Radiation Processes

1
Radiation Processes

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

2
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
3
Photoionization
e-

• Atom absorbs photon

Atom, ion or molecule
Cross-section (s) characterized by edges
corresponding to ionization edges.
4
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
5
Example of photoelectric absorption

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

interstellar cloud
star
observer
I
I
n
n
6
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
7

• 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

8
Integrating over length from source...
Including all elements in the line of sight
9
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
10
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...

11
Clumping of the ISM

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

At a distance, d100 pc
Average ISM density
12
Smooth versus clumpy

• star

observer
smooth
clumpy
Cold dense clouds
Hot medium
13
Numerical example

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

14
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.

15
Thomson Scattering

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

electron
, where
16
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
17
Compton scattering

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

electron
q
frequency change
18
Compton scattering (cont.)

• On average,

19
Electron-positron pair production
e-

• g-ray

y
q
x
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
20
Minimum g-ray energy required

• Must first demonstrate that
  is a relativistic invariant.

Rest energy of particle,
21

• Thus, from and
  ,

And this is a relativistic invariant
22

• Total initial momentum,
• thus

23

• But since ,
• and -

24
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
25
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
26
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.

27
Photon versus particle density

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

9
3
Corresponding to about 10 photons / m
6
3
No of nuclei in space is about 10 / m
28
Synchrotron Self-Absorption
e-
e-
Relativistic electrons moving in a magnetic field
29
Synchrotron Emission

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

and for a power law electron spectrum
30
Blackbody turnover

• Assume Synchrotron power-law cut off, nmax, 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.

31
On the Rayleigh-Jeans side...
n
Rayleigh-Jeans approximation to blackbody...
32
Source distance

• For dsource distance and Rsource size,

33
Total flux at Earth...

• So total energy flux at Earth is given by

34
SSA spectrum
35
and SSA frequency

• Substituting for W then

and
36
SSA in Compact X-ray sources
18

• 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
37
Radiation processes (summary)

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

38
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

39
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
40
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!!!

41

• RADIATION PROCESSES
• END OF TOPIC