Radiation Processes

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Radiation Processes

• High Energy Astrophysics
• jlc_at_mssl.ucl.ac.uk
• http//www.mssl.ucl.ac.uk/

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• Interaction of radiation with matter
  Photoelectric absorption and the ISM Thomson and
  Compton scattering Pair production Synchrotron
  self-absorption Inverse Compton scattering
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Absorption Processes

• Photon emission processes have corresponding
  absorption processes
• We will consider
• X-ray absorption.

Emission processes Recombination Inverse
Compton e-/e annihilation synchrotron emission
Absorption process Photoionization electron
scattering e-/e pair production synchrotron self
absorption
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Photon Absorption Process Cross Sections

• Absorption coefficients are plotted
• against photon energy for the three
• processes
• - Photoelectric absorption
• - Compton effect
• - Pair production

• Absorber is lead plots shift
• up and down in energy with
• Z increasing or decreasing
• Photoelectric absorption is
• dominant at low energies
• and pair production at high
• energies (E gt 2moc2) while
• the Compton effect is
• dominant at intermediate
• energies

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Photoionization
e-

• Atom absorbs photon

Atom, ion or molecule
Cross-section (s) characterized by edges
corresponding to ionization edges.
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Photoelectric Absorption Cross-section
The photoelectric absorption cross-section for
photons with En gt EI and hn ltlt mec2 is given by
-
sK 4v2 sT a4 Z5 (moc2/n)7/2
where EI is the electron binding energy, a is the
fine structure constant and sT is the Thomson
cross-section
Note dependence on Z5 and on n-7/2
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Example of photoelectric absorption

• eg. soft X-rays from a star absorbed by ISM

interstellar cloud
star
observer
I
I
n
n
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How much passes through?

• Take a path of length dl (metres)
• is the number density ( ) of element
  Z.
• Cross-section offered by element Z at energy
• E is given by

dl (m)
dV
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• The fraction of volume dV which is blocked by the
  presence of element Z is
• Thus fraction of flux F lost in volume dV is
• or

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Integrating over length from source...
Including all elements in the line of sight
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Optical depth

• This becomes

This is t, the optical depth, which has no
dimensions
This is the effective cross-section, weighted
over the abundance of
elements with respect to hydrogen
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Interstellar Medium Absorption Cross-section
The effective photoelectric absorption
cross-section, seff, is plotted against
wavelength in Å for the interstellar medium for
an assumed set of interstellar element
abundances (Morison and McCammon, 1983, Ap.J.,
270, 119)
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Column density

• The column density given by
• is the number of H atoms per m2 column
• Column density is measured from the 21cm
• atomic hydrogen line - but not foolproof.
• There is a factor of 2 uncertainty, wide beams,
• molecular hydrogen contamination...

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Clumping of the ISM

• Take an example at low energies, e.g. at

At a distance, d100 pc
Average ISM density
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Smooth versus clumpy

• star

observer
smooth
clumpy
Cold dense clouds
Hot medium
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Numerical example

• Through the smooth medium -
• Through the clumpy medium -

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Electron scattering

• Thomson scattering
  - the scattering of a photon by an
  electron
• where the photon energy is much less than
• the rest mass of the electron.
• Compton scattering
  - photons have a much higher energy in
  this
• case and lose some of their energy in the
• scattering process.

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Thomson Scattering

• low-E photon scattered by electron -
• Thomson cross-section is given by -

electron
, where
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Thomson scattering cont.

• If N number of particles per

then fraction of area blocked by a square metre
of path
1m
1m
If R is the extent of the absorbing region along
the line of sight,
( optical depth)
and
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Compton scattering

• In Compton scattering, wavelength increases
• and frequency decreases i.e. photon energy
• decreases

electron
q
frequency change
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Compton scattering (cont.)

• On average,

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Electron-positron pair production

Two photons, one of which must be a g-ray with E
gt 2mec2, collide and create an electron-positron
(e-/e) pair. This is therefore a form of g-ray
absorption
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Minimum g-ray energy required

• Must first demonstrate that
  is a relativistic invariant.

Rest energy of particle,
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• Thus, from and
  ,

And this is a relativistic invariant
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• Total initial momentum,
• thus

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• But since ,
• and -

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Calculating the minimum energy

• Assuming e and e- have no momentum
• and since
  ,

Which gives us this expression for the energy of
the g-ray photon
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And this is...

• found by simply making the denominator as
• large as possible, ie when cos(q) -1, or when
• q180 degrees.

g-ray
e-/e photon
And the minimum g-ray energy is given by
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Photon-nucleus pair production

• In the laboratory, it is more usual to consider
  photon-nucleus production. So why do we
  ignore it in space?
• Photons and nuclei have a similar cross-section,
  and the g-ray does not differentiate much between
  another photon or a nucleus.
• Then we must compare the photon density with the
  particle density in space.

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Photon versus particle density

• e.g. for 3 K m-wave background photons -

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Corresponding to about 10 photons / m
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No of nuclei in space is about 10 / m
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Synchrotron Self-Absorption
e-
e-
Relativistic electrons moving in a magnetic field
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Synchrotron Emission

• Electrons, mainly responsible for emission at
  frequency n, have energy, E, given by

and for a power law electron spectrum
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Blackbody turnover

• Assume Synchrotron power-law cut off, nmax, is
• given by
• and assume each electron emits and absorbs only
  at
• this peak frequency. Then, we will replace this
  with
• the mean energy per particle for a thermal source
  or
• E kT

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On the Rayleigh-Jeans side...
n
Rayleigh-Jeans approximation to blackbody...
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Source distance

• For dsource distance and Rsource size,

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Total flux at Earth...

• So total energy flux at Earth is given by

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SSA spectrum
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and SSA frequency

• Substituting for W then

and
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SSA in Compact X-ray sources
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• X-ray frequency, n10 Hz
• If F 10 J m s Hz - typical X-ray
  source value
• d 10 kpc and B 10 Tesla
• (the field for a neutron star)
• This gives a maximum for R of 1 km for SSA of
  X-rays to occur (ie for n to be observable in
  the X-ray band).
• but a neutron star diameter is 10 to 20km

-29
-2
-1
n
8
a
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Radiation processes (summary)

• Thermal - Bremsstrahlung
  electron energies photon energies
  to produce X-rays, b v/c 0.1
• Non-thermal - Synchrotron and Inverse Compton

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Synchrotron Emission

• For an electron spiralling in a magnetic field B
  with
• energy E, the peak radiated frequency, nm is
• nm g2 B e/2 p mo
• E2 B e/2 p mo3 c4
• But E g mo c2 - for a relativistic
  electron
• Hence g2 2 p mo nm/B e

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Electron energies required

• Synchrotron emission
  depends on the magnetic field strength.
  Assuming equipartition of energy - starlight,
  cosmic rays magnetic fields have all the
  same energy density in Galaxy
• and from , gt B6x10
  Tesla
• To produce X-rays of nm 1018 Hz, we need

-10
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Inverse Compton Scattering
For a relativistic electron colliding with a low
energy photon, gIC2 hnfinal/hninitial

• For X-ray production consider
• - starlight lthngt 2eV (l6000A)
• - 3K background lthngt 3x10 eV
• then
• for stars
• for the 3K background
• We need cosmic rays!!!

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• RADIATION PROCESSES
• END OF TOPIC