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

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

A unified time-dependent view A unified time-dependent view of relativistic jetsof relativistic jets

G. HenriG. HenriLaboratoire d ’Astrophysique de Grenoble, FranceLaboratoire d ’Astrophysique de Grenoble, France


Why is variability important ?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


Good data availableGood data available

Highly sensitive instruments in gamma-ray (e.g. HESS) are crucial tools to get well resolved light curves.


Simple modelsSimple 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

BBRR


Time dependent modelsTime 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)

€

n(γ ) = n0γ2 exp −

γγ0

⎛

⎝ ⎜

⎞

⎠ ⎟

€

n(γ ) = n0γ−p

(peaked around 0)


A one-zone model with a pile-upA one-zone model with a pile-up

One-zone injection of a pile-up distribution during a finite time

Saugé & H. 2004


Limits of the 1-zone modelLimits 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?


From the blob to the jetFrom 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


The « Two flow » model 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

QuickTime™ et undécompresseur TIFF (LZW)

sont requis pour visionner cette image.

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 « slow » MHD componentThe « 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)


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 !

hvs X,e+e-


Recipe for a stratified, variable jetRecipe 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


Parametrized by a « shifted » power-law

€

R(z) = R0ZZ0

+RiR0

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ω ⎡

⎣

⎢ ⎢

⎤

⎦

⎥ ⎥

ω

Jet geometryJet geometry

Determined by MHD solutions (inner funnel)

Assuming some interconversion process

€

B(z) = B0R(z)R0

⎡

⎣ ⎢

⎤

⎦ ⎥

−λ

Conservation of poloidal flux Bp R(z)-2

Conservation of current B R(z)-1 ∝

€

1< λ < 2

R0Ri

z0

Z=0


Particle energy distributionParticle energy distribution

In the spirit of 1-zone model, we adopt a pile-up distribution

€

n(γ;z;t) = n0(z;t)γ 2 exp −γ

γ0(z;t)

⎛

⎝ ⎜

⎞

⎠ ⎟

Apparent power-law can be reproduced by a spatial convolution of peaked functions (e.g. standard accretion « multicolor » disk model)


Evolution of particle distribution along Evolution of particle distribution along the jetthe jet

Reacceleration necessary (short cooling time)

0 evolves following acceleration vs cooling

€

dγ0dτ

=Qacc − Psync − PIC

€

Qacc =Q0zz0

⎛

⎝ ⎜

⎞

⎠ ⎟

−η

exp(−zzc

)

Where acceleration is assumed to follow a power-law with a spatial cut-off

Total particle flux evolves through pair production and annihilation


Bulk Lorentz factorBulk 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.

€

b,eq (z) ≈zRi

⎡ ⎣ ⎢

⎤ ⎦ ⎥

1/ 4

Cold plasmaCold plasma

Hot plasmaHot plasma

Slowly accelerating

Saturates to a asymptotic Lorentz factor(works only with external reheating (Compton rocket)-> 2-flow model only ! )


Compton equilibrium velocityCompton 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 ?

€

b(z) ≈ 1+Γb∞

−a −1

1+z0z

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

a

Parametrized to vary from 1 to

€

b∞on a scale z0


Bulk Lorentz factorBulk Lorentz factor

Bulk Lorentz factor constrained by Bulk Lorentz factor constrained by opacity opacity

Cospatial distribution of soft photons -> Cospatial distribution of soft photons -> ≥ 50 (Begelman et al ≥ 50 (Begelman et al 2008)2008)

Pair production necessary for the 2-flow model, needs Pair production necessary for the 2-flow model, needs ~1 !! ~1 !!

Choose the lowest value of Choose the lowest value of bb compatible with pair production compatible with pair production and variability.and variability.

Stratified jet helps for lower Stratified jet helps for lower b..b..


Limits on Lorentz factorLimits on Lorentz factor

Minimal constraint with hardest distribution (pile-up)

H. & Saugé 2006


Steady state solutionsSteady 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)


Steady state solutionsSteady 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


Time dependent solutionsTime 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.


Variability constraints.Variability constraints.

€

Δtobs ≈z0βc

(1− β cosi) ≈z0

Γbδc≈z0

Γb2c

≈R0δc

i

Z0=cΔt


PKS 2155-304 flarePKS 2155-304 flare

b:15cosi:1Ri: 1.1e+14 cmR0: 1.78e+14 cmZ0: 2e+15 cmZmax: 5e+19 mB: 5 GQ0: 6.5Ntot(z0) : 40 cm-3 (quiesc.)600 cm-3 (flare): 0.2 : 1.9 : 1.27


Pair production flarePair production flare

With the chosen parameters, intense pair production occurs during a flare.

Strongly non linear behavior


Delayed variabilityDelayed variability

Larger wavelengths variability is delayed and smoothed

TeV

injection

optical

X-ray


The video….The video….

>200Gev flux


Physical grounds for variabilityPhysical 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….


Comments on bulk Lorentz factorComments 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?


FutureFuture

•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

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

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