The Inverse Compton Process

The inverse Compton process describes the interaction of a charged particle with a pho- ton in which the charged particle transfers some of its energy to the photon, upscattering the latter to higher energies (Figure 2.3). This is the opposite process to Compton scat- tering whereby the photon imparts energy to the electron during interaction, while itself losing energy. The Compton process is thought to be responsible for producing the high energy peak of the SED.

Inverse Compton scattering relies on the transformation of the energy and frequency of the photon during interaction between the moving frame of the electron (i.e. in this frame the electron is at rest) and the laboratory (observer) frame in which the electron and the scattered photon appears to be moving. The energy boost to the photon in the observer’s frame occurs as a consequence of the two transformations. The first is from the observer’s frame to the rest frame of the electron and the second transforms the energy and frequency of the scattered photon back into the rest frame of the observer.

Consider a charged particle, i.e. an electron, moving relativistically with energy

γmec2 interacting with a photon of frequency ν′, then in the rest frame of the electron,

Figure 2.3: This schematic represents inverse Compton process where the charged par- ticle interacts with a lower energy photon, resulting in the photon being upscattered to higher energies.

νe= ν′γ (1 + β cos θ) (2.7)

where γ is the Lorentz factor, θ is the angle between the incident and scattering direc- tions. In the rest frame of the electron, the photon is backscattered and thus moves with slightly less energy. However, in the rest frame of the observer, the energy and frequency of the photon appears much higher as a result of the transformation from the rest frame of the electron to the rest frame of the observer. The scattered energy of the photon in the rest frame of the observer is given by:

hν≈ 4γ2hν (2.8) This expression is valid if the incident photon energy in the rest frame of the electron is≪ mc2_{. This is known as inverse Compton scattering in the Thomson regime. Interac-}

frame of the electron≫ mc2. For the latter, the resulting energy of the scattered photon in the rest frame of the observer is given by:

hν≈ γmec2 (2.9)

The interaction cross-section will change between the Thomson and Klein-Nishina regimes depending on the energies of both the interacting photon and electron. In the following sections the IC process in these two regimes will be discussed.

Emission in the Thomson Regime

As discussed, the interaction occurs in the Thomson regime when the energy of the photon in the rest frame of the electron is hν≪ γmec2. In the classical limit, the IC

process is dominated by the Thomson cross-section in which the classical radius of the particle becomes an important aspect of the interaction. First, consider the Thomson scattering cross-section, σT:

σT = 8π 3 r 2 e (2.10) σT = 8π 3 ( e2 4πϵ_◦mec2 )2 (2.11) where re = e2 4πϵ_◦mec2

represents the classical radius of the electron. The total energy loss rate for an electron in the Thomson regime is:

( dE dt ) IC = 4 3σTcUrad (_v c )2 γ2 (2.12) where Uradis the energy density of the photon radiation field.

A characteristic feature of interaction in the Thomson regime is that the photons are scattered isotropically over a wide range of angles in the rest frame of the electron. In addition, the energy of the photon increases by γ2. In the Thomson regime, the relativistic electrons only transfer a small fraction of their energy during interaction and thus, a single relativistic electron may undergo several IC interactions.

Emission in the Klein-Nishina Regime

The interaction occurs in the Klein-Nishina regime if the energy of the low-energy photon in the rest frame of the electron approaches mec2. In the Klein-Nishina (K-

N) regime, the incident photon must have energy that fulfils the criterion such that 2γhν ≫ mec2in the rest frame of the electron. Thus, the quantum relativistic cross-

section for scattering must be applied. This also occurs when the photons are of low energy, i.e. hν ≪ mec2but the electrons move ultra-relativistically with γ≫ 1.

The latter is more typical of the blazar jet environment.

Both these cases lead to a scattering cross-section given by the following:

σK−N = πr2e 1 x ( ln 2x + 1 2 ) (2.13) where x = _mhν

ec2 and reis the classical electron radius. In the K-N regime, the IC

scattering of the photons is anisotropic and the gain in energy is only by a factor of γ, unlike the energy gain of a factor γ2 in the Thomson regime. In addition,

σK−N is smaller than σT. The decrease in the interaction cross-section in the K-N

regime reduces the efficiency of the IC process in this regime. The electron, on the other hand, loses a larger fraction of its total energy during interaction and as such undergoes only one IC interaction.

The similarity between the total energy loss rates in the synchrotron and IC processes (Equations 2.3 and 2.12 respectively) is a result of the energy loss rates being dependent on the electric field that accelerates the electrons in its rest frame, regardless of the ori- gin of that field. The difference between the total energy loss rates in both processes is the energy density of the magnetic field, Umag which affects the synchrotron process

and the energy density of the radiation field, Uradwhich affects the IC process. This fea-

ture is particularly important when considering the processes and emission produced in different leptonic emission scenarios (see Section 2.6).