Paul AlexanderEvolution of Radio Sources Evolution of Compact Radio Sources Paul Alexander University of Cambridge.

Paul Alexander Evolution of Radio Sources

Evolution of Compact Radio Sources

Paul AlexanderUniversity of Cambridge


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


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


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!


Self-similar Evolution


• Structure is self-similar from scales of a few kpc to Mpc



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


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


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


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


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


• 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


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





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





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





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


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


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



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!


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

Paul AlexanderEvolution of Radio Sources Evolution of Compact Radio Sources Paul Alexander University of Cambridge.

Documents

physics of radio

jet jet

radio sources critical

selfsimilar phase jet

l1a jet

recollimationsolution

l1b jet sideways ram

length scales jet density