# 7.9 Compton scattering

Electromagnetic radiation interacts strongly with electrons. If a photon encounters an electron, there is a high probability that a **scattering** interaction will occur. In the low-energy non-relativistic regime, i.e. where *h* *m*_{e}*c*^{2} the interaction is called **Thomson scattering**, and its likelihood is described by the classical **Thomson scattering cross-section**, σ_{e}. In general, interactions between a photon and an electron include quantum mechanical and relativistic effects which modify the classical Thomson scattering process. The process in the regime where quantum and relativistic effects are included is known as **Compton scattering**, and a full discussion requires quantum electrodynamics, which is beyond the scope of this course. One of the immediate effects of the quantum nature of light is that the scattering of a photon by an electron is, in general, an **incoherent** process, i.e. in general energy will be exchanged between the electron and the photon, so the incoming and outgoing photons differ in frequency. Whenever the electron has sufficient kinetic energy compared to the photon, energy can be transferred from the electron to the photon. This is the so-called **inverse Compton process**, and is important in astrophysics.

## SAQ 6

Question: What frame of reference would you choose to assess whether ‘the electron has sufficient kinetic energy compared to the photon'?

### Answer

The rest frame of the observer is the obvious choice, since this is the frame in which the initial and final energies of the photon are to be measured. In the case of inverse Compton scattering occurring in an AGN, the rest frame of the AGN itself is a sensible alternative choice, since both the initial and final photon energies will be affected by the cosmological redshift.

For a population of relativistic electrons threaded by a magnetic field, loss of energy from the electrons due to synchrotron emission (see Section 7.5), *P* _{synch}, and the loss of energy from the electrons due to the inverse Compton process, *P* _{compt}, are related by the ratio of the magnetic field energy density, *U* _{mag}, and the photon energy density, *U* _{rad}:

The physical reason behind this simple relationship is that from a quantum viewpoint the synchrotron and inverse Compton processes are analogous. Synchrotron radiation involves scattering of electrons by the quanta associated with the magnetic field, while in inverse Compton scattering the electrons are scattered by real photons: quanta of electromagnetic radiation.

Radiation which has been boosted to higher energies by the inverse Compton process is often referred to as having been **Compton upscattered**. In the case of AGN, photons emitted by the synchrotron process can themselves be inverse Compton scattered by the population of relativistic electrons emitting them, thus emerging from the source with higher energies than they initially had. This is the so-called **synchrotron self-Compton (SSC)** process.