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 × 10¹¹ 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 × 10¹⁷ - 5.3 × 10¹⁸ 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.