1. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 A unified time-dependent view of relativistic jets G. Henri Laboratoire d ’Astrophysique de Grenoble, France

2. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Why is variability important ? Theoretical models of jets are often underconstrained : Steady-state models can fit instantaneous spectra with a large range of parameters and even basic assumptions (e.g. hadronic/leptonic models) Multi - , high sensitivity observations showing variability are much more constraining

3. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Good data available Highly sensitive instruments in gamma-ray (e.g. HESS) are crucial tools to get well resolved light curves.

4. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Simple models Assume leptonic models, basically synchrotron + SSC Simplest models = 1 zone « blob », homogeneously filled by B field, relativistic particles, moving relativistically with  b Must specify B, R,  b and particle distribution bb B R 

5. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Time dependent models 1-zone models can be transformed in time dependent models assuming some particle injection law (impulsive or continuous) Particle energy distribution : Power -law (1st order shock acceleration); (or broken power-law) Quasi-maxwellian or « pile-up » (2nd order diffusive acceleration, impulsive) (peaked around  0 )

6. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 A one-zone model with a pile-up One-zone injection of a pile-up distribution during a finite time Saugé & H. 2004

7. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Limits of the 1-zone model Does not reproduce the low energy part of the spectrum Evolution of geometrical parameters (Katarzynski 05..) ? Emission of « old » flares?

8. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 From the blob to the jet How to account for the long range emission? « Blob in jet » model (Katarzynski et al.) Successive flares -> succession of blobs Continuous emission -> time-dependent injection

9. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 The « Two flow » model  Two flow model : 2 distinct flows (Sol, Pelletier, Asséo ‘85, H. & Pelletier ‘91), introduced first for explaining radio observations (similar to later « spine in jet » model, Ghisellini et al.) MHD jet e - p+ mildly relativistic *carries most of the power *fuelled by accretion disk *large scale structures, hotspots Ultra relativistic e + -e - pair plasma * Generated in the « empty » funnel, no baryon load. * Produces high energy photons and relativistic motions * Energetically minor component

10. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 The « slow » MHD component Baryonic jet can be emitted from the accretion disk through MHD mechanism ( a la Blandford-Payne) (Ferreira et al., ‘97, ‘04) B field extract angular momentum and power from the JED (Jet Emitting Disk) Powerful, but only mildly relativistic (0,5 - 0,9 c)

11. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Formation of the relativistic pair plasma In situ generation of pair plasma in the inner MHD funnel (H.& Pelletier 91, Marcowith et al. ‘95) Produced through gamma-ray emission Injection of some relativistic particles X-ray and gamma-ray emission by IC and/or SSC  annihilation forms new pairs Continuous reacceleration by MHD turbulence necessary for a pair runaway to develop. Limited by the free energy available: saturation must occur at some point. Intermittent production possible and even probable !

12. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Recipe for a stratified, variable jet 1)A geometry R(z,t) 2)A B-field distribution B(z,t) 3)A Lorentz factor  b(z,t) 4)A Particle distribution n( ,z,t) Even in « thin » jet, 1-D approximation, requires full function of z and t : much more involved than 1-zone models To describe a continuous jet, one needs

13. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Parametrized by a « shifted » power-law Jet geometry Determined by MHD solutions (inner funnel) Assuming some interconversion process Conservation of poloidal flux Bp  R(z) -2 Conservation of current B   R(z) -1 ∝ R0R0 RiRi z0z0 Z=0

14. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Particle energy distribution In the spirit of 1-zone model, we adopt a pile-up distribution Apparent power-law can be reproduced by a spatial convolution of peaked functions (e.g. standard accretion « multicolor » disk model)

15. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Evolution of particle distribution along the jet Reacceleration necessary (short cooling time)  0 evolves following acceleration vs cooling Where acceleration is assumed to follow a power-law with a spatial cut-off Total particle flux evolves through pair production and annihilation

16. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Bulk Lorentz factor Light e+-e- very sensitive to the radiation field In an anisotropic photon field from an accretion disk, Compton force can be accelerating (radiation pressure) or decelerating (Compton drag) following bulk  b -> Bulk equilibrium Lorentz factor for which the aberrated net photon flux vanishes. Cold plasma Hot plasma Slowly accelerating Saturates to a asymptotic Lorentz factor (works only with external reheating (Compton rocket)-> 2-flow model only ! )

17. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Compton equilibrium velocity Compton rocket model does not seem to work for TeV blazars  b too low at small distances (imposed by variability) TeV blazars = BL Lacs = weak accretion disk !! (cf MHD accretion disks) Other acceleration (hydrodynamic?) mechanism ? Parametrized to vary from 1 to on a scale z 0

18. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Bulk Lorentz factor Bulk Lorentz factor constrained by  opacity Cospatial distribution of soft photons ->  ≥ 50 (Begelman et al 2008) Pair production necessary for the 2-flow model, needs  ~1 !! Choose the lowest value of  b compatible with pair production and variability. Stratified jet helps for lower  b..

19. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Limits on Lorentz factor Minimal constraint with hardest distribution (pile-up) H. & Saugé 2006

20. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Steady state solutions Instantaneous SED is a complicated convolution of the whole history of the jet, integrated all over the length. High energy data dominated by a single or a few flares Low energy data averaged over numerous flares (duty cycle f)

21. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Steady state solutions Construction of a « fake constant flaring state » by multiplying low energy points by f -1 (estimated from flaring duty cycle) Boutelier T., PhD thesis

22. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Time dependent solutions Procedure Construct a set of fake « constant » states (varying density and/or acceleration rate) from quiescent to « fake flaring » state Find a history of injections to fit light curves, taking into account light travel time.

23. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Variability constraints. i Z0=ctZ0=ct

24. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 PKS 2155-304 flare  b :15 cosi:1 R i : 1.1e+14 cm R 0 : 1.78e+14 cm Z 0 : 2e+15 cm Z max : 5e+19 m B: 5 G Q 0 : 6.5 N tot (z 0 ) : 40 cm-3 (quiesc.) 600 cm-3 (flare)  : 0.2 : 1.9  : 1.27

25. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Pair production flare With the chosen parameters, intense pair production occurs during a flare. Strongly non linear behavior

26. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Delayed variability Larger wavelengths variability is delayed and smoothed TeV injection optical X-ray

27. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 The video…. >200Gev flux

28. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Physical grounds for variability In the model, variability is reproduced by a small variation of initial density and/or acceleration rate only. Could be the result of non-linear feedback and hysteresis cycle, but very difficult to simulate (-> weather forecasts !) Pair production threshold sharply peaked-> strongly instable Onset of « Active » periods (yr time range) : changes in accretion rate, MHD structure Rapid flares (min to hr range) : bursts in pair production ? Leaves more room for complex variability pattern (possible long distance reacceleration sites in MHD jet, knots….

29. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Comments on bulk Lorentz factor Although in the lowest part of allowed range, bulk Lorentz factor still too high to be compatible with the « unification » model of radiogalaxie. Weak geometrical collimation ? Must go beyond the 1-D « thin jet » approximation. ( see Lenain et al… work ) FRI galaxy (unbeamed counterpart of BL lacs)  j > 1/  b 1/  b Lack of superluminal motion? Radial  b gradient?

30. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008 Future TeV HESS 2, CTA GeV GLAST Hard X-rays : SIMBOL-X Will hopefully bring a complete coverage of high quality data…. High sensitivity, time and energy resolved observations are a key factor to test models