Alma Mater Studiorum Universit`a degli Studi di Bologna ... - Inaf

1.2. Non-thermal emission mechanisms of active galaxies 3
fields in astrophysical sources.
Lorentz factorγ(electron energyǫ=γm e c 2 ) is:
dǫ
dt
The synchrotron power emitted by a relativistic electron with
[ erg
]
≃ 1.6×10 −3 (B [µG] sinθ) 2 γ 2 (1.1)
s
where θ is the pitch angle between the electron velocity and the magnetic field direction.
This equation illustrates the degeneracy between particle energy and magnetic field: a given
synchrotron power can be produced by a highly energetic particle in a low magnetic field or vice
versa.
The spectral distribution for a single electron can be assumed to be approximately
monochromatic since it peaks sharply at a frequency:
ν c [GHz]≃4.2×10 −9 γ 2 (B [µG] sinθ). (1.2)
From Eq. 1.2, it is derived that electrons ofγ≃10 4 in magnetic fields of B≃10µG produce
synchrotron radiation in the radio band (ν c ∼ 4 GHz), whereas electrons ofγ ≃ 10 7−8 in the
same magnetic field radiate in the X-rays. A representative example is given by the nearby active
galaxy Pictor A, where the spectrum of the jet from radio to X-ray wavelengths can be described
as synchrotron emission from a population highly energetic particles with a distribution of Lorentz
factors (Wilson, Young & Shopbell 2001).
For a homogeneous population of electrons with an isotropic pitch-angle distribution and a
power-law energy spectrum with the particle density between energiesǫ andǫ+dǫ given by
N(ǫ)dǫ= N 0 ǫ −δ dǫ, (1.3)
the total intensity spectrum, in optically-thin regions has the functional form:
S (ν)∝ν −α , (1.4)
where the spectral indexα=(δ−1)/2. This spectrum of Eq. 1.4 is described as non-thermal,
since the energy spectrum of the emitting particles is not Maxwellian - i.e. it does not have a
single temperature.
1.2.2 Polarization of synchrotron radiation
In the optically-thin case, for a homogeneous and isotropic distribution of relativistic particles
whose energy distribution follows the power law of Eq. 1.3 and in a uniform magnetic field, the
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