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

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

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)

Synchrotron Spectra

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)

Compton Scattering

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

Klein-Nishina Effects sT 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

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).

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

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

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

EBL Absorption (Finke et al. 2010)

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

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