A unified time-dependent view of relativistic jets

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

2. 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 - l , high sensitivity observations showing variability are much more constraining Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

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

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

5. 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 g0) Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

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

7. 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? Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

8. 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 Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

9. Ultra relativistic e+-e-pair plasma • * Generated in the « empty » funnel, no baryon load. • * Produces high energy photons and relativistic motions • * Energetically minor component 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 Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

10. 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) Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

11. 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 • g-g 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 ! Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

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

13. Jet geometry Determined by MHD solutions (inner funnel) Parametrized by a « shifted » power-law Z=0 R0 Ri z0 Conservation of poloidal flux Bp a R(z)-2 Conservation of current Bja R(z)-1∝ Assuming some interconversion process Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

14. 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) Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

15. Evolution of particle distribution along the jet Reacceleration necessary (short cooling time) g0 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 Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

16. Cold plasma Hot plasma 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 Gb -> Bulk equilibrium Lorentz factor for which the aberrated net photon flux vanishes. Slowly accelerating Saturates to a asymptotic Lorentz factor (works only with external reheating (Compton rocket)-> 2-flow model only ! ) Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

17. Compton equilibrium velocity Compton rocket model does not seem to work for TeV blazars Gb 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 z0 Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

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

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

20. 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) Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

21. 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 Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

22. 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. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

23. Variability constraints. Z0=bcDt i Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

24. PKS 2155-304 flare Gb:15 cosi:1 Ri: 1.1e+14 cm R0: 1.78e+14 cm Z0: 2e+15 cm Zmax: 5e+19 m B: 5 G Q0: 6.5 Ntot(z0): 40 cm-3 (quiesc.) 600 cm-3 (flare) w: 0.2 l : 1.9 z : 1.27 Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

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

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

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

28. 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…. Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

29. 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) 1/Gb Qj > 1/Gb Lack of superluminal motion? Radial Gb gradient? FRI galaxy (unbeamed counterpart of BL lacs) Blazar Variability across the Electromagnetic Spectrum, Palaiseau, Apr 22-25 2008

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