- By
**primo** - Follow User

- 107 Views
- Updated on

Download Presentation
## Radiation Processes

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

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

Photoionization

e-

Atom absorbs photon

Atom, ion or

molecule

Cross-section (s) characterized by edges corresponding to ionization edges.

Example of photoelectric absorption

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

interstellar cloud

star

observer

I

I

n

n

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

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 :

Integrating over length from source...

Including all elements in the line of sight:

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

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...

Clumping of the ISM

Take an example at low energies, eg at ...

At a distance,

d=100 pc

Average ISM density

Numerical example

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

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.

Thomson Scattering

low-E photon scattered by electron -

Thomson cross-section is given by -

electron

, where

Thomson scattering cont.

then fraction of area blocked by a square metre of path =

If N = number of particles per

1m

1m

If R is the extent of the absorbing region along the line of sight,

( = optical depth)

and

Compton scattering

In Compton scattering, the photon wavelength increases, ie its energy decreases.

electron

q

frequency change

Compton scattering cont.

On average,

Electron-positron pair production

e-

y

g-ray

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.

Minimum g-ray energy required

Must first demonstrate that is a relativistic invariant.

Rest energy of particle,

Thus, from and ,

And this is a relativistic invariant

But since ,

and -

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

And this is...

found by simply making the denominator as large as possible, ie when cos(q)=-1, ie when q=180 degrees.

g-ray

e-/e+ photon

And the minimum g-ray energy is given by:

Minimum energy for mm-wave photon

g-ray photon interacts with mm-wave

First converting to eV :

l=1.2mm corresponds to hn=10 eV

-3

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.

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

Blackbody turnover

max

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.

logF

blackbody

synchrotron

R-J

logn

On the Rayleigh-Jeans side...n

Rayleigh-Jeans approximation to blackbody...

Total flux at Earth...

So total energy flux at Earth is given by:

logF

n

logn

n

a

Optically-thick regime

Optically-thin

n lies at the point where the observed synchrotron flux equals the blackbody limit.

a

SSA spectrumSSA in Compact X-ray sources

18

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 -

-29

-2

-1

n

8

a

Radiation processes (summary)

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

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 , => B=6x10 Tesla To produce X-rays,

-10

Inverse Compton Scattering

Consider starlight: <hn> ~ 2eV (l~6000A)

or 3K background photons, <hn> ~3x10 eV

then

= for stars

= for the 3K background, to produce X-rays. We need cosmic rays!!!

-4

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

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.

Ratio of IC to Synchrotron Xrays

For example:

Galactic X-rays require (stars)

(3K)

but for synchrotron

Ratio IC to Synchrotron (cont.)

Thus:

So which is more important for producing

X-rays via IC; starlight or 3K background?

X-rays from IC scattering

(no. X-rays produced from starlight per )

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

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.

Download Presentation

Connecting to Server..