*Astron. Astrophys. 354, L53-L56 (2000)*
*Letter to the Editor*
## The angular function for the Compton scattering in mildly and ultra relativistic astrophysical plasmas
**
S.Y. Sazonov**^{ 1,2} and
R.A. Sunyaev^{ 1,2}
^{1} MPI für Astrophysik, Karl-Schwarzschild-Strasse 1, 86740 Garching bei München, Germany
^{2} Space Research Institute (IKI), Profsoyuznaya 84/32, 117810 Moscow, Russia
*Received 10 December 1999 / Accepted 21 December 1999*
**Abstract**
Compton scattering of low-frequency radiation by an isotropic
distribution of (i) mildly and (ii) ultra relativistic electrons is
considered. It is shown that the ensemble-averaged differential
cross-section in this case is noticeably different from the Rayleigh
phase function. The scattering by an ensemble of ultra-relativistic
electrons obeys the law , where
is the scattering angle; hence
*photons are preferentially scattered backwards* . This contrasts
the forward scattering behaviour in the Klein-Nishina regime.
Analytical formulae describing first-order Klein-Nishina and
finite-electron-energy corrections to the simple relation above are
given for various energy distributions of electrons: monoenergetic,
relativistic-Maxwellian, and power-law. A similar formula is also
given for the mildly relativistic (with respect to the photon energy
and electron temperature) corrections to the Rayleigh angular
function. One of the manifestations of the phenomenon under
consideration is that hot plasma is more reflective with respect to
external low-frequency radiation than cold one, which is important, in
particular, for the photon exchange between cold accretion disks and
hot atmospheres (coronae or ADAF flows) in the vicinity of
relativistic compact objects; and for compact radiosources.
**Key words:** scattering
radiation mechanisms:
non-thermal
plasmas
accretion, accretion disks
*Send offprint requests to:* S.Y. Sazonov
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### Contents
© European Southern Observatory (ESO) 2000
Online publication: January 31, 2000
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