Radiation Processes. High Energy Astrophysics email@example.com http://www.mssl.ucl.ac.uk/. Absorption Processes. So far, considered the production of X-rays. Now, will consider X-ray absorption. Emission processes Recombination Inverse Compton e-/p+ annihilation
High Energy Astrophysics
So far, considered the production of X-rays.
Now, will consider X-ray absorption.
e-/p+ pair production
synchrotron self absorption
Atom absorbs photon
Atom, ion or
Cross-section (s) characterized by edges corresponding to ionization edges.
eg. soft X-rays from a star absorbed by ISM
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:
Thus the fraction of flux lost in volume dV is:
Including all elements in the line of sight:
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
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...
Take an example at low energies, eg at ...
At a distance,
Average ISM density
Cold dense clouds
low-E photon scattered by electron -
Thomson cross-section is given by -
then fraction of area blocked by a square metre of path =
If N = number of particles per
If R is the extent of the absorbing region along the line of sight,
( = optical depth)
In Compton scattering, the photon wavelength increases, ie its energy decreases.
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.
Must first demonstrate that is a relativistic invariant.
Rest energy of particle,
And this is a relativistic invariant
Assuming e+ and e- have no momentum…
and since ,
Which gives us this expression for the energy of the g-ray photon
found by simply making the denominator as large as possible, ie when cos(q)=-1, ie when q=180 degrees.
And the minimum g-ray energy is given by:
g-ray photon interacts with mm-wave
First converting to eV :
l=1.2mm corresponds to hn=10 eV
eg., for 3K m-wave background photons -
Corresponding to about 10 photons / m
No of nuclei in space is about 10 / m
Relativistic electrons moving
in a magnetic field
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.
So total energy flux at Earth is given by:
Substituting for W then:
X-ray frequency, n=10 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 -
Consider starlight: <hn> ~ 2eV (l~6000A)
or 3K background photons, <hn> ~3x10 eV
= for stars
= for the 3K background, to produce X-rays. We need cosmic rays!!!
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
Power radiated in the two processes is about equal in the case of equipartition of energy
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.
Galactic X-rays require (stars)
but for synchrotron
Ratio = (no of electrons with )
(no of electrons with )
So which is more important for producing
X-rays via IC; starlight or 3K background?
(no. X-rays produced from starlight per )
(no. X-rays produced from 3K per )
We know that
Thus ie 3K photons more important!
assuming for :
thus synchrotron dominates over IC in Galaxy
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.