KleinNishina effects in blazars

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Klein-Nishina effectsin blazars

• Rafal Moderski
• Copernicus Astronomical Center
• POLAND

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Rafal Moderski, Copernicus Astronomical Center,
POLAND
Klein-Nishina effects in blazars
Inverse Compton energy losses When high energy
electrons scatter photons with energies h?mc2/4?
the electron cooling rate is substantially
reduced due to the Klein-Nishina effect the
reduction of the cross-section for scattering.
The rate of inverse-Compton energy losses of
relativistic, isotropically distributed electrons
is where and ue0 is the energy distribution
of the ambient radiation field, e0h?/mec2,
b4?e0 In Thompson limit (bltlt1) fKNFKN1, while
in the extreme Klein-Nishina case
Fig. 1 The function FKN(b) computed for
monoenergetic (mono) and power law (a00.0 and
a00.5) energy distributions of the external
photon field. The solid lines show the results
of the exact calculations while the dashed lines
are the analytical approximations fKN(1b)-1.5
for monoenergetic distribution, and FKN(1b)a0-1
for power law distributions.
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Rafal Moderski, Copernicus Astronomical Center,
POLAND
Klein-Nishina effects in blazars
Energy distribution of electrons The
Klein-Nishina effects change the steady state
electron energy distribution due to inefficient
cooling of the high energy electrons through
Compton scattering. The continuity version of the
kinetic equation for the electron is where Q is
the electron injection function. A steady state
solution of the continuity equation is and
where we assumed that electron energy losses are
dominated by inverse Compton process and by
synchrotron radiation and qu0/uB
Fig. 2 Steady state electron energy
distributions for power-law electron injection
function, Q?-p, and mono-energetic ambient
radiation field. Solid lines - exact results
dotted lines - results obtained using the
continuous energy loss approximation for all
Compton scattering. The model parameters are
p2, q30 bmax 1 10 100 1000.
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Rafal Moderski, Copernicus Astronomical Center,
POLAND
Klein-Nishina effects in blazars
Spectrum The Klein-Nishina effects do not
influence the IC component of the spectrum the
decreased efficiency of Compton scattering is
compensated by the corresponding increase in
their equilibrium density. The synchrotron
component, though, changes significantly. Spectra
of both synchrotron and inverse-Compton emission
for a steady-state electron distribution are
approximately given by where is the
average energy of photon produced by the
scattering of photon of energy e0 by electrons
with energy ?
Fig. 3 Inverse-Compton plus synchrotron
spectra of steady sources with model parameters
p2 q30 bmax1,10,102,103,104 e010-4 B1G.
Upper panel - mono-energetic ambient radiation
field. Lower panel power-law ambient radiation
field with a00.5. Solid lines exact
calculations. Dotted lines - calculations using
continuous energy loss approximation. Dashed
lines - Compton spectra computed using the
continuous energy loss approximation and the
delta-function approximation. The dashed line in
the lower panel is the asymptotic power law
(a-0.5) for the IC spectrum at high energies.
To show convergence to this spectrum for
increasing bmax, the lower panel also shows the
IC spectra obtained for bmax105, 106, and 107.
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Rafal Moderski, Copernicus Astronomical Center,
POLAND
Klein-Nishina effects in blazars
Synchrotron bump The hardening of the electron
distribution is reflected in the synchrotron
component as a_formation of the synchrotron
bump. The synchrotron spectrum at high
energies asymptotes to a spectrum with the same
slope as the low energy (Thomson regime)
asymptote but with a normalization that is a
factor q higher. An interesting consequence of
the very different behaviors of the high energy
portions of IC and synchrotron spectra is that
for the case of a flat electron injection
spectrum (plt2), the luminosity of the synchrotron
peak will exceed the luminosity of the IC peak no
matter how large we make q.
Fig. 4 Synchrotron spectral 'hardening', ?a, as
a function of b. Model parameters bmax8, and
q10, 100, 1000.