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Interaction of radiation with matter
- simple radiative transfer - synchrotron self-absorption
- photoelectric absorption - Compton and inverse Compton scattering * - pair production
4C15/SS7 (2006/2007)
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Radiation processes and their inverse processes
Photon emission processes have their correspondingabsorption processes.
Emission processes
recombination
e−/e+ annihilation
synchrotron emission
Absorption process
photo-ionization
e−/e+ pair production
synchrotron self-absorption
inverse Compton scattering Compton scattering
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Radiative transfer - basic formulation
Radiative transfer equation
absorption emission scattering
Emission and absorption only
Optical depth (absorption)
absorbing medium
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Radiative transfer - formal solution
Formal solution to the radiative transfer equation
source function
homogeneous medium
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Radiative transfer - opaque and transparent
opaque - large optical depth
transparent - small optical depth
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Radiative transfer - thermal emissionWhen the emission and absorption are in local equilibrium, the emission and absorption coefficient are related by the Planck function.
Kirochoff’s law:
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Synchrotron self-absorption (I)
for power-law electron energy distribution
synchrotron absorption and emission coefficients:
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Synchrotron self-absorption (II)
synchrotron source function
optically thin spectrum
optically thick spectrum
electron energy distribution
absorbed synchrotron spectrum
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Thermal absorption of cyclotron radiation
Rayleigh-Jean spectrum
optically thick part
optically thin part
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Internal thermal absorption
some features:
- Rayleigh-Jean (black body) spectrum at low frequency - peak frequency at which the optical depth is about unity
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Some common photon processes in high-energyastrophysics
MeV
Z
- photoelectric effect - Compton scattering - pair production
Lead
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Photoioniztion
ion or atom
electron
photon energy
cro
ss-s
ectio
n
ionization edge
photon
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Photoelectric absorption cross-section
For ,
the photoelectric absorption cross-section for photons is given by
,
where is the electron binding energy, is the fine-structure
constant, and is the Thomson cross-section.
Note that it depends on and on .
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Photoelectric absorption of soft X-rays byinterstellar media (ISM)
interstellar cloud
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Attenuation by ISM photoelectric absorption (I)
Consider a volume element witha thickness and with anelement Z which has a numberdensity of .
Suppose that the cross-sectionof the element is .
The fraction of the volume element blocked by the presence of theelement Z is .
The fraction of the flux lost in the volume element is therefore
.
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Attenuation by ISM photoelectric absorption (II)
Integrating over the light path in theISM yields
Including all elements in the line-of-sight,
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Attenuation by ISM photoelectric absorption (III)
Suppose that the flux attenuationcan be expressed as
effective cross-section weightedover the abundance of elementswith respect to hydrogen
line-of-sight hydrogen column density
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Effective cross-section and absorption features
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Electron-positron pair production (I)
θ
Two photons, one of which must have energy , collide andcreate an electron-positron ( ) pair. The process is effectively aform of gamma-ray absorption
photon
gamma-ray photonelectron
positron
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Electron-positron pair production (II)4-momenta of the 2 photons
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Electron-positron pair production (III)4-momenta of the electron-positron pair
For minimum photon energies, it requires that electron-positron pairdoes not have linear momentum.
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Electron-positron pair production (IV)
The minimum energy of one of the photons must therefore be largerthan the electron/positron rest mass.
Conservation of energy-momentum implies
Hence, we have
It follows that
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Electron-positron pair annihilation
photon
photon
electron
positron
θ
It is a reverse process of electron-positron pair production.