Eva Lefa MPI-K/LSW Heidelberg Based on work in collaboration with - - PowerPoint PPT Presentation

Eva Lefa

MPI-K/LSW Heidelberg

Based on work in collaboration with Felix Aharonian and Frank Rieger

HEPRO III, Barcelona, June 27-July 1, 2011

• EBL and very Hard Gamma-ray spectra of Blazars
• Solution/interpretation through standard leptonic

scenarios

• Self-consistent Synchrotron self-Compton model
• power-law distribution with high “low energy cut-off”

in an expanding source

• Relativistic maxwellian-like distributions
• External Compton scenario

• Blazars’ TeV photons interact with EBL via
• Deformation of the emitted spectrum
• The spectra of some sources appear very hard with photon index

Γ≤1.5 even for the lowest level of EBL (1ES1101-232,1ES0229+200…) Aharonian et al. 2006 Ee

• 2 electron index

Eγ

• 1.5 TeV photon index (Thomson)

and steeper for Klein-Nishina regime

• “Exotic” scenarios

 Lorentz invariance violation (Kifune 1999 and others)  DARMA scenario (De Angelis et al. 2009)

• “Astrophysical” scenarios

 Secondary γ-rays from CR protons (Essey et al. 2011)  Up-scatter of CMB photons from extended jet (Bottcher et. al 2008)  Cold ultrarelativistic wind (Aharonian et al. 2002)  Internal absorption (Aharonian et al. 2008, Zacharopoulou et al. 2011)

• Within standard leptonic models? (homogeneous, 1-zone SSC)

We need hard electron energy distributions

 relativistic shocks/shear flows can produce distributions harder than

(eg. Derishev et al. 2003, Stecker et al. 2007) BUT: any hard injection spectrum of electrons, after radiative (synchrotron or Thompson) losses, gets a standard form “Ee

• 2”

• Katarzynski et al. 2007: homogeneous 1-zone SSC model of power-law

electrons with large value of electron minimum cut-off

• Hardest possible index at TeV range

(Tavecchio et al. 2009 for 1ES 0229+200 with γmin~5.105)

Electrons develop a γ -2 wing below γmin due to synchrotron losses

• Very low magnetic field (B ~ 4.10-4G)
• Practically no cooling
• Extremely large electron energy density

expansion of the source?

Tavecchio et al. 2009

• Need to consider time-depended solutions

(for radiative losses Mastichiadis & Kirk ‟98, Coppi & Aharonian „99)

• Adiabatic losses dominate over synchrotron losses when
• Spherical relativistic expansion with

constant velocity R=Ro+u(t-to) constant injection of power-law electrons

• Solution to kinetic equation

e.g. B~0.1G, R~1015 cm, γ<106

time

• γ0 at electrons  ν1/3 at synchrotron spectrum 

injected γ0min contribution dominates at low energies  hard slope can remain at TeV (for timescales relative to the source size) and relax assumptions for the parameters (B~0.1 G)

Cut-off frequencies drop: Adiabatic cooling: due to MF reduction Synchrotron cooling: due to evolution of γmin time

B~0.1G, R~1015cm, γmin ~5.105

• In reality synchrotron losses may alter the electron distribution at

high energies higher than raises with time so if then no modification at the hard TeV range

• Narrow distributions, Minimum cut-off ?
• Stohastic acceleration + synchrotron losses

(Schlickeiser 1985, Aharonian et al. 1986, and investigated later for modeling blazars e.g. Saugé & Henri 2004; Katarzynski et al. 2006, Giebels et al. 2007...)

• Steady state solution to Fokker-Planck equation:

relativistic Maxwell-like distribution

• Cut-off energy: at balance

between acceleration and losses, can take values of ~105 and more

 Fν ~ ν1/3 at TeV range (very good agreement with narrow power-law)  B-field of the order 0.1G (more reasonable parameters)  Energy losses under account

γc =1.5 105 γ‟c=3 γc B=0.08 G R=5.1014 cm (B/Bcr) γ3

c >>1

Compton peak at the electron cut-off energy

TeV data obtained with HESS, corrected for 2 EBL models of Francheschini, high level-red points, low level–green

• Electrons up-scatter external photon field, e.g. disk photons (of

planckian distribution) after reprocessed/rescattered by BLR clouds

• In ECS scenarios we can get even harder spectra Fν~v at TeV range

B=1G γc =4.104 T~2. 104 Γ=13

• Combination of narrow distributions, e.g. 3-4 blobs with maxwellian-like

electrons of different “temperatures” γc and same parameters

• Same energy in each blob -> power-law like spectra of index 2
• Hard features may arise in the spectrum if the energetics of a single

component change: very different γc, more energy, different doppler factor… EED SSC spectrum



Neronov et al. 2011: 30 days very hard flare with photon index Γ=1.1 at 10-200 GeV , no variability below 10 GeV (Γ=1.8)

Neronov et al. 2011



Neronov et al. 2011: 30 days very hard flare (photon index Γ=1.1) at 10-200 GeV , no variability below 10 GeV (Γ=1.8)

• Even very hard spectra can be approached within

standard emission scenarios under certain assumptions

• Limiting case for SSC is Fν~ν1/3, for ECS Fν~ ν1
• Narrow power-law electrons + adiabatic losses:

recover the hard TeV spectrum, higher MF

• Maxwell-like electron distributions can form naturally

hard TeV spectra under radiative losses

Thank you!