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!