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

2. Paul AlexanderEvolution 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 V j ~ 0.8c

3. Paul AlexanderEvolution 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

4. Paul AlexanderEvolution 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!

5. Paul AlexanderEvolution of Radio Sources Self-similar Evolution

6. Paul AlexanderEvolution of Radio Sources Structure is self-similar from scales of a few kpc to Mpc Self-similar Evolution

7. Paul AlexanderEvolution of Radio Sources Dynamical Model: self-similar phase jet: p j,  j, v j cocoon: p c,  c, v c swept-up gas hotspot: p h, v h atmosphere: T x,  x =  0 (r/a 0 )  Problem characterised by D  half-angle  Two length scales Assume throughout that c s in cocoon is sufficiently large that p c (t) is constant within the cocoon

8. Paul AlexanderEvolution of Radio Sources jet: p j,  j, v j cocoon: p c,  c, v c swept-up gas hotspot: p h, v h D  half-angle  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 process At the hotspot Drives forward expansion Drives sideways expansion For D >> L 1 get fully self-similar solution Independent dimensional quantities D, t, Q 0,  X =  0 a 0  Dynamical Model: self-similar phase atmosphere: T x,  x =  0 (r/a 0 ) 

9. Paul AlexanderEvolution of Radio Sources Compact sources: length scales Jet density = external density at L 1b Jet sideways ram pressure = external pressure at L 1a jet: Q,  j, v j

10. Paul AlexanderEvolution of Radio Sources Dynamical Model: Early Evolution Initial stage from D < L 1b to jet reconfinement In the rest-frame of the contact surface But Integrating jet: Q,  j, v j cocoon: p c,  c hotspot: p h, v h, V h ~  3/2 D 2 L 1 atmosphere:  x =  0 D r x Governing equations Energy conservation: radio source Cocoon dynamics

11. Paul AlexanderEvolution of Radio Sources Dynamical Model: Early Evolution 0.0001 0.001 0.01 0.1 1 10 100 0.11101001000 Solution jet: Q,  j, v j cocoon: p c,  c hotspot: p h, v h, V h ~  3/2 D 2 L 1 atmosphere:  x =  0 D r x

12. Paul AlexanderEvolution of Radio Sources Sideways ram pressure Cocoon pressure At some point Dynamical Model: Recollimation Solution jet: Q,  j, v j cocoon: p c,  c D DD Reconfinement shock must reach axis Transition to self-similar evolution

13. Paul AlexanderEvolution of Radio Sources Luminosity Evolution Indicative: calculate p 7/4 V Ignore relativistic and radiative transfer effects Jet overdense P  D 1/4 ph/pcph/pc

14. Paul AlexanderEvolution of Radio Sources Luminosity Evolution Indicative: calculate p 7/4 V Ignore relativistic and radiative transfer effects Jet underdense P  D 7/8 ph/pcph/pc Recollimation begins

15. Paul AlexanderEvolution of Radio Sources Luminosity Evolution Indicative: calculate p 7/4 V Ignore relativistic and radiative transfer effects Self-similar evolution inside galaxy P  D 2/3 All constants now determined ph/pcph/pc Radiative losses become important Self-similar evolution:

16. Paul AlexanderEvolution of Radio Sources Luminosity Evolution Indicative: calculate p 7/4 V Ignore relativistic and radiative transfer effects Self-similar evolution in halo P  D (8-7  )/12 ph/pcph/pc Synchrotron and inverse compton losses become important Self-similar evolution:

17. Paul AlexanderEvolution of Radio Sources Perturbing this evolution To form a cocoon require before external pressure collimates/disrupts the jet L 1a >> L 1b To reach the self-similar phase cocoon require before external pressure collimates/disrupts the jet L 1a >> L r If cocoon comes into pressure balance with external gas recollimation distance is always L 1a, 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

18. Paul AlexanderEvolution 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

19. Paul AlexanderEvolution 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!

20. Paul AlexanderEvolution 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 scale Ideal SKA science: high resoution high fidelity imaging