**3.3. Inverse Compton radiation**

Relativistic electrons in a radiation field can scatter and transfer energy
to photons through the inverse-Compton (IC) effect.
This situation where the wave gains energy from the electron is the
inverse of the usual Compton scattering. The frequency of the scattered wave
_{out} is related to that
of the incident wave
_{in} as:

(28) |

In astrophysical applications, the IC plays a very important role
since the relativistic electron population responsible for synchrotron
emission scatters the ubiquitous 3K microwave background photons. The
Planck function at T = 2.73 K peaks near a frequency of
~ 1.6 × 10^{11}
Hz, therefore from Eq. 28 the relativistic electrons of energy
= 1000 -
5000 will be responsible for IC emission in the X-ray domain,
respectively at ~ 2 × 10^{17} - 5.3 × 10^{18} Hz,
corresponding to ~ 0.9 - 22 keV. Microwave background
photons are then turned into X-ray or gamma photons.

Given that synchrotron and IC emission originate from the
same, assumed power-law, relativistic electron population
(Eq. 6), they share the same spectral index
.
The spectral index relates to the index of the power-law electron
energy density distribution as
=
2 + 1, and to
the photon index of the IC emission as
_{X} =
+ 1.