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:
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.