Radiation Processes

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Radiation Processes

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

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Absorption Processes

• So far, considered the production of X-rays.
• Now, will consider X-ray absorption.

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

• Atom absorbs photon

Atom, ion or molecule
Cross-section (s) characterized by edges
corresponding to ionization edges.
4
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
6

• The fraction of volume dV which is blocked by the
  presence of element Z is
• Thus the fraction of flux 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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Column density

• The column density is given by
• 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, eg 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, the photon wavelength
  increases, ie its energy decreases.

electron
q
frequency change
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Compton scattering cont.

• On average,

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Electron-positron pair production
e-

• g-ray

y
q
x
e
e-/e photon
Two photons, one of which must be a g-ray,
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, ie when q180
  degrees.

g-ray
e-/e photon
And the minimum g-ray energy is given by
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Minimum energy for mm-wave photon

• g-ray photon interacts with mm-wave
• First converting to eV
• l1.2mm corresponds to hn10 eV

-3
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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

• eg., for 3K m-wave background photons -

9
3
Corresponding to about 10 photons / m
6
3
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 Spectrum

• Flux emitted as a function of frequency

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Blackbody turnover

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

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

• For dsource distance and Rsource size,

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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
• Assume F 10 J m s Hz
• 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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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
• from , gt B6x10
  Tesla To produce X-rays,

-10
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Inverse Compton Scattering

• Consider starlight lthngt 2eV (l6000A)
• or 3K background photons, lthngt 3x10 eV
• then
  
• for stars
• for the 3K background, to produce
  X-rays. We need cosmic rays!!!

-4
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Non-thermal process (cont.)

• Energy distribution of cosmic ray particles
  within a unit volume has the form
• (over at least part of the energy range)
• We use this to determine the relative importance
  of synchrotron and IC processes

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• Power radiated in the two processes is about
  equal in the case of equipartition of energy
• ie when
• ie an electron with a given g loses energy
  equally rapidly by the two processes
• However, it does not mean that X-rays are
  produced at the same rate in the two cases.

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Ratio of IC to Synchrotron Xrays

• For example
• Galactic X-rays require
  (stars)
• 
  (3K)
• but for synchrotron

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Ratio IC to Synchrotron (cont.)

• Ratio (no of electrons with )
• (no of electrons with )
• But

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Ratio IC to Synchrotron (cont.)

• Thus
• So which is more important for producing
• X-rays via IC starlight or 3K background?

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X-rays from IC scattering

• (no. X-rays produced from starlight per )
• (no. X-rays produced from 3K per )

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IC - starlight versus 3K

• We know that
• and
• Thus ie 3K photons more important!

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IC or synchrotron for X-rays?

• Remember
• assuming for
• thus synchrotron dominates over IC in Galaxy

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Synchrotron emission

• Synchrotron emission requires very high energy
  particles however - and electron energy
  distribution may well have tailed off if there is
  no continuous re-supply.
• Also 3K radiation extends outside our Galaxy.
• Extragalactic radiation depends on whether
• there are enough electrons to produce IC.