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

2. Synchrotron Radiation
Relativistic electrons:
nsy ~ 4.2*106 (B/G) g2 Hz
e-n/nsy
Log(In)
n1/3
Log(n)
nsy

3. Synchrotron Radiation
Power-law distribution of relativistic electrons:
Ne(g) ~ g-p
jn ~ n-a a = (p-1)/2
kn ~ n-b b = (p+4)/2
Opt. thick
log(In)
Opt. thin
n5/2
n-(p-1)/2
Log(n)

4. Synchrotron Spectra

5. Compton Scattering 𝜀's = 𝜀′ 1+𝜖′(1 −𝑐𝑜𝑠  ′ )
In the electron rest frame:
𝜀's = 𝜀′ 1+𝜖′(1 −𝑐𝑜𝑠  ′ )
For e' << 1 → e's ≈ e' (elastic scattering – Thomson Regime)
For e' >> 1 → e's ≈ 1 (inelastic scattering –
Klein-Nishina Regime)

6. Compton Scattering

7. Compton Spectra
n-(p-1)/2
g1 = 10
g2 = 106
p = 2
e0 = 2*10-5

8. Klein-Nishina EffectssT
sKN
Klein-Nishina (Compton scattering) cross section declines at eg ~ 1. eg 1 Fn
Cut-off in the resulting Compton-scattered spectra around esc ~ 1/e e2 e1
1/e
esc

9. Total Energy Loss Rate of Relativistic Electrons
-dg/dt
Compton Scattering
Synchrotron
Klein-Nishina
Thomson g
1/e
Compton energy loss becomes less efficient at high energies (Klein-Nishina regime).

10. gg Absorption and Pair Production
Threshold energy ethr of a g-ray to interact with a background photon with energy e1: 2
ethr =
e1 (1 – cosq) e+ e- q
epk ~ 2/e1 eg e1

11. VHE gamma-rays interact preferentially with IR photons:
gg Absorption
Delta-Function Approximation:
VHE gamma-rays interact preferentially with IR photons:

12. Spectrum of the Extrgalactic Background Light (EBL)
Starlight
Dust
(Finke et al. 2010)

13. EBL Absorption
(Finke et al. 2010)

14. gg Absorption Intrinsic to the Source
Importance of intrinsic gg-absorption is estimated by the Compactness Parameter:
Radiation Transfer Equation gives:

15. Pair Production Spectrum
Simplest approximation:
g+ = g- = (e1 + e2)/2
(e0 = 2g)
Interaction of two power-law photon spectra with indices a = 1.5