•Relativistic Electrons, ‘nonthermal’ synchrotron emission
•Energy E, Lorentz factor γ = (1-v2/c2)-1/2
•Relativistic beaming: cone angle 1/γ
•νmax = 0.069 γ2(eB/mc) sinψ where the angle is between the line of sight
and B.
•For isotropic
velocity distribution, <ν>=5E2B, with frequency in MHz, E in GeV, and B in μG.
•One to one
relationship between frequency and energy, and a power-law
flux distribution means a power-law energy distribution. Fν = k1ν-α, then N(E) = k2E-λ.
And λ = 2α + 1
•Optically thick
at low frequencies (synchrotron self-absorption) and Fν = k1ν2.5 (see, eg. Brotherton et al. 2002)
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