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Paul Alexander Evolution of Radio Sources
Evolution of Compact Radio Sources
Paul AlexanderUniversity of Cambridge
Paul Alexander Evolution of Radio Sources
Radio-mode Feedback
Fanaroff & Riley Class-I 3C 66B
Fanaroff & Riley Class-II
3C 219
• AGN Feedback via radio sources critical for evolution of massive galaxies
With AGN Feedback
No AGN Feedback
Cygnus A radio and X-ray
= 60 kpc = 180 lt yr
0.01c
Vj ~ 0.8c
Paul Alexander Evolution of Radio Sources
Feedback on galactic-scale
CoralZ: De Vries, Snellen, Schilizzi, Mack, and Kaiser 2009
Need to understand source evolution on pc – kpc scales
Key to understanding physics of radio-mode feedback in galaxies
Paul Alexander Evolution of Radio Sources
Evolution on Large Scales
Schilizzi and McAdam 1975
• Never been able to use radio sources as distance indicators
• Looking at them you just can’t tell how far away they are!
Paul Alexander Evolution of Radio Sources
Self-similar Evolution
Paul Alexander Evolution of Radio Sources
• Structure is self-similar from scales of a few kpc to Mpc
Self-similar Evolution
Paul Alexander Evolution of Radio Sources
Dynamical Model: self-similar phase
jet: pj, rj, vj
cocoon: pc, rc, vc
swept-up gas
hotspot: ph, vhatmosphere: Tx, rx=r0(r/a0)-b
• Problem characterised by
D
W half-angle q
X
jjj
jjj
vAM
vAQ
30 2
1
• Two length scales
12/11
2/32/1
322
2/1
390
2/1
30
1
2
1
pcmkg10W10
56
22
LL
c
vQ
v
QL
b
jX
jX
• Assume throughout that cs in cocoon is sufficiently large that pc(t) is constant within the cocoon
Paul Alexander Evolution of Radio Sources
jet: pj, rj, vj
cocoon: pc, rc, vc
swept-up gas
hotspot: ph, vh
D
W half-angle q
• At some point cocoon pressure equals sideways ram-pressure of the jet
• jet comes into pressure balance with the cocoon via an oblique shock
critical feedback process22jjjc vpp
• At the hotspot
cjjh pvp 2
Drives forward expansion
Drives sideways expansion
• For D >> L1 get fully self-similar solution
• Independent dimensional quantitiesD, t, Q0, rX = r0a0
b
3
0
050
53
01
51
00
30
Q
a
tac
a
tQD
Dynamical Model: self-similar phase
atmosphere: Tx, rx=r0(r/a0)-b
Paul Alexander Evolution of Radio Sources
Compact sources: length scales
12/11
23
3
302
1
2
1
44
8
LL
Dv
vA
v
QL
b
X
j
jX
jjj
jX
• Jet density = external density
at L1b
X
vX
XXa
c
vM
MML
L
222
2
1
1 1.0~sin4
• Jet sideways ram pressure =
external pressure at L1a
Xjj pv 22 sin
jet: Q, rj, vj
Paul Alexander Evolution of Radio Sources
Dynamical Model: Early EvolutionInitial stage from D < L1b to jet reconfinement
In the rest-frame of the contact surface
But
Integrating
hjjjj pLLv ~~)( 20
2
322
jj vD
Q
11
22/1
11
b
jb L
tvLD
jet: Q, rj, vj
cocoon: pc, rc
hotspot: ph, vh, Vh ~ W3/2 D2L1
atmosphere: rx=r0
D
rx
cpr ~20
Governing equations
Energy conservation: radio source
01
1
1
11
1
Qdt
dVp
dt
dpV
dt
dVp
dt
dpV
hh
c
c
hh
c
cc
c
ccc
c
tp
rt
xtt
c d
2/1
)( 01
xxrVjL
xc d)(
0
2
Cocoon dynamics
b
j
LD
vD
11
Paul Alexander Evolution of Radio Sources
Dynamical Model: Early Evolution
0.0001
0.001
0.01
0.1
1
10
100
0.1 1 10 100 1000
2/ jj
c
LvQ
p
1LD
10-6
10-4
0.01
1
100
104
106
108
1010
0.1 1 10 100 1000
31L
Vc
Solution
2/3
1
2/14
2
1
31
4/3
2/1
1
2/14
1
121
4/1
2/1
11
~
~
112
L
DK
L
DLV
L
DK
L
D
Lv
Qp
L
tvLD
c
j
c
b
jb
jet: Q, rj, vj
cocoon: pc, rc
hotspot: ph, vh, Vh ~ W3/2 D2L1
atmosphere: rx=r0
D
rx
cpr ~20
Paul Alexander Evolution of Radio Sources
• Sideways ram pressure
• Cocoon pressure
• At some point
Dynamical Model: Recollimation
Solution
1
2/3
121
4/1
2/1
1
2/14
1
121
4/1
for~
~
LDL
D
Lv
Q
L
DK
L
D
Lv
Qp
j
j
c
jet: Q, rj, vj
cocoon: pc, rc
D 22
2
1
22 sinsin jXb
jj vL
Dv
42/1
1
22
2
1
3/11.014~
sin
L
L
vL
Dp
r
jXb
c
aD
Reconfinement shock must reach axis
Transition to self-similar evolution
Paul Alexander Evolution of Radio Sources
Luminosity Evolution
• Indicative: calculate p7/4V
• Ignore relativistic and radiative transfer effects
0.1
1
10
0.1 1 10 100 1000 10000 100000
bLD 1
cP
• Jet overdense
• Pn D1/4
ph/pc
2/3
1
2/14
2
1
31
4/3
2/1
1
2/14
1
121
4/1
2/1
11
~
~
112
L
DK
L
DLV
L
DK
L
D
Lv
Qp
L
tvLD
c
j
c
b
jb
Paul Alexander Evolution of Radio Sources
Luminosity Evolution
• Indicative: calculate p7/4V
• Ignore relativistic and radiative transfer effects
0.1
1
10
0.1 1 10 100 1000 10000 100000
bLD 1
cP
• Jet underdense
• Pn D7/8
ph/pc
2/3
1
2/14
2
1
31
4/3
2/1
1
2/14
1
121
4/1
2/1
11
~
~
112
L
DK
L
DLV
L
DK
L
D
Lv
Qp
L
tvLD
c
j
c
b
jb
Recollimation begins
Paul Alexander Evolution of Radio Sources
Luminosity Evolution
• Indicative: calculate p7/4V
• Ignore relativistic and radiative transfer effects
0.1
1
10
0.1 1 10 100 1000 10000 100000
bLD 1
cP
• Self-similar evolution inside galaxy
• Pn D2/3
• All constants now determined
ph/pc
Radiative losses become important
Self-similar evolution:
33
53
01
DcV
tacD
2
001
2D
a
Dp
xh
2
22 )1(
)1(2jj
j
jh vc
22
22 )1(
)1(2
jjj
jcjc vcpp
Paul Alexander Evolution of Radio Sources
Luminosity Evolution
• Indicative: calculate p7/4V
• Ignore relativistic and radiative transfer effects
0.1
1
10
0.1 1 10 100 1000 10000 100000
bLD 1
cP
• Self-similar evolution in halo
• Pn D(8-7b)/12
ph/pc
Synchrotron and inverse compton losses become
important
Self-similar evolution:
33
53
01
DcV
tacD
2
001
2D
a
Dp
xh
2
22 )1(
)1(2jj
j
jh vc
22
22 )1(
)1(2
jjj
jcjc vcpp
Paul Alexander Evolution of Radio Sources
Perturbing this evolution
• To form a cocoon require before external pressure collimates/disrupts the jet L1a >> L1b
• To reach the self-similar phase cocoon require before external pressure collimates/disrupts the jet L1a >> Lr
• If cocoon comes into pressure balance with external gas recollimation distance is always L1a , source shape very long and thin with
• Cocoon and hotspot RT unstable – need to consider swept-up gas in the evolution – some will form FR-I’s some will simply blow bubbles
6~22.0~ 2/12/1
1
1
XX
b
a MandML
L
8/33
1.03/125
XM
XX cDcD
for365.1
~2/1
Paul Alexander Evolution of Radio Sources
Perturbing this evolution
• Jet suffers KH instability
• External medium is cocoon (if formed) or external gas• In a power-law atmosphere
• Declining atmospheres help stabilise the jet to KH instability; estimate
e
j
e
jj c
vrD
21
~max
6/)2(max DD
D
kpcmkg10W10
5.2~2/1
322
2/1
370
max
XQ
D
Paul Alexander Evolution of Radio Sources
Self-similar Evolution
Vries, Snellen, Schilizzi and K.-H. Mack 2010
CoralZ: De Vries, Snellen, Schilizzi, Mack, and Kaiser 2009
Tests of radio source models usually use P-D tracks
VLBI delivers real measured speeds!
Paul Alexander Evolution of Radio Sources
Conclusions• Radio mode feedbak proposed as critical ingredient of galaxy
evolution
How efficient is it? How long does is last?
How does it work
• Answering these questions means studying radio source evolution Developed analysis of evolution for partially collimated
jets Discuss stability as well as dynamics: calculate efficiency
next
• What is really required are detailed observations of radio sources and their interactions on galactic scaleIdeal SKA science: high resoution high fidelity imaging