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Understanding Blazar Variability and Relativistic Jets: Time-Dependent View

This study explores the importance of blazar variability in constraining theoretical models of relativistic jets. It discusses simple and time-dependent models, injection laws, plasma formation, jet components, geometry, and particle distributions. The research emphasizes the need for high-quality data and sensitive instruments to enhance our understanding of blazar emission mechanisms. The presentation at the Blazar Variability conference in 2008 highlighted the complexities of jet dynamics and the challenges in modeling the electromagnetic spectrum variations.

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Understanding Blazar Variability and Relativistic Jets: Time-Dependent View

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  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

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