Thomson, Compton, and inverse Compton sca3ering Ghisellini 5.1 5.4 Rybicki & Lightman 3.4, 7.1, and 7.2
Thomson, Compton and inverse compton
Outline IntroducHon Thomson sca3ering Dipole approximahon Thomson cross sechon Compton sca3ering Compton wavelength Klein- Nishina cross sechon
Inverse Compton and processes around it
J.J. Thomson Discovered the electron (Noble price 1906) Explained sca3ering when Replica of his cathode tube
Athur H. Compton 1927 Nobel Price for Compton sca3ering: parhcle nature of waves
His data
Cosmic rays IonizaHon of air increase with AlHtude also Theodor Wulf and Domenico Pacini Victor Hesse 1913: Noble in 1939
Cosmic ray spectrum It is a power law spectrum
How to measure them Pampa Amarilla, ArgenHna Auger experiment: extensive air shower
The origin
GalacHc cosmic rays First direct proof: Fermi gamma- ray observatory
Ultra high energy Cosmic Rays thought to be extragalachc AcHve galachc nuclei? Gamma ray burst?
AcHve GalacHc Nuclei
Ultra high energy Cosmic Rays Various experiments suggest CR clustering in the direchon of CenA Centaurus A the nearest AGN 3 Mpc away, Black hole of 3 10 7 Msun, giant radio lobes out to 250 kpc
Blazar spectrum
Blazar spectrum
Gamma ray burst
What are elashc collisions?
Thomson sca3ering: ν << m e c 2 /h Dipole approximahon Thomson cross sechon: Polarized wave Unpolarized waves
Dipole approximahon When there are many parhcles with r i, u i and q i, with i=1,2,3, N, the radiahon field at large distances can be approximated by adding E rad for each parhcle The retarded Hmes are different for each parhcle. This can be ignored when the size of the system is small compared to the wavelength: λ >> L
SummaHon over individual charges E rad becomes the summahon over the individual charges: Where the electric dipole moment is given by:
GeneralizaHon of the Larmor formula in terms of the dipole moment
Electron sca3ering = Thomson sca3ering The force due to a linearly polarized wave is: In terms of the dipole approximahon with d=er:
The emi3ed power and cross sechon RewriHng the Larmor formula gives: The flux of the incoming wave is: The cross sechon is defined by:
Sca3ering of unpolarized waves Consider the superposihon of two linearly polarized orthogonal waves The emission in direchon is obtained by sca3ering from over angle and over
Pa3ern of polarized sca3ered radiahon
Pa3ern of unpolarized radiahon
Results The amount of polarizahon depends on the sca3ering angle: The total cross sechon:
Compton sca3ering Compton wavelength Compton sca3ering: Klein- Nishina cross sechon
Sca3ering of photon by an electron
DerivaHon of Compton wavelength ConservaHon of energy: ConservaHon of momentum: For a photon: p = hf/c and hf = pc Electron energy before and aoer: ConservaHon of energy gives then:
conhnued The momentum of the electron: ConservaHon of momentum gives: Make use of the scalar product:
conhnued Rearranging and subshtuhng gives: This gives us the compton wavelength:
Results Compton wavelength: 0.002426 nm for an electron For long wavelengths the sca3ering is close to elashc, and one can assume that there is no change in photon energy
Klein- Nishina cross sechon The change in photon energy can be wri3en as: The differenhal cross sechon for unpolarized emission is:
conhnued Klein- Nishina in terms of the thomson cross sechon: Limits Small energies: Large energies:
Total Klein- Nishina cross sechon
The differenhal Klein- Nishina cross sechon
Photon energies aoer sca3ering
Results Compton cross sechon decreases large photon energies Sca3ering becomes preferenhally forward for large photon energies For large sca3ering angles and when x >> 1, the sca3ered photon energy is x 1 ~ 1/2