Il (tl) = Il (0) e- ( )t l + Bl(T) (1 – e- ( )t l )

Synchrotron Radiation

nsy ~ 4.2*106 (B/G) g2 Hz

Relativistic electrons:Lo

g(I n

)

Log( )nnsy

n1/3

e- /n nsy

Synchrotron RadiationPower-law distribution of relativistic electrons:

log(

I n)

Log( )n

Ne(g) ~ g-p

jn ~ n-a = (a p-1)/2

n-(p-1)/2

Opt. thin

kn ~ n-b = b(p+4)/2

Opt. thick

n5/2

Synchrotron Spectra

Compton ScatteringIn the electron rest frame:

's =

For e' << 1 → e's ≈ e' (elastic scattering – Thomson Regime)

For e' >> 1 → e's ≈ 1 (inelastic scattering – Klein-Nishina Regime)

Compton Scattering

Compton Spectra

n-(p-1)/2

g1 = 10g2 = 106

p = 2e0 = 2*10-5

Klein-Nishina Effectss K

N

eg

1

sTFn

e2 es

c

e1

Klein-Nishina (Compton scattering)

cross section declines at eg ~ 1.

Cut-off in the resulting Compton-scattered spectra around esc ~ 1/e

1/e

Total Energy Loss Rate of Relativistic Electrons

g

-d/

gdt

Synch

rotron

Compton Scattering

1/e

ThomsonKlein-Nishina

Compton energy loss becomes less efficient at high energies (Klein-Nishina regime).

gg Absorption and Pair ProductionThreshold energy ethr of a g-ray to interact with a background photon with energy e1:

ethr = 2

e1 (1 – cosq)

e1

eg

e+ e-

q

epk ~ 2/e1

gg AbsorptionDelta-Function Approximation:

VHE gamma-rays interact preferentially with IR photons:

Spectrum of the Extrgalactic Background Light (EBL)

(Finke et al. 2010)

Starlight

Dust

EBL Absorption

(Finke et al. 2010)

gg Absorption Intrinsic to the SourceImportance of intrinsic gg-absorption is estimated by the

Compactness Parameter:

Radiation Transfer Equation gives:

Pair Production Spectrum

Interaction of two power-law photon spectra with indices = 1.5a

Simplest approximation: g+ = g- = (e1 + e2)/2

(e0 = 2 )g