii) data at 1.6 GHz with three weighting schemes(violet square, cross, and circle). The single (orange solid line) and double (brown solid line) power-law models are fitted to the
profile, where we show the case of the sharpness parameter n = 100 here. Statistics (f -test) shows that the data are better fitted
by double power-law models (with all n) than by a single power law (see also Section 3). Furthermore, the double power-law
model is also supported by the VLA data (gray plus signs) and VLBI cores (gray triangles and squares), as discussed in Section
4.1. Note that the VLA data and VLBI cores are not included in the regression analysis.
Middle and bottom panels: the relative residuals of the jet radii for the single ( rSP = r/rSP 1) and double ( rDP = r/rDP
1; n = 100) power-law models. The single power law shows a systematic deviation at the two ends of the distance scale, while
the double power laws (i.e., for all n) show uniformly distributed relative residuals on all distance scales.
We conclude that the jet structure is described by a parabolic shape upstream (z / ra , a ' 2) and a conical shape downstream(a ' 1) with a transition located at a characteristic distance z0 = (1 2) ⇥ 105 rs (brown dashed line), which is fairly close to
the sphere of gravitational influence (SGI) of the SMBH (rSGI ' 5 ⇥ 105 rs , black dashed line) in order of magnitude.

The profile of jet width covering the range fromthe Schwarzschild radius scale to the galactic scale
Distance from the BH

100

101

102

103

104

105

M 87 core 6251 Tseng+ 2016
NGC
NGC 6251
NGC 6251 core
M87 Asada & Nakamura 2012

RSa

r

106

107

108

109

106

105

104

103

102

5

BH scales < 10 Rs

Galactic scale

Jet width W(r) (Rs)

Jet Radius r [rs]The
Thestructural
structuraltransitiontransition→→Transition
Transitionofofthe
thepressurepressuregradient?
gradient

107

SGI (NGC 6251)

Bondi radius (M 87)

M 87

101

100

De−projected Distance from Core z [rs]∝rFigure 3. Combined radius
profiles of the jets in NGC 6251 and M87, with
their jet radii and deprojected distances normalized
1.0
0.5

W(r) ∝ rP

ext of the measurements can be found in Figure 2, AN12 and NA13
by their Schwarzschild radii (rs ). The detailed descriptionaLikewise, M87 shows a parabolic shape (z / r , a ' 1.7) in the upstream region, a conical shape (a ' 1) in the downstream
region, and a structural transition at a few 105 rs , corresponding
to the Bondi radius of M87 rB ' 3.8 ⇥ 105 rs (dotted-dashedP
5 jetline), while the SGI of NGC 6251 is rSGI ' 5 ⇥ 10 rs (dashed line). The similarities of the two jet structures suggest thatthe collimation process of AGN jets is fundamentally characterized by their external galactic medium, which is gravitationallycontrolled by the SMBH and its host galaxy.

Parabolic

Conical

0

200

400
milliarcsecond

600

800

otted at −1, 1, 1.4142, . . ., 1024 × 2.12 mJy beam−1 , which is three times the residual rms noise in the first epoch image. The synthesizedmas with the major axis at a position angle of 73.◦ 4 for the first epoch. Model components and trajectories are represented by green circles

ure is available in the online journal.)

Introduction

Correspondence between the jet collimation
and acceleration regions in M87

GHz (area)
A 43 GHz
A 43 GHzGHzAsada & Nakamura 2014

distance from the core [mas]Deceleration

Kovalev et al. 2007: VLBA at 15 GHz
Reid et al. 1989: Gloabal VLBI at 1.6 GHz
Cheung et al. 2007: VLBA at 1.6 GHz
Biretta et al. 1999: HST
Biretta et al. 1995: VLA at 15 GHz
Meyer et al. 2013: HST
Ly et al. 2007; VLBA 43 GHz (area)
Walker et al. 2008: VLBA 43 GHz
Acciari et al. 2009: VLBA 43 GHz

Acceleration

This work: EVN at 1.6 GHzC∝ onicr 1 al

at 15 GHz

Jet speed[c]velocity [c]Lorentz factor

BA at 15 GHz
al VLBI at 1.6 GHz
BA at 1.6 GHz

Bondi radius

Jet widthW(r) [RS]Jet radius (Rs).06the apparent velocity as a 10
functionof the projecteddeprojected distance from the core [rs ]Measurements by VLBA at 15 GHz (black circles),Figure3.
Distributionof the velocity and Lorentz factor as a function of the& 1.7
Nakamura
2012; Hada+2013
purple circle), our measurements (redAsada
circles),VLBA
MERLINGHz(AN12)
deprojected distance from the core. Measurements are illustrated in the same), HST (blue circles), VLA at 15 GHz(lightblue
EVN 1.7 GHz manner(AN12)
5
as in Figure 2. The dashed line represents the expected line, Γ ∼ z(b−1)/b ,10 the subluminal speed
ent ±1σ . EVN points connect
VLBA 2.3 GHz due(H13)
to the MHD acceleration in parabolic streamline (e.g., Komissarov et al.
most jet with VLBA at 15 GHz and the superluminal
5.0 GHz 2009)(H13)with its power-law index b = 1.7 (Asada & Nakamura 2012). Deviation
ST-1 using HST and VLBA. We also VLBA
plotted VLBA
the predicted line is large at the distance <104 rs , since the expected line
(H13)
y Walker et al. (2008) and Acciari
et VLBA
al. (2009)8.4
as a GHz from
4
10
is
only
applicableH13) for relativistic regimes.
he velocity measurements by Ly et al.VLBA(2007) as15
the GHz (AN12,
color version of this figure is available in the online journal.)
VLBA
24 GHz (A(H13)
voking the proper motion is different fromthe othersin their papers, we cannot include theerror bar43
on GHz (AN12, H13)
VLBA
these fast proper motions as10a 3differentVLBA
phenomenon
86 GHz (H13)

ure is available in the online journal.)

EHT

Pa

c
oli 0.56
b
r
ra

r

)∝

230 GHz (D12, A15)

W(

102

me that it does not change at all along the2orentz factor Γ = 1/(1−β) and velocity
10cosθ).
ph the velocity and the Lorentz factor in thef our EVN measurements are connected to1egions sampled in previous measurements.
t the increase of the velocity from nonBH
o relativistic (0.97 c) speeds takes place
0.1
deprojected distance from0.1the core.1 If we 10

simply assume that the observed proper motions represent the
speed of the bulk flows, the gradual acceleration of the bulk
flow takes place from 200 rs up to 5 × 105 rs over three ordersof magnitude of the distance.
We note that a similar apparent acceleration has been observedin the jet of Cyg A from 0.2 c to 0.7 c at 2–10 × 103 rs(Krichbaum et al. 1998) and for NGC 315 from 1.1 c ISCO
to 2.5 c at
5–20 × 103 rs (Cotton et al. 1999). However, these accelerations
are seen in a limited range of the jets at around 103 rs . This isprobably due to the sensitivity limit, and a limited part of the
5 for thosegradualof 10
the4 jet is 10
seen
102 acceleration
103
106 objects.
107
108
De-projected distance along jet (Rs)3
Distancefrom the BH r [RS]Asada & Nakamura 2014 discovered that the jetcollimation region is corresponding to theacceleration region in M87.

Acceleration

Deceleration

W(r) ∝ r 0.5∝ r 1.0

Parabolic

Conical5Aim of this work
We measured the jet width profiles covering the range fromthe blackhole gravitational sphere (< 10456) to the galactic scale•

Previous 2 samplesd this work 3 samples à total 5 samples• Increase the number of samples• Clarify the characteristics of jets
(e.g. properties and differences)

3 targets in this work

APPROACH

Targets

30 kpcNGC 4261@VLA 5GHz

Does the structure change depending on thetype of jet ?
FR-I : edge-darkened
FR-IIedge-brightened

FR-I

weak jetpowerful jet

Previous works
FR-I
FR-I
M87

NGC 1052 @VLBA 15GHz
300 k light year

NRAO

NGC 6251 @ VLA
http://www.werner.lu/pn/phd/ngc6251.html

FR-II

FR-I
~ 4 kpc

Cygnus A @VLA

3 targets in this work

APPROACH

Targets

30 kpcNGC 4261@VLA 5GHz

FR-I

Plasma torus

exists in NGC 1052
Kameno et al. 2001;
Kameno et al. 2003

FR-I
NGC 1052 @VLBA 15GHz
300 k light year

FR-II

Other 2 samples appears to host thin discCygnus A @VLAAPPROACH

Distance
1

4CH
;4M A

16.7

0

8 A

5

5

31.6

BH

LA

.

4.9 1.0

108

9

CB

4

=NL

N L H NL IM N If

-

G

249

7.5 109

20

108

)

5 F ICC60B
9B6G CB
T

Type Ig+(T

5 F ICType II

g

) T

1.5

)

5 F ICType Ig

S-+T 
103+

G

Type I

)

76

MBI

( +

B6

+0

2.

+

A6FF
M¤M

(

2.
(
F

Targets

Selection points
Massive black hole nearby galaxy
The jet is covering the scale of structural transition (~105 RS)
Bi-polar jet can be seen continuously

6 2

108

     

Type I.TAPPROACH

Telescopes and frequencies

Very Long
Baseline Array(VLBA)
Base line length
Resolutions
Frequencies

8611km0.17 mas~10mas
yy
1.4/2.3/4.9/8.4/15/22/43
GHz

VLBI
Space Observatory
Programme(VSOP)
30,000 km

Very Large Array
(VLA)

36 km

0.4~1.2 mas

0.1~8 arcsec

1.6/4.8 GHz

1.6/8.3/22 GHz

DATATelescopes

NGC 4261

VLBA

VLA

NGC 1052

VSOP
VLBA
VLA

Cygnus A

VLBA
VLA

Frequency ν
[GHz]

date

1.4/2.3/5.0/8.4

5/July/2003

15/22/43

28/June/2003

1.4

Apr/1994

5.0

22/Apr/1984

1.6

7/Aug/2001

4.8

31/Jul/2001

2.3/8.4/15.4

17/Aug/2001

15.4/22.1/43.2

24/Jul/2000

Sawada-satoh et al. 2009

8.3

20/Jun/1998

NRAO Archive AR0396

43

Oct/2007-2009

Boccardi et al. 2016

4.9

Oct/2002-2003

Bach PhD. thesis

22

4/Mar/1994

NRAO Archive GK0012

4.9

1984

Perley et al. 1984 (NED)

Original data

Haga et al. 2015

Open data by C.C. Cheung

Kameno et al. 2003

28

CHAPTER 2. NGC 4261

METHOD

Measuring method of jet width
VLBA@15(Data sets from haga+2015)(a) VLBA GHz
15.3 GHz(c) VLBA 15.3 GHz

x

0.007
0.006

Intensity (Jy/beam)

Intensity [Jy/beam]

r

0.008

0.005
0.004
0.003

θobs

0.002
0.001
0
-0.00106 09-3(b) VLA 4.86 GHz

-2

-1

0

1

2

3

Relative Declination (miliarcsec)
0.016
0.014

(d) VLA 4.86 GHz

Definition of “de-convolved jet width” Wjet
Intensity (Jy/beam)

DECLINATION (B1950)

08

07

06

05

0.012
0.01

⎛ −(x − b) 2 4ln 2 ⎞Fitted⎟⎟= a exp ⎜⎜2
Gaussian
θ obs
⎝
⎠
2
2
θ obs
= W 2jet + θ beam

0.008
0.006
0.004
0.002
0

04

-0.00203-0.00412 17 10

05

00

16 55

50

45

RIGHT ASCENSION (B1950)

40

35

30

-150

-100

-50

0

50

100

150

Relative Declination (arcsec)

Figure 2.12: (a) 15 GHz√ VLBA image. Contours−1start from the 3 sigma image RMS noise andincrease by factors of 2 (1σ = 0.358 mJy beam ). Vertical line on the image represents theMeasuring method of “radiation” profile
only for NGC 4261

BL
C L
GBN L A H L C HB

VLBA@1GHz

sliced along the jet axis

0.07

輝度分布 (Jy/beam)
Intensity

METHOD

輝度(Jy/beam)
使用箇所
Intensity[Jy/beam]

0.06

Used range

0.05

Opticallythin
thin and, >3σ>3σ
optically

0.04
0.03
0.02
0.01
0
0
-0.01

200

400

600

800

1000

1200

13

10

y = 0.2904

METHOD

Measuring method of the BH position
0.00001

0.0001

0.001

0.01

1
0.1

Correcting the core shift effect
There is not always the black hole at the origin of the jet image
Effect of optical thickness (frequency dependent)high freq.

Porth+ 2011

Jet width y (mas)low freq.

0.1

It will change the results
1.0

0.1

Jet

1

10

0.01

y = 0.0166x0.4692
0.001

y = 0.0275x0.5521
0.0001

Corrected core shift effectNo correction
0.00001

Distance from the BH x (mas)
AJ

CJ

2

CJ 22G
new VLBI AJ• NGC 4261: Already measured the BH position (Haga+2016)5

(AJ)
BachPhD
AJ 4.9GHzposition
BachPhD CJ
GHz• Cyg A:We decide the BH position by using the measured
core
in4.9Bach
2004
VLBI AJ) (2)• NGC 1052: We decide the origin of jet by using the measured
jet speedin(newVermeulen+2003

V

n



RESULTS• Jet width profiles• NGC 4261
• NGC 1052
• Cygnus A• Radiation profile• NGC 4261
15

RESULTS

Approaching jet (AJ) width profiles

10
10
10
10

6

4

2

0

10

0

2

4

6

8

10
10
10
10
De-projected distance r (RS)

10

10

9

10

8

10

7

10

6

10 5
10

4

10

3

10

2

10

1

10

0

1010

-1

Cygnus A-7

9

1GHz VSOP
2GHz VLBA
5GHz VLBA
5GHz VSOP
8GHz VLBA
15GHz VLBA
15GHz VLBA
22GHz VLBA
43GHz VLBA
8GHz VLA

-6

10

10

Projected distance (arcsec)

-5

10

10

-4

-3

10

-2

10

-1

10

0

10

1

10

2

10

10

2

VLBI 43 GHz AVLBI 4.9 GHz AJ
VLA 22 GHz AJ
VLA 4.9 GHz AJ

8

10

10

101

107

0

10

6

10

-1

10

5

10

-2

10

4

10

-3

10

3

10

-4

10

2

10

-5

10

1

10

-6

10

0

10

-1

10

10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9
De-projected distance r (RS)

-7

10
-1

10

0

10

1

10

2

3

4

5

6

10
10
10
10
10
De-projected distance r (RS)

7

10

8

10

9

10

De-convolved jet width (arcsec)

1081GHz VLBA
2GHz VLBA
5GHz VLBA
8GHz VLBA
15GHz VLBA
22GHz VLBA
43GHz VLBA
5GHz VLA
1.4GHz VLA

De-convolved jet width W (RS)De-convolved jet width W (RS)1010NGC 1052

De-convolved jet width W (r) (RS)NGC 4261

RESULTSCounter jet (CJ) width profiles

10
10

8

6

1GHz VLBA
2GHz VLBA
5GHz VLBA
8GHz VLBA
15GHz VLBA
43GHz VLBA
5GHz VLA

10 4
10
10

2

0

10 0

10 2
10 4
10 6
10 8
De-projected distance r (RS)

10

10
10

8

10

7

10

6

10

5

10

4

10

3

10 2
10

1

10

0

10
10

-1

1GHz VSOP
2GHz VLBA
5GHz VLBA
5GHz VSOP
8GHz VLBA
15GHz VLBA
15GHz VLBA
22GHz VLBA
43GHz VLBA
8GHz VLA

9

10

8

10

107

-7

-6

10

Projected distance (arcsec)

-5

10

10

-4

-3

10

-2

10

-1

10

0

10

1

10

2

10

10

2

VLBI 43 GHz CJVLBI 4.9 GHz CJ
VLA 22 GHz CJ
VLA 5 GHz CJ

10

101
0

10

6

10

-1

10

5

10

-2

10

4

10

-3

10

3

10

-4

10

2

10

-5

10

1

10

-6

10

0

10

-1

10 -1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10109 10-1
De-projected distance r (RS)

-7

10
0

10

1

10

2

3

4

5

6

10
10
10
10
10
De-projected distance r (RS)

7

10

8

10

9

10

De-convolved jet width (arcsec)

109Cygnus A

De-convolved jet width W (r) (RS)De-convolved jet width W (RS)10

NGC 1052

De-convolved jet width W (RS)NGC 4261

±0.02, for the approaching and counter sides, respectively. The respective redu
values are 0.53 and 0.68, suggesting that the fitting was robust or potent
tedRESULTS
due to over-sampling because multi-frequency measurements might prov
e independent measurements.
Fittingfunctionand& results
Because previous
studiesof M87 (Asada
Nakamura 2012) and NGC 6251 (Tsl. 2016) found a transition in these jet width profiles, we then performedn Power-law (PL) fit
tional fitting for
NGC 4261 using a broken power-law function to probe a fla
9
&
=
)
&
signature in the )upper
streamside
7#%
8 (Figure 2.13). The obtained fitting functio
De-convolved jet width W (RS)

10

10

10

8

10

6

1GHz VLBA
2GHz VLBA
5GHz VLBA
8GHz VLBA
15GHz VLBA
22GHz VLBA
43GHz VLBA
5GHz VLA
1.4GHz VLA

10 4
10

2

10

0

10 0

n Broken power-law (BPL) fit

Wjet (r) = W0 2

au −ads!

rrb"a u !

!

r
1+
rb

10 2
10 4
10 6
10 8
De-projected distance r (RS)"s " ad −au
s

,

10 10

(

NGC 4261
NGC 1052
Cygnus A
re W0 is the scaleWidth
factor,aisthepower-law
index
for
the
upstreamjet, ad isu
AJ Width CJ radiation AJ Width AJ width CJ width AJ width CJ
er-law index
jet, rb is the break location,and s gis the sharph
2xPL g
PL for thehdownstreamg (here,g we use g
BPLthe break
he profile atthe fixedgvalue sg= 10). - The fitted
paramelts are listed in Table 2.2. The reduced χ2 values are 0.464, 0.515, and 0.570
approaching jet, counter jet, and combined cases, respectively. The fit solut
cate that the structures of the approaching and counter jets are consistent;Fitting results ( r =103~109 RS)

RESULTSij

The approaching and counter jet structure is symmetric within the error
NGC 4261 and NGC 1052 have a structural transition. Cygnus A does not have a transition but have a big gap in one orderl The jet width varies by source
CHAPTER 2. NGC 4261

10

Approaching jet
Counter jet
Combined

rb ~1.29

8

10 7

104 Rs

10

6

6

10

10

5

10

104

10

2

10

9

10

approaching jet
receding jet
approaching jet (binned)
receding jet (binned)
combined

rb ~0.99

10

NGC 4261

10

0

10

2

4

6

8

10
10
10
10
De-projected distance r (RS)

10

-4

-3

10

-2

10

-1

10

0

10

1

10

2

10

10

2

10

101

10

104 Rs

3

0

10

6

10

-1

10

5

10

-2

10

4

10

-3

10

3

10

-4

10

2

10

-5

10

1

10

1

NGC 1052
10 1

10 2

10 3
10 4
10 5
10 6
De-projected distance z (RS)

10 7

10 8

-6

10

0

Cygnus A

10

-1

10

-1

10

0

10

1

10

2

3

4

5

6

10
10
10
10
10
De-projected distance r (RS)

7

10

8

10

-7

10
9

10

NGC 4261

NGC 1052

Cygnus A

0.51 0.13 parabolic

0.03

0.06 over-collimation

0.55

0.02 parabolic

0.92

0.03 conical0.51

0.03 parabolic

Figure 2.15:
Comparison between approaching jet and counter jet.
Red andgreen plots describe measured jet width for approaching side and counter side, respectively.
Red, green and blue lines are power-law fitting of the measured
jet width profile for approaching side, counter side, and combined data, respectively.

Power-law index in upstream

Projected distance (arcsec)

-5

10

7

4

0
10 10 10 0

10

-6

10

Approaching jet
Counter jet

8

10 2

0

-7

10

De-convolved jet width (arcsec)

108

approaching + counter

De-convolved jet width w (RS)De-convolved jet width W (RS)1010

De-convolved jet width W (r) (RS)34

Power-law index in downstream 1.05 0.01 conicalRadiation profile along the jet axis
-1

Flux density per mas at 1 GHz F’ (Jy mas )RESULTS

10

1

10

0

10 -1

(NGC 4261)∝ r -1.43

0.02∝ r -2.50

10 -2
10 -3
10

-4

10

-5

10

-6

rb1=(2.31

10 2

10 3

0.40) x104 RS

spectral index –o.7

0.02

1.4GHz VLBA
2.3GHz VLBA
5GHz VLBA
8.4GHz VLBA
15GHz VLBA
22GHz VLBA
43GHz VLBA
1.4GHz VLA
5 GHz VLABest fiterror∝ r 0.53

10 4
10 5
10 6
10 7
De-projected distance r (RS)

10 8

0.12

10 9

Radiation profile along the jet axis
-1

Flux density per mas at 1 GHz F’ (Jy mas )RESULTS

10

1

10

0

10 -1

(NGC 4261)∝ r -1.43

0.02∝ r -2.50

10 -2
10 -3
10

-4

10

-5

10

-6

rb1=(2.31

0.40) x104 RS

spectral index –o.7

0.02

1.4GHz VLBA
2.3GHz VLBA
5GHz VLBA
8.4GHz VLBA
15GHz VLBA
22GHz VLBA
43GHz VLBA
1.4GHz VLA
5 GHz VLABest fiterror∝ r 0.53

0.12

consistent with the position of the structural transition
10 2

10 3

10 4
10 5
10 6
10 7
De-projected distance r (RS)

10 8

10 9

Radiation profile along the jet axis
-1

Flux density per mas at 1 GHz F’ (Jy mas )RESULTS

10

1

10

0

(NGC 4261)

region (ii)

10 -1

∝ r -1.43

0.02∝ r -2.50

10 -2
10
10

spectral index –o.7

-3

region (i)0.02

1.4GHz VLBA
2.3GHz VLBA
5GHz VLBA
8.4GHz VLBA
15GHz VLBA
22GHz VLBA
43GHz VLBA
1.4GHz VLA
5 GHz VLABest fiterror
region (iii)-4

rb2 ~ 106 RS(the-5 Bondi radius 5 108 RS)∝ r 0.53

0.12

10The second transition point
10

-6

10 2

10 3

10 4
10 5
10 6
10 7
De-projected distance r (RS)

10 8

10 9

DISCUSSION• Physical properties
calculated by using the jet width profileand the radiation profile- NGC 4261
• Discussion about characteristics of 5 samples• Difference between FR-I and FR-II• Torus in NGC 1052
• Jet width deference in 5 samples• A big gap in Cygnus A

Calculation procedure of the physical properties
using jet width and radiation profiles of NGC 4261
Jet width profile

6

10

4

-1

10 2
10

0

10 0

10 2
10 4
10 6
10 8
De-projected distance r (RS)10 10

De-projected distance from the central engine r [R S]

Calculation results

10

1.4GHz VLBA
2.3GHz VLBA
5GHz VLBA
8.4GHz VLBA
15GHz VLBA
22GHz VLBA
43GHz VLBA
1.4GHz VLA
5GHz VLA
error
Best fit

0

10

-1

10

-2

10 -3
10

-4

10 -5
10

-6

10

-7

10 2

10 3

10 4
10 5
10 6
10 7
De-projected distancer (RS)

10 8

10 9

・ Synchrotron Theory
・ Equipartition Assumption

Synchrotron
Synchrotron
luminosity per jet luminosity per unit
3
length [erg/s/Rs] volume [erg/s/Rs ]Magnetic field
B(r) [G]Jet pressure
P(r) [dyn/cm2]

Magnetic energy
B(r)2W(r)2 [erg]
10

5

10

4

10

3

-1

10

Approaching jet
Counter jet
Best fit2

10 8Flux profile

10 1

2

Measurements

10

Flux density per mas at 1 GHz
F‚Äô (Jy mas )S

Jetwidth W(r) [R ]De-convolved jet width W (RS )10

Magnetic field energy B W(r) (Jy mas )DISCUSSION

10 2
10

1

10

0

10

-1

10

1.4GHz VLBA
2.3GHz VLBA
5GHz VLBA
8.4GHz VLBA
15GHz VLBA
22GHz VLBA
43GHz VLBA
2

10

3

1.4GHz VLA
5GHz VLABest fit VLBABest fit VLA
error
4

5

6

10
10
10
10
De-projected distance r (RS)

7

10

8

10

9

DISCUSSION

jet properties

A. Synchrotron luminosity per volume:
M I 1 9(r)W(r)

Lsyn/v [erg/s/Rs3]

θbeam

B. Synchrotron luminosity per unit jet length: Lsyn/l [erg/s/Rs]
C. Jet pressure:P(r) [dyn cm-2]

D. Magnetic field strength:

B(r) [G]Beq = (6π(1+k) c12 Lsyn Φ−１ V-1 )2/7
E . Magnetic energy:

B(r)2W(r)2 [erg]UB = ½ µ0-1 Beq2 πW(r)2

Parabolic

105 RS

ConicalDISCUSSION

34

1.4GHz VLBA
2.3GHz VLBA
5GHz VLBA
8.4GHz VLBA
15GHz VLBA
22GHz VLBA
43GHz VLBA
1.4GHz VLA
5GHz VLABest fit VLBABest fit VLA

10 32

Synchrotron Luminosity of the unit volume

δ L syn (erg s

-1

-3

RS )

10

A. Synchrotron luminosity per unit volume Lsyn/v [erg/s/Rs3]

10 30
10

28

(i)

conicalparabolicxx2

104 RS

106 RS

10 26
10

24

rb2

10 22
10

(ii)

(iii)

(i) ∝ r -2.82(ii) ∝ r -4.37(iii) ∝ r -1.55

20

10 18
10

rb1

16

10 2

10 3

10 4
10 5
10 6
10 7
10 8
De-projected distance r (RS )

10 9

0.03
0.01
0.27

DISCUSSION

Synchrotron Luminosity of the unit lengthdLsyn (erg s-1 RS-1 )10

B. Synchrotron luminosity per unit jet length Lsyn/l [erg/s/Rs]

38

1.4GHz VLBA
2.3GHz VLBA
5GHz VLBA
8.4GHz VLBA
15GHz VLBA
22GHz VLBA
43GHz VLBA
1.4GHz VLA
5GHz VLABest fit VLBABest fit VLA

10 37

10 36

10 35

(i)

Parabolic

Increasing
the luminosity

10 34

10

10 31 2
10

(ii)
10 3

10 4

10 5
10 6
10 7
De-projected distance r (R S )

(iii)
10 8

104 RS 106 R
S(i) ∝ r -1.48(ii) ∝ r -2.34(iii) ∝ r 0.51

10 33

32

Conical

10 9

0.02
0.01
0.12

DISCUSSION

C. Jet pressure50

CHAPTER 2. NGC 4261

1.4GHz VLBA
2.3GHz VLBA
5GHz VLBA
8.4GHz VLBA
15GHz VLBA
22GHz VLBA
43GHz VLBA
1.4GHz VLA
5GHz VLABest fit VLBABest fit VLA
kolokythas(2015)
O’sullivan(2011)
O’sullivan(2011)

-2

10

-4

10

Jet pressure P (dyn cm -2 )P(r) [dyn cm-2]

-6

10

(i)

-8

10

Pjet
104 RS10

10-12 2
10

3

10

4

5

6

7

8

10
10
10
10
10
De-projected distance r (RS)106 RS(i) ∝ r -1.61 0.02(ii) ∝ r -2.51 0.01
(iii) ∝ r -0.58 0.06

(iii)

(ii)

-10

ConicalParabolic910

Figure 2.25: Radial profile of jet pressure. The horizontal axis shows distance from the central
engine, which is taken account for the core shift eﬀect. The vertical axis shows jet pressure. Color
variation describes each observed frequency; orange: 1.4 GHz with VLA, gray: 5.0 GHz VLA, red:
1.4 GHz with VLBA, green: 2.3 GHz with VLBA, blue: 5.0 GHz with VLBA, purple: 8.4 GHz with
VLBA, light blue: 15 GHz with VLBA, yellow: 22 GHz, black: 43 GHz VLBA, respectively. Red

2920

E. O’Sullivan et al.

1739

FR I radio galaxy 3C 270

Table 7. Physical parameters of 3C 270 and its components.
RegionDISCUSSION

rmin(arcsec)rmax(arcsec)

Vtot(kpc3 )

S240 MHz(mJy)

S1550 MHz
(mJy)

α obs

L1550
(1022 W Hz−1 )

Beq
(µG)

Pradio(10−12 dyn cm−2 )West Lobe
1
2
3
4

10
33
63
168

33
63
168
242

1724
3861
12 0812551

316 ± 16650 ± 33
3138 ± 157
897 ± 45

0.62
0.62
0.55
0.50

3.6
7.3
35
10

5.0
4.9
5.5
6.0

1.42
1.36
1.73
2.06

East Lobe
5678998 ± 80
2067 ± 165
8741 ± 700
2262 ± 181

10
33
63
168

33
63
168
282

1056
1646
9753
4668

408 ± 33976 ± 785868 ± 469
5755 ± 460

146 ± 7287 ± 142310 ± 116
2202 ± 110

0.55
0.66
0.50
0.52

1.6
3.2
26
25

4.6
4.9
5.3
6.5

1.21
1.39
1.64
2.43

C. Jet pressure

P(r) [dyn cm-2]

CHAPTER 2. toNGCexternal
4261
comparedpressure in kpc scale

50←VLA image
Thet =lobe
B pressure
1590[(1 + z)ν
]
Myr,
(2)
B +B
measuredbyis expressed in GHz, and B and B
in µG (Parma
where ν= 3.2
et al. 2007). B is the equipartition magnetic field and B
Kolokythas+2015
is the equivalent magnetic field strength of the cosmic microwave
0.5
eq

rad

2
eq

2
CMB

break

2922

E. O’Sullivan et al.

break

−0.5

eq

eq

CMB

CMB

background (CMB) radiation at zero redshift, and equation (2) thus

Downloaded from http://mnras.oxfordjournals.org/ at Uchu Kagaku Kenkyujo on January 19, 2016-210

and constant over the whole of the source lifetime when radiative
losses dominate over expansion losses. Neglecting reacceleration
processes, the radiative age (the time since the last period of injection of relativistic electrons began) can be obtained as

1.4GHz VLBA
2.3GHz VLBA
5GHz VLBA
8.4GHz VLBA
15GHz VLBA
22GHz VLBA
43GHz VLBA
1.4GHz VLA
5GHz VLABest fit VLBABest fit VLA
kolokythas(2015)
O’sullivan(2011)
O’sullivan(2011)

Figure 10. Regions used for the estimation of the volume and the otherthe expected
X-ray
luminosityof the LMXB
basedon
includesboth
inverse Compton
and population,synchrotron
losses.
physical parameters described in Table 7. The 3.2 µJy (4σ ) contour isthe relationof Kim& Fabbiano(2004)and taking
a totalfield
K-bandUsing
equation(2) andthe meanmagnetic
for the source,
shown to indicate the limit of the detected lobe emission.
11(Ellis & O’Sullivan
luminosity
ofwe
2.2estimated× 10 LK ⊙5 µG,
a radiative
age of ∼292006,
Myrscaled
for thetowestern lobe
our chosen ∼37
distance).
that thisone.
is likely
to bederived
an overesMyr We
for notethe eastern
We alsoan estimate ofwhere Ee is the energy of the electron population, V is the volume, timate,and
since
we
have
alreadyexcludedallresolved
point
sourcesadvance speed of the lobe tip, υ adv /c, where c is the speed ofµ0 is the permeability of free space (4π in cgs units or 4π × 10−7 but wethe
expect the profile to be largely unchanged. The luminosity
light. This velocity was calculated as υ adv = LD/τ rad , assuming a
in SI), φ is the filling factor of the plasma (assumed to be 1) and is converted
to an expected number of counts in our band using asimpleconstant
using
the islinear
k is the energy ratio of the non-radiating particles to the radiating power-law
modelwith " velocity= 1.8. A andsimilarscalingused distanceto deter- (LD) from
Figure 1. (a) Chandra
0.3–3
keV
binnedby atip
factorof 2 jetandassmoothed
withfroma Gaussianof σ = 16 pixels (15.8 arcsec). VLA 1.5-GHz contours arethebackofimage,the lobe
to theof themeasured
the radio
relativistic electrons. We assume k = 1, indicating equal
energy mine
expectedcoronallybinariesbyand-6
overlaid, starting
3σ theabove
the rms contribution
noise level of from
0.3 mJybeam−1 active
and increasing
factors of 2. The restoring beam size is 16 × 15.1 arcsec2 (Half-Power∼ 0.004c
imagesin Section
4.examineWethatfor both
lobes
υ adv
cataclysmic
variables,
based
the found
relationof Sazonov
et al.
(2006)
in radiating and non-radiating particles. The factor ϵ describes
theHPBW).
Beamwidth,
Annularregions−1
used
to on
the surface
brightness
acrossthecavityrim
are marked in white. (b) XMM–Newton 0.3-3 keV waveletfor thewesternlobesourcesandkm
s−1diffuse
for theeast- Dark linear features show chip gaps and bad columns,(∼1300APEC∼1200
model.
Surfaceusing
a s0.5-keV,
solar
abundanceordering of the magnetic field and we adopt ϵ = 3, indicatinga and scalingsmoothed MOS+pn
image,
withkmscaleschosento exclude
point
and emphasize
emission.
brightness
profilesweredeterminedusing
ellipticalregions
chosenern
one).
tangled magnetic field, as in O’Sullivan et al. (2011b). and should be ignored. (c) XMM–Newton residual map, showing the image after the removal and filling of point sources, and subtraction of the best-fitting
to match
light
axial
1.24a andpo-environment
surfacebrightness
modelthefor optical
the galaxy
anddistribution,
largergroupwithhalo,smoothed
withGaussianof σ = 4 pixels (17.6 arcsec). The solid ellipses indicate the optical
By
comparison,
the sound
speed
in ratiothe IGMinthethoughWe find Beq ∼ 5 µG for both eastern and western lobes,◦ several smaller galaxies in the field. The dashed ellipses indicate the regions used to define the cavity size and position. (d)D25 contours of
NGCangle
4261 68.
and3 (where
the estimatedposition angle
is definedas the angle
around
NGC
4261,
from
the measured
X-ray temperathe outer parts of the lobes (regions 4 and 8) have higherXMM–Newton
Beq , close sition
residual map,
as in the lower
panel,Regions
overlaidcorresponding
with VLA contours
and the partial annuli used to extract the surface brightness profiles
betweenthe increases
major-axis
andleft-handduewest).
the core toto 590 km s−1
ture,
from
about
380 km s−1 nearto the estimate for the source as a whole ∼6.4 µG. For
thisthefield
acrosscavitytherims.
X-ray jets were excluded, but testing shows that these make only
beyond ∼100 arcsec. The advance speed of the lobe tip therefore(see later), electrons at γ min = 100 radiate at ∼5 MHz.
a minor contribution in the central bins of the profile. It is clear thatappears
tomap
be supersonicrelative to for
thean
IGM.
Conversely,
Alfvén-8
the monoenergetic
exposure
and PSF, profile
determineden-thatful, butthesimplyto provide an approximation to the core emission,
the observed
surfacebrightness
is steeper
thanexpecteds−1(usingplasmaspeed inthelobe
isphotonabout
105 kmofbut
ergy of 1 keV,forapproximating
thethemeanenergythemoredata. extended
Athe lobe
tothanallow it properto be subtracted. A second β-model was added to model
emissionfromstellarpopulation,
5.3 Radiative age
ties deducedin Section
6.2).thatThatmuchis,
speed
expansion
lobeemission, with the slope and core radius fixed atbackground image
consistingof thescaledparticle-only
image
large-scale
group
the Chandra
1-keV
PSF,
confirmingof andtheofemission
in of theis strongly
sub-Alfvénic,
and so andwillunconnot excite magnetic
OOT
imagefromwasused,
and convolved
the values shocks
determined from the ROSAT (rcore = 1.68 arcmin, β =thisevents
band
ariseshotgas.
When considering the development of the radio jets andscaled
lobes,pnwe
in theused
lobes.
The internal
speed of 0.31,
the waves
Davis inet theal. 1995), but a low normalization was found forvolvedflat models wereto accountfor the characteristic
X-ray backgroundadopt a simple conceptual model, in which at any given time
plasmathis component, suggesting that the central β-model accounted forandbackground,respectively.
magnetized
relativistic
plasma were calculated fromis rapidly transported out from the central engine to the tip
ofany
the residual
jet. 3.3 particle
Spectral properties of the cavity rims
most of the emission in the field. Fig. 2 shows the XMM–Newton
Experimentation showed that modelling
the AGN as a pointc
At this point the jet flow is halted by contact with the IGM, and the!narrow(3)υA =radialprofile, with fitted model components forsource (a delta
functionorGaussianconvolved
the
Given
the
ongoingjetuactivity
in, thesystem, itwith
is possible
thatthe surface brightness
ptcl +Pradio
plasma driven out of the jet moves out radially to form thelobe.
In
1 +expanding.
radio
lobes
are
still
If
they
are
expanding
subsonically,
comparison.
PSF)
was
not
effective,
probably
becauseoftheemission
from
the
2Pmag
-10
this model, the age of the lobe plasma is linked to the distancealongbright ofrims
consistof compressedgas which may
To examine any residual structure, we subtracted the best-fitting
jets anddensetheirgas X-rayin the centre
themustgalaxy.
We therefore
modelled
the jet; the back of the lobes (close to the nucleus) formedwhen
iscooling
thewasAlfvén
speed
expressed
in m s−1model, uIfptclfrom
is thewhereThe
expectedtoυ A
bemodelmorethan itssincesurroundings.
an enimage in which the point sources had been removed
the core
withbea β-model.
fixedrapidly
to be circular,
the jet only extended a few kiloparsecs, while the tips oflobes they
the the DMFILTH task), and then the OOT readergy
densitynorth
of or
the
relativistic
particleandreplaced
Pmag is(usingareexpanding
at
above
sound
the lobesand
willthetheextendedemission
towards
andsouththetended
tospeed,drivepopulation
thehave only formed recently. In principle, backflows could
develop,magnetic
field
cause ellipticities.
shock
heating
ofpressure.
the surroundinggas. Using
XMM–Newton,
out streak was subtracted. The resulting residual map is shown inmodel
to extremeThebest-fitting
parameters
for this+1.2
significant temperature+0.01
differences between the cavity
transporting younger plasma away from the jet tips intomodel
regionsof rwe= 1.0noFigs 1(c) and (d). The emission north and south of the core produces
were
corefound−1.0 arcsec and β = 0.55−0.02 , but we again
rims
andregions
immediately
insideandoutsidethecavities.
Thisemphasize
thestrongest residuals, but structures associated with the radio lobes
the lobe formed at earlier times. However, in the absenceof such athat this model is not intended to be physically meaning6 D I S CsinceU S StheI OregionsNisunsurprising,used
arenecessarily
large
and
flow, or external forces causing reacceleration, plasma in the lobes⃝
includeunresolved
point
sources
and
gas
at
a
range
of
temperatures.
C 2011 The Authors, MNRAS 416, 2916–2931
is expected to age passively, with the high-frequency break in its-12
6.1theTheof thesourceC 2011 RAS
While
fieldageof viewof theACIS S3 CCD limits our ability to Monthly Notices of the Royal Astronomical Society ⃝spectral index falling to lower frequencies over time.
examine the edges of the radio lobes with Chandra, we can examine
2
3
4
5
6
7
8
9
Before considering the implications of our radiative age measureThe radiative age of the radio source of NGC 4261 can be calcuthe southern parts. Fig. 1(a) shows a series of partial elliptical anFigure 4. 0.3–2 keV Chandra image of the core of NGC 4261, withments,
weusedfirsttodiscuss
potential
sourcesof error
inacross
our approach. We
lated
if the break frequency of the source is known (e.g. Myers & nuli whichweresearch fora surfacebrightness
jump
0.493 arcsec pixels smoothed with a Gaussian of σ = 2 pixels (upper panel)
have performed
relatively
simplethe 1.55–4.86-GHz
Spangler1985).
The magnetic
field is considered
to be The
uniform the south-east
and adaptively
smoothed
Chandra temperaturemap (lower panel).
lobe edge.a These
regions
weremodellingchosen to of
match
the
S
colour bar indicates the approximate gas temperature in keV. The two panels
shape of the apparent surface brightness feature, with large widths
have the same alignment and angular scale.
to increase the signal-to-noise ratio in each bin. Fig. 5 shows the
MNRAS
450,is1732–1744(2015)
exposure-corrected surface brightness in eachbin. A peakfound
Figure 2.25: Radial profile of jet pressure. The horizontal axis shows distance from the centrala Chandra image of the core and jets. As noted by Worrall et al.
at the position of the lobe rim, where the surface brightness exceeds
engine, which is taken account for the core shift eﬀect. The vertical axis shows
jettherepressure.
Color(2010),
are wedge-likesurface brightness decrements in thethat immediately outside the rim at > 3σ significance (a 3.4σ difarea 5.0
immediately
and red:south of the western X-ray jet, and aference between bins 3 and 4). This corresponds reasonably well
variation describes each observed frequency; orange: 1.4 GHz with VLA, gray:GHz northVLA,
suggestion of similar structure on the eastern side (see also figs 2 andwith the feature observed in the XMM–Newton images.
1.4 GHz with VLBA, green: 2.3 GHz with VLBA, blue: 5.0 GHz with VLBA,4purple:
8.4
GHz
with
of Worrall et al. 2010). The emission bordering these decrements is
If this surface brightness increase is the result of a shock, the stanVLBA, light blue: 15 GHz with VLBA, yellow: 22 GHz, black: 43 GHz VLBA,
respectively.
Red
somewhatbrighter and extends
to a larger radius than the emission
dard Rankine–Hugoniot jump conditions (e.g. Landau & Lifshitz

-4

(i)

10

10

(ii)

←Chandra image
O’sullivan+2011↑ XMM-Newton image

Measured
the temperature of hot gas gatheredby the lobe
and the electron density(iii)

Pext=nkT ; n=ne

10

Downloaded from http://mnras.oxfordjournals.org/ by guest on January 19, 2016

Jet pressure P (dyn cm -2 )10

Pext : External pressure of the lobe

10

10

10

10
10
10
10
10
De-projected distance r (R )10

gas temperature kev

FR I radio galaxy 3C 270

1739

Table 7. Physical parameters of 3C 270 and its components.
RegionDISCUSSION

C. Jet pressurermax(arcsec)

Vtot(kpc3 )

S240 MHz(mJy)

S1550 MHz
(mJy)

α obs

L1550
(1022 W Hz−1 )

Beq
(µG)

Pradio(10−12 dyn cm−2 )West Lobe
1
2
3
4

10
33
63
168

33
63
168
242

1724
3861
12 0812551

316 ± 16650 ± 33
3138 ± 157
897 ± 45

0.62
0.62
0.55
0.50

3.6
7.3
35
10

5.0
4.9
5.5
6.0

1.42
1.36
1.73
2.06

East Lobe
5678998 ± 80
2067 ± 165
8741 ± 700
2262 ± 181

10
33
63
168

33
63
168
282

1056
1646
9753
4668

408 ± 33976 ± 785868 ± 469
5755 ± 460

146 ± 7287 ± 142310 ± 116
2202 ± 110

0.55
0.66
0.50
0.52

1.6
3.2
26
25

4.6
4.9
5.3
6.5

1.21
1.39
1.64
2.43

P(r) [dyn cm-2]

CHAPTER 2. NGC 4261
compared
to external pressure in kpc scale

50

-4

10
-2

-6

10

(i)

The jet pressure2922 E. O’Sullivan
al.
≒ The
hot etgas
pressure in X-ray @ >107 RS
trad = 1590

-8

The jet pressure measurement of this study
is consistent with the X-ray
result at
kpc scales↑ XMM-Newton
image

10

Downloaded from http://mnras.oxfordjournals.org/ by guest on January 19, 2016

The first measurement of
the pressure distribution
hotin <107 RS by using VLBI/radio interferometry.

(iii)

(ii)

-10

(2)

where ν break is expressed in GHz, and Beq and BCMB in µG (Parmaet al. 2007). Beq is the equipartition magnetic field and BCMB = 3.2
is the equivalent magnetic field strength of the cosmic microwave
background (CMB) radiation at zero redshift, and equation (2) thus
Figure 10. Regions used for the estimation of the volume and the othertheincludes
expectedboth
X-ray
luminosityof theand
LMXB
population,
based oninverseComptonsynchrotron
losses.
physical parameters described in Table 7. The 3.2 µJy (4σ ) contour isthe relationof Kim &(2)Fabbiano(2004)
taking a fieldtotal forK-bandUsing equationand themeanandmagnetic
the source,
shown to indicate the limit of the detected lobe emission.
11
L(Ellis&O’Sullivan
2006,
scaledtoluminosity
of
2.2
×
10
K⊙
5 µG, we estimated a radiative
age of ∼29 Myr for the westernlobe
ourchosendistance).
We
note
that
this
is
likelytobeanoveresand ∼37 Myr for the eastern one. We also derived an estimate ofwhere Ee is the energy of the electron population, V is the volume,
timate,
since
we
have
alreadyexcludedallresolved
point
sources
the advance speed of the lobe tip, υ adv /c, where c is the speed ofµ0 is the permeability of free space (4π in cgs units or 4π × 10−7
but we expect the profile to be largely unchanged. The luminosity
light. This velocity was calculated as υ = LD/τ rad , assuming a
in SI), φ is the filling factor of the plasma (assumed to be 1) andis converted to an expected number of countsadv
in our band using a
Figure1. energy(a) Chandra
keV non-radiating
image, binned byparticles
a factor ofto2 andGaussianσ = 16with
pixelsarcsec).
VLAthe1.5-GHz
simpleofconstantvelocity
andA using
lineardistance(LD) fromk is theratio0.3–3
of thethe smoothedradiatingwith a power-law
model"(15.8= 1.8.
similarscaling
iscontours
used
toare
deter−1
2 (Half-Poweroverlaid, starting 3σ above the rms noise level of 0.3 mJy beam and increasing by factors
2. Thebeam
sizetip
is 16
theofthebackofrestoring
the lobe
to theof ×the15.1
jetarcsec
as active
measuredfrom
relativistic electrons. We assume k = 1, indicating equal energy
mine
expected
contribution
fromcoronallybinaries
andthe radio
Beamwidth, HPBW). Annular regions used to examine the surface brightness across the cavityrim
aremarkedinwhite.
(b)
XMM–Newton
0.3-3
keV
waveletimages invariables,
Section based
4. Weonfoundthat forboth lobes
adv ∼ 0.004c
cataclysmic
the relationof Sazonov
et al.υ(2006)
in radiating
and image,non-radiating
The factor
ϵ describesthesmoothed
MOS+pnwith scalesparticles.
chosen to exclude
point sourcesand emphasize
diffuse emission. Dark
linear features show chip gaps and bad columns,
−1
for
the
westernlobe
and ∼1200
km sSurface
for the east(∼1300
km
s−1
and
scalingusing
0.5-keV,solar
orderingof ignored.
the magnetic
field andresidual
we adopt
ϵ = 3, theindicating
andshould be(c) XMM–Newton
map, showing
image aftera the removal
and fillingof apointsources,andabundance
subtraction APECof themodel.
best-fittingbrightness
profilesweredetermined
ellipticalchosenern
surfacebrightness
model
for thegalaxyand largeretgrouphalo, smoothed with a Gaussianof σ one).
= 4 pixels(17.6
arcsec).
The solidusing
ellipsesindicateregions
the opticaltangledmagnetic
field,
as in
O’Sullivanal. (2011b).
toindicate
match
the
distribution,
with
axial
ratio
1.24
and
poBy comparison,
theto
sound
speed
insizetheandIGM
in theenvironment
D25We
contours
smaller galaxies
in the field.
Thethoughdashed ellipses
the opticalregions lightuseddefine thecavityposition.
(d)∼ 54261µGand
forseveral
both eastern
and western
lobes,
find of
BeqNGC
3 4261,(wherethepositionangle
is brightness
definedasprofiles
theangletemperaangle
68.◦annuli
XMM–Newton
residualmap,
as in(regions
the lower 4
left-hand
and thepartialused
to extract
thesurfacearoundNGCestimatedfromthemeasured
X-ray
closecontourssition
the outer partsof thelobes
and 8)panel,
have overlaid
higher with
Beq , VLA
−1
betweenthemajor-axisandduewest).
Regions
corresponding
to km s−1
across the cavity rims.
ture, increases from about 380 km s near the core to 590
to the estimate for the source as a whole ∼6.4 µG. For this field
the X-ray jets were excluded, but testing shows that these make only
beyond∼100
arcsec.
Theadvance
speed
of
the
lobe
tip
therefore= 100 radiate at ∼5 MHz.
(see later), electrons at γ
a minorcontribution
inantheapproximation
central bins oftothethe
profile.
It is clear thatthe monoenergetic exposureminmap and PSF, determined for an enful, but
simplyto beprovidecore
emission,
appears
tosupersonicrelative to the IGM.
Conversely,
the Alfvénthe observed
surface brightnessissteeperthanthat
expectedergy of 1 keV, approximating the mean photon energy of the data. A
to allow
it to be subtracted.
A secondprofile
β-model
was
added
to
model
5
km s−1 (using
theextended
lobe plasma
properin thefrom
lobetheis about
10
forspeedemissionstellarpopulation,
background
image
consisting of the scaled particle-only image andlarge-scalegroup emission,
with theslope and but
coremoreradiusfixed atthan
5.3 Radiativeage
deducedin Section
6.2). Thatthat
is, speedof
ofthe
expansionof the lobe
theties
Chandra
1-keV
PSF,theconfirming
emission= 1.68 arcmin,
β = inscaled pn OOT events image was used, and convolved and unconthe values
determined
from
ROSAT (rcore muchis bandstrongly
sub-Alfvénic,
so will notwas
excitemagnetic
shocksfrom hot
When flat
considering
the useddevelopment
and lobes, we 0.31,thisDavisetarisesal. 1995),
but gas.
a lowandnormalization
found
for
volvedmodels wereto accountofforthe
theradio
X-rayjets
backgroundin the lobes.
The internal
speedof thefor
waves in thesuggestingthat thecharacteristic
central β-modelaccounted
andanya residual
particle background,
adopt
simple conceptualmodel, inrespectively.
which at any given time plasma this component,
relativistic
plasmacalculated fromofmagnetizedtheemissionin the field.
Fig.
2were
shows
showedthat themodellingAGN
as atippoint
is Experimentation
rapidly transportedout from
central theengineto theof the jet. most 3.3
Spectralpropertiesof thecavityrimsthe XMM–Newtonbrightness
sourcedeltathefunctionconvolved
c profile, with fitted model components for
At this(apoint
jet floworisnarrowhalted Gaussian
by contact
with the with
IGM,theand the radial surface, in the system, it is possible that the(3)υA =the!ongoing jet activity
Given
PSF)
wasdriven
not effective,
probably
becausethe emission
fromuptcl +Pradio
plasmaout of thejet moves
outofradially
to formthethelobe. In comparison.
1are+
radio
lobesany
still2P
expanding.
they
are expanding
subsonically,
examineresidual
structure,Ifwesubtracted
the best-fitting
jets
densethegasagein theof thegalaxy.
We thereforemagthisandmodel,of centre
the lobe
plasmais linked
to the modelled
distance along Totheir
X-raybrightinrims
mustof compressedgasremoved
which maymodel froman imagewhich
theconsist
point sources
had been
the core with a β-model. The model was fixed to be circular, since
the jet; the back of the lobes (close to the nucleus) formed whenis be
the Alfvénmore
expressed
in m s−1 , u ptcl is
the enυ A tobewhereexpected
rapidly
and replaced(usingthe cooling
DMFILTHtask),and thanthen its
thesurroundings.
OOT read- If
the extended emission towards north and south tended to drive theespeedthejet
only
extendedafew
kiloparsecs,
while
the
tips
of
the
lobes
ergy
densityoftherelativistic
particle
population
andPmag is thetheyareexpanding
at
or
above
the
sound
speed,
thelobes
out streak was subtracted. The resulting residual map is shownin willmodel to extreme ellipticities. The best-fitting parameters for thishave only
recently.
In principle, backflows
could develop, Figs 1(c)
+1.2
+0.01
magnetic
fieldpressure.
cause
shock
heatingof thenorthsurroundinggas.
XMM–Newton,
and(d). Theemissionand southof Using
the coreproducesmodel
were formed
rcore = 1.0−1.0 arcsec and β = 0.55−0.02 , but we again
we foundresiduals,
no significant
temperature
differences
betweencavitytransporting
plasmaaway fromjet tips into
regions of the strongest
emphasize
thatyounger
this model
is not intended
to bethephysicallymeaningbut structuresassociatedwith theradio thelobes
rims and regions immediately inside and outside the cavities. This
the lobe formed at earlier times. However, in the absence of such a
6
D
I
S
C
U
S
S
I
O
N
is unsurprising, since
the regions used are necessarily large and⃝flow, or external forces causing reacceleration, plasma in the lobes
C 2011 The Authors, MNRAS 416, 2916–2931
includeunresolved
point
sourcesand gas at aSociety
range of⃝C temperatures.
Monthly
Notices of
the Royal
Astronomical
2011 RAS
is expected to age passively, with the high-frequency break in its
6.1
The
age
of
the
sourceWhile the field of viewof the ACIS S3 CCD limits our ability tospectral index falling to lower frequencies over time.
examine the edges of the radio lobes with Chandra, we can examine
Before considering the implications of our radiative age measureThe radiative age of the radio source of NGC 4261 can be calcuthe southern parts. Fig. 1(a) shows a series of partial elliptical anFigure 4. 0.3–2 keV Chandra image of the core of NGC 4261, withments,
firstuseddiscuss
potential
sourcesbrightnessof error injump
our acrossapproach. We
lated 0.493
if thearcsec
breakfrequency of the source is known (e.g. Myers &nuliwhichwe
wereto search
for a surface
pixels smoothed with a Gaussian of σ = 2 pixels (upper panel)
performed
relativelyof tothematch
1.55–4.86-GHz
Spangler1985). The
magnetic
field
is considered
to beuniform
and adaptively
smoothed
Chandratemperaturemap (lower
panel).
The
thehavesouth-east
lobe aedge.
These simple
regionsmodellingwere chosenthe←Chandra image
O’sullivan+201110

10-12 210

0.5
Beq[(1 + z)νbreak ]−0.5 Myr,22
Beq + BCMB

Downloaded from http://mnras.oxfordjournals.org/ by guest on January 19, 2016-2and constant over the whole of the source lifetime when radiative
losses dominate over expansion losses. Neglecting reacceleration
processes, the radiative age (the time since the last period of injection of relativistic electrons began) can be obtained as

Downloaded from http://mnras.oxfordjournals.org/ at Uchu Kagaku Kenkyujo on January 19, 2016

1.4GHz VLBA
2.3GHz VLBA
5GHz VLBA
8.4GHz VLBA
15GHz VLBA
22GHz VLBA
43GHz VLBA
1.4GHz VLA
5GHz VLABest fit VLBABest fit VLA
kolokythas(2015)
O’sullivan(2011)
O’sullivan(2011)10

Jet pressure P (dyn cm )rmin(arcsec); n=n(In the case of the jet P=nkT
pressure
is controlled by
the external pressure)
3

10

4

5

6

7

8

10
10
10
10
10
De-projected distance r (RS)

9

10

kev

colour bar indicates the approximate gas temperature in keV. The two panels
have the same alignment and angular scale.

Figure 2.25: Radial profile of jet pressure. The horizontal axis shows distance from the central
engine, which is taken account for the core shift eﬀect. The vertical axis shows jet pressure. Colora Chandra image of the core and jets. As noted by Worrall et al.
variation describes each observed frequency; orange: 1.4 GHz with VLA, gray: 5.0 GHz VLA, (2010),
red: there are wedge-like surface brightness decrements in thearea immediately north and south of the western X-ray jet, and a
1.4 GHz with VLBA, green: 2.3 GHz with VLBA, blue: 5.0 GHz with VLBA, purple: 8.4 GHz withsuggestion of similar structure on the eastern side (see also figs 2 and
4 of Worrall et al. 2010). The emission bordering these decrements is
VLBA, light blue: 15 GHz with VLBA, yellow: 22 GHz, black: 43 GHz VLBA, respectively. Red

somewhat brighter and extends to a larger radius than the emission

shape of the apparent surface brightness feature, with large widths
to increase the signal-to-noise ratio in each bin. Fig. 5 shows the
MNRAS
1732–1744
exposure-corrected surface brightness ineach bin.450,
A peakis found (2015)
at the position of the lobe rim, where the surface brightness exceedsthat immediately outside the rim at > 3σ significance (a 3.4σ difference between bins 3 and 4). This corresponds reasonably wellwith the feature observed in the XMM–Newton images.
If this surface brightness increase is the result of a shock, the standard Rankine–Hugoniot jump conditions (e.g. Landau & Lifshitz

DISCUSSION

Magnetic field Strength B (G )D. Magnetic field strength
10

1

10

0

10 -1

(i)

(ii)

B(r) [G]1.4GHz VLBA
2.3GHz VLBA
5GHz VLBA
8.4GHz VLBA
15GHz VLBA
22GHz VLBA
43GHz VLBA
1.4GHz VLA
5GHz VLABest fit VLBABest fit VLA

10 -2

10

(i) ∝ r -0.81 0.01(ii) ∝ r -1.25 0.01
(iii) ∝ r -0.29 0.03

-3

(iii)

10 -4

10 -5 2
10

10 3

10 4
10 5
10 6
10 7
De-projected distance r (RS)

10 8

10 9

E. Magnetic energy ∝ B2W(r)2 [erg/RS]

10 5

-1

(ergmascm-2))
Magnetic field energy B W(r) (Jy

DISCUSSION

4

10

3

10

2

10

1

10

0

(i)

(ii)
(iii)

2

2

10

10

-1

The total energy per unit jet length
1.4GHz VLBA
2.3GHz VLBA
5GHz VLBA
8.4GHz VLBA
15GHz VLBA
22GHz VLBA
43GHz VLBA

10 2

10 3

1.4GHz VLA
5GHz VLABest fit VLBABest fit VLA
error

Sharply
increasing

10 4
10 5
10 6
10 7
10 8
De-projecteddistance
Distance
fromthe BHr (R[Rs]S)

Decrease the energy in (i) and (ii)
Energy is injected into the magnetic field in (iii)

10 9(i) ∝ r -0.24 0.01(ii) ∝ r -0.48 0.01
(iii) ∝ r -0.83 0.15

DISCUSSION

The transition of spectral index in region (iii)-0.2

The spectral index change -1.6 → - 0.6 in >10 RS -0.4
→ Evidence of the particle acceleration→ The kinetic energy is dissipatedinto the particle energy(and also magnetic energy)

Spectral index

α

8

10-4

sp.index
1GHz VLA
5GHz VLA

-0.6

-5

10

-0.8
-1.0
-1.2

-6

10

-1.4
-1.6
-1.8
-2.0
7
10

(iii)

(ii)

(i)
Magnetic energy→ Acceleration
Parabolic

104 RS

Conical-1
Flux density per mas F’ (Jy mas )

0

8

10
De-projected distance r (RS)radiation

Dissipation
kinetic energy → Electron andmagnetic field
106 RS Conical

9

10

-7

10

Pext
Pjet

DISCUSSION

10

5

10

4

10

3

10

2

2

(i)(ii)

(i)

10 1

10

Decrease the energy in (i) and (ii)
Energy is injected into the magnetic field in (iii)

1.4GHz VLBA
2.3GHz VLBA
5GHz VLBA
8.4GHz VLBA
15GHz VLBA
22GHz VLBA
43GHz VLBA
1.4GHz VLA
5GHz VLABest fit for VLBABest fit for VLA

2-2

MagneticMagnetic
energyB2W(r)2 [erg/RS]
field energy B W(r) (erg cm )Energetics of the jet from forming to dissipation(ii)

Parabolic

0

10

2

10

3

(iii)

10

4

(iii)

The first suggestion of the jet energetics
by using observational results

Conical561010De-projected distance r (RS)Distance from the BH

10

7



10

8

10

[Rs]

9

BH gravity sphere

Magnetic energy→ Acceleration
Parabolic

104 RS

Galactic gravity sphere

(iii)

(ii)

(i)

Magnetic energy → Kinetic energy(+ radiation energy?)
à bulk Acceleration
Kinetic energy → Magnetic energyà bulk Deceleration

Conicalradiation

Dissipation
kinetic energy → Electron andmagnetic field
106 RS Conical

Pext
Pjet

DISCUSSION

Comparison of 5 samples

Jet structure and transition

FR I

Nagai et al. 2014n Parabolic à Parabolic• Cygnus A a~0.5à0.5

FR II

De-convolved jet width W (RS)n Parabolic à Conical• M87
a~0.5à1• NGC 6251
a~0.5à1• NGC 4261
a~0.5à1
p Over-collimation à Conical• NGC 1052
a~0.03à1• (3C 84a~0.25à?)

1010
108
6

10

M87
NGC 6251
NGC 4261
NGC 1052
Cygnus A

104
2

10

ISCO

0

10

100

102
104
106
108
De-projected distance r (RS)1010

MilliJY/BEA

150

100

DISCUSSION

50

Over-collimation and plasma torus
0

400

200
0
-200
MicroArc seconds

700

500
300
100
MicroArc seconds

3. Transverse slice profile of the jet. The left and right figures show the
3C 84 also host plasmaFigure
torus
and
over-collimation
structure
profilesalong (a) and(b), indicatedby the dashed lines in Figure 1, respectively.
NGC 1052 hosts
plasma torus
factor estimated from the VLBI proper motions. We also perThe Astrophysical Journal, 785:53 (6pp), 2014 April 10

Nagai et al.

200

400

600

FigureSame
map as Figure 1, but the contours are plotted at the −20, 20,
formed a spectral energy distribution (SED)
fit to2.theobserved−1
440, . .speed,. , 640but
mJy
broadband spectrum using the estimated 28,
apparent
it beam with the convolved beam, FWHM 0.20 × 0.15
10
0.5
are the same contour levels and beam sizemas,
at the position
LL
failed to reproduce the optically thin radio
spectrumobservedangle 0◦ . TheseRR
by VLBI (Paper II).
as those reported in Dhawan et al. (1998).
power-law
fit
for
LL
While several possible scenarios to reconcile the discrepancy
0.0
power-law fit for RR
between radio and γ -ray properties have been discussed inupper limit (LL)
earlier works (Papers I, II, and III), it is of great interest to(a)upper limit (RR)
-0.5 the morphology of the 3C 84 jet wasinvestigate the presence of stratified structurewith a velocity
November
1. At that time,
gradient (Ghisellini et al. 2005) in the jetlimb-brightened,of 3C 84. According and all images available up to 2013 July 28 areto this scenario, the radio emission is mostly coming from theagreement-1.0with the image presented here. In theslower sheath, while the emission from inthevery
spine goodis beamingaway from the line of sight. Therefore,VLBA
the limb43
brightening
GHz images during the period 2002–2008 (Paper II),(b)
can be observed along the jet if the spine-sheathstructurestructureis-1.5
the transverse
was not very clear. This is probably due
present. Clear evidence of limb brightening is found in several
to 501the(Girolettilack ofet dynamic
range. Dhawan et al. (1998), Romney
AGNs such as M87 (Junor et al. 1999), Mrkal.
2008), Mrk 421 (Piner et al. 2010), and et1144+35(Giovannini-2.0 (2001) reported the 43 GHz VLBA
al. (1995),
and Lister
et al. 1999), but no clear signature of limbimages
brighteninghas
beenof 3C 84 as of 1990s. From those images, no clear
found in 3C 84 thus far. To detect the limb brightening, high-2.5
limb direction
brightening
though similar angular resolution
spatial resolutions that can resolve the transverseof the was seen,
jet and high dynamic range images are required.
In this paper, we
was achieved.
One might also think that this is due to the lackreport a new Very Long Baseline Array (VLBA)
observation
at-3.0
of dynamic range. However,
we note that the most sensitive
10 3
43 GHz to investigate the transverse structure of the jet in 3C 84.
4
5
10 3
10
10
by Dhawan et al. (1998) achieved better image noise
We mainly focus on discussing the originobservationof limb brightening,
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
deprojecteddistance
from
the
core
[rg]
but we also present the collimation profilethat canobtained
MilliArc integration
seconds
thanourbeobservation,
thanks to a much longer
time
by resolving transverse direction.
1. 43andGHz total
map of 3C 84. The
are plotted at the Figure 4. Jet width profile. The open squares and open circles represent the(73% duty cycle for Figure
14 hr)
theintensity
participationof contours
one Very
The redshift of 3C 84 corresponds to the angular scale oflevel of 5.43 × (−1.41, 1, 1.41, 2.83, 4, 5.66, 8, 11.3, 16, 22.6, 32, 45.3, 64,
measurement for LL and RR maps, respectively. The filled triangle indicates
Largeantenna.90.5,
We128,also
createdan−1 .image
with the181, 256)
mJy beam
The peak intensity
is 2.17same
Jy beam−1 . The
0.344 pc mas−1 assuming H0 = 70.7 km s−1
Mpc−1Array, ΩM = 0.27,
color range is from 100 mJy beam−1 to 700 mJy beam−1 . The ellipse shown the upper limit constrained by the FWHM of a single Gaussian component.
and ΩΛ = 0.73. The mass of the centralcontour
super massive
black
levelsandconvolved
beam
as
the
image
presented
inatthebottomleft
corneroftheimage
indicates
the
FWHM
of
the
convolved
The error of jet width is smaller than the size of each symbol. The horizontal
hole was estimated to be 3.4 × 108 M⊙ Dhawan(Wilman etetal.al.
2005),The FWHM
the convolved beam
is 0.24visible
× 0.13 mas(seeat the position(1998), beam.
but thelimb ofbrightening
is still
axis is shown in the deprojected distance, assuming the viewing angle of 25◦ .
which yields 103 rg = 9.5×10−2 mas, where rg is Schwarzschildangle 0.◦ 69. The white dashed lines (a) and (b) indicated in the figure are the
Figure2).
Therefore,
theapparent
transverse
structure
of
the
jet
Both vertical and horizontal axes are shown in the unit of Schwarzschild radius.
slice locations for Figure 3.
radius.
MilliArc seconds

Jet width [rg]C1

C3

W ∝ r 0.25

0.03

C2

has indeed changed recently, and this change has occurred at

3C 84 jet suggests
Pext ∝ r-1 (Nagai+14)
Here, we adopt 3.4 × 10 M for the black hole mass (Wilman et al. 2005).
8⊙

2. OBSERVATIONS AND DATAANALYSIS
least
before 2010 November(firstepochself-calibrationsof Boston program)
both phase andamplitudeusing the DIFMAP The dashed and dotted lines are the power-law fits for LL and RR data, and theresultant power-law indices are 0.25 ± 0.03 for both cases.

softwarepackage (Shepherd
al. Lister1994). 2001).
The observations were carried out using
VLBA1999
stations
and10after
April (theobservation
epochetof
at 43 GHz on 2013 January 24. The data consists of eightThe
resolvedjetintransverse
direction
allowsus to study
3.
RESULTS
intermediate frequencies (IFs) with a 32 MHz bandwidth forthepolarization.
jet width Bothprofile. We produced the slice profiles of the total
separation between two outer components as the jet width.
each IF. Total bandwidth is 256 MHz per
Figure1shows
theself-calibrated
image
of 3C 84. In previous
right-hand and left-hand circular polarizations
were acrossobtained,the jet at different cross-sections along
intensity
the jet. mostly The slice at 0.15 mas from the core is represented by a single
studies
it
was
shown
that
the
parsec-scale
structureand only parallel-hand correlations (RR and LL) were obtained
The slices were madeconsisted
at everyof0.15
step (roughly
same
three mascomponents.
We have thedetected
the same Gaussian due to the lack of resolution. We regard the FWHM asin the correlation process because the polarization information
structure,a finerthe
scale
structure
is visible
from our image. the upper limit of the jet width. Figure 4 shows the jet width as a
sizeWeas performed
the synthesizedbeam)butfrom
core
along
the positionis outside the scope of this observation.
aThebrightcore
andone-sidedjetstructureisclearly
seen.
The
◦
◦
Walker+1995
phase-referencing mode observation by switching
the pointing
angle −10
up to 1.5 mas
and alongposition0 frombeyond.
◦jet position
angletheis −170
up toangle
1.2 masthe core and function of the distance from the core. The power-law fit yields
between the target source and the calibrator, J0313+4120. The◦
Examples of the slicethen
profilesshown
inposition
Figureangle
3. Theslightlyarechangesto the−180slice. At the end a power-law index of 0.25 ± 0.03. The change in the jet widthobservation consisted of many different scans for 3C 84 andof the jet, there
is a brightknot-likefeature. While thisprofilesarescanwellis represented
by twoGaussiancomponents.
To feature as a function of the distance indicates the collimation profile ofthe calibrator as well. The integration timefor eachwasrepresentedbyasingleGaussiancomponent(labeled
C3 in
10 s. Total observing time for 3C 84 evaluate
is about 45theminutes,
jet width,wefittedtwo
Gaussians
to
the
slice
Figure 1) in the previous studies, multiple subcomponents are the jet, which is a key quantity in the study of the jet formationand the overall observations, including calibrator scans, were
profiles and measuredseen
thefrom
separation
thepatternpeaks
of jetthedirection mechanism. This will be discussed in Section 4.2. The issue
this image. between
The changing
of thespanned over 8 hours. The scans for 3C 84 were spread evenly
is approximately
consistent Gaussianwith the previously
detected path of of how to determine the jet width may be controversial. We
In uvsome cases
an additional
component
over different hour angles, and therefore Gaussians.
we obtained good
C3
motion(Paper
II).
There
is
an
elongatedfeature(C2)
coverage. In this paper, we do not presentbetween
the phase-referencing
two Gaussians
wasandwhichweinvokes
regarded
the toward
the west
fromrequired,
the C3 region,
the backflow
from also evaluated the jet width by the separation between the outerimage but focus on the self-calibrated image. The purpose of
C3. However, C2 was already been present before the emergencephase-referencing analysis is to measure the core-shift effectof C3. Therefore, the origin of C2 and its connection with C3
3 is(e.g., Hada et al. 2011). This will be reported in a forthcoming
not very clear. We did not detect any significant emission frompaper (T. Haga et al., in preparation).
the counter-jet side.
The data reduction was performed using the AIPS developed
The most remarkable finding is that the limb brightening isby the NRAO. An a priori amplitude calibration was performed
evident along the approaching jet, which is the “restarted” jetusing the aperture efficiency and system noise temperature proassociatedwith an ongoing activity started in 2005. Similar
vided by each station. The opacity correction for the atmosphericquality of images have been available from the Web site ofattenuation, fringe fitting, and bandpass calibration were apBoston
University’s
blazar monitoring program9 since 2010
plied. For the deconvolution of the synthesized image, we used

Kameno+2001

The external pressure by plasma torus makes P∝r0(cylindrical) à Over collimation

CLEAN and the self-calibration technique. Final images wereobtained after a number of iterations with CLEAN as well as

9

http://www.bu.edu/blazars/VLBAproject.html

DISCUSSION

The transition point is nearby the plasma torus size
De-convolved jet width W (RS)910approaching jet
10 8counter jet
7bin-approaching10
bin-counter
10 6
approaching jet
5counter jet
10combine
10 4
3
10
10 2
1
10
Plasma torus size ~ 0.5 pc
0
10(Kameno+ 2003)
-1
10
-1
0
1
2
3
4
5
6
10
10
10
10
10
10
10
10
De-projected distance r (RS)

10

7

10

8

10

9

The torus (over-)collimates the jet in NGC 1052 (and 3C 84) ?

DISCUSSION

Comparison of 5 samples

about Jet width10

p Narrow jet : 2 sources• M87 ( i~11 deg)
• NGC 6251 ( i~19deg)
p Broad jet : 3 sources• NGC 4261 (i~63 deg)
• NGC 1052 (i~86 deg)
• Cygnus A (i~75 deg)

De-convolved jet width W (RS)

10

108
6

10

M87
NGC 6251
NGC 4261
NGC 1052
Cygnus A

104
2

10

inclination
Narrow jet

small

Broad jet

large

ISCO

0

10

100

102
104
106
108
De-projected distance r (RS)1010

DISCUSSION

Layer of the jet
3C 84
RadioAstron 22 GHz

M87
VSOP 5 GHz(Asada et al. 2016)

p Limb-brightening (Observation)p Spine--sheath (Theoretical model)

Crediti: RadioAstron /G.Giovannini(UniBo/INAF),
M.Orienti (INAF)

Inner and outer layer
have different speed

CygnusA
VLBI 43 GHz (Boccardi et al. 2016)

DISCUSSION

Beaming/de-beaming effect due to jet speed and inclination
Inclination small: faster layers get large Doppler factor (Brightening)
Inclination large: Slow layers are relatively brighter than fast layer
although both layer get dark

Narrow
M87, NGC 6251

NGC 4261
NGC 1052
Cyg A

g
Beaminning)(Brighte

Broad

De-beaming
Dimmining)
inclination i

8

10

107

Assumptions in each layer (1) different brightness temperature(2) different jet speed

Projected distance (arcsec)

-5

10

6

10

-4

-3

10

-2

10

-1

10

0

10

1

10

2

10

10

2

10

101
0

10

-1

10

5

10

-2

10

4

10

-3

10

3

VLA

10

2

10

1

10

-1

10

-4

10

-5

10

VLBA

0

10

à Think the beaming effect viewing from inclination ~75 deg
Co-moving flame
No beaming effecta-6

10

VLBI 43 GHz AJ
VLBI 4.9 GHz AJ
VLA 22 GHz AJ
VLA 4.9 GHz AJ
VLBI 43 GHz CJVLBI 4.9 GHz CJ
VLA 22 GHz CJ
VLA 5 GHz CJ

-1

10

0

10

1

10

2

3

4

5

De-convolved jet width (arcsec)

Big jump in Jet-width
profile (Cygnus A)

-7

10

9

10

De-convolved jet width W (r) (RS)DISCUSSION

-6

10

-7

10
6

10
10
10
10
10
De-projected distance r (RS)

7

10

8

10

9

10

Gradually accelerated

Low brightness(<106K)
Slow outer layer

High brightness (>108K)
fast layer

Observer flame
Beaming effecta
VLBI beam (>107K)
cannot detect outer layer
because of detection limit

VLA beam (>102K)
cannot detect inner fast layer
because of de-beaming effectn Brightness ration Flux ratio

Intrinsic brightness ratio
between inner and outer layer
TslowBint/TfastBint = 0.01
p=2-α; α~0.7(spectral index)
Γ: jet speed
δ: Doppler factor
W: Jet width
i: inclination angle
θ: Resolution of telescope

outer

Lorentz factor(slow layer)

Big jump in Jet-width
profile (Cygnus A)
5
4
3
2
1

Lorentz factor(slow layer)

DISCUSSION

5
4
3
2
1
1

0.001

1

0.01

5

0.01

(a) Brightness ratio

0.1

1

10
15
Lorentz factor (fast layer)
0.1

5

We considered quantitatively

1

20

25

(b) Flux ratio
10

10
15
Lorentz factor (fast layer)

VLBI beam
non-accelerated area

10

100
20

25

VLA beam
Accelerated area
inner cannot
detect because of
the de-beaming
effectcannot detect because of detection limit of telescope

DISCUSSION

Big jump in Jet-width
profile (Cygnus A)
10

9

10

Projected distance (arcsec)

-5

10

10

-4

-3

10

-2

10

-1

10

0

10

1

10

2

10

10

2

VLBI 43 GHz AJ
VLBI 4.9 GHz AJ
VLA 22 GHz AJ
VLA 4.9 GHz AJ
VLBI 43 GHz CJVLBI 4.9 GHz CJ
VLA 22 GHz CJ
VLA 5 GHz CJ

8

10

107

De-convolved jet width W (r) (RS)

-6

6

10

10

1

10

0

10

-1

10

5

10

-2

10

4

10

-3

VLA

3

10

10

-4

10

2

10

-5

10

VLBA

1

10

-6

10

0

10

-1

10

-7

10
-1

10

0

10

1

10

2

3

4

5

6

10
10
10
10
10
De-projected distance r (RS)

7

10

8

10

9

10

De-convolved jet width (arcsec)-7

Recent theoretical models suggest that outerlayer is faster than the inner one,e.g. Nakamura+ 2018
It is also possible that the big jumpin Cygnus A jet is really expanding …
We have to more study for this mysterySummary
We found common / different properties of AGN jet
width profiles and approached its forming mechanism
1. Structure development (distance dependence)l The structural transition point depends on the objectl Bipolar jets are quantitatively symmetricl Jet locally over-collimated by plasma torusl The structural transition differs between FR-I and FR-II type
2. Multi-layered structure?
l 5 samples of jet width suggests multi-layer structure,l which causes differences in apparent jet width dependingon the Inclination angle (beaming effect).

Summary
We suggest the energetics of NGC 4261 jet by observational
measurements (jet-width & radiation profiles) at first.
Increasing the magnetic energy andluminosity per unit jet length

Decreasing the magnetic fieldenergy and radiation

Balanced the Jet pressure
and the external pressure

Structuraltransition

(ii)

(i)

radiation

Dissipation
kinetic energy → Electron andmagnetic field
Conical104 RS
106 RS Conical
BH gravity sphere
Galactic gravity sphere

Magnetic energy→ Acceleration
Parabolic

(iii)

Pext
Pjet