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Radiation Processes. High Energy Astrophysics [email protected] 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 - PowerPoint PPT Presentation
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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
PhotoionizationAtom absorbs photon
e-
IEAtom, ion or
molecule 3h
h
Cross-section () characterized by edges corresponding to ionization edges.
Example of photoelectric absorption
eg. soft X-rays from a star absorbed by ISM
star interstellar cloud observer
I
I
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:
Zn 3m
))(( 2mEZdl (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 :
dlEn ZZ )(
dlEFndF ZZ )(
dlEnF
dFZZ )(
Integrating over length from source...
dlnEdlEnF
dFZZZZ )()(
))(exp(0 dlnEFF ZZ
Including all elements in the line of sight:
Z H
HZZ dln
nnEFF )(exp0
Optical depth
This becomes: Heff NEF ).(exp0
This is ‘’, the optical depth, which has no dimensions
Z H
ZZeff n
nEE )()(
This is the effective cross-section, weighted over the abundance of
elements with respect to hydrogen
Column densityThe 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...
dlnN HH
Clumping of the ISM
Take an example at low energies, eg at ...
22410,1.0 mkeVh eff
3610 mH m18103
Average ISM density At a distance,
d=100 pc
Smooth versus clumpy star observer
smooth
clumpy
Cold dense clouds36 /104 m
Hot medium36 /101.0 m
36 /10 m
Numerical example• Through the smooth medium -
• Through the clumpy medium -
224 /103 mdN HH
002424
0 05.020
10103exp FF
FF
224618 /103.0101.0103 mNH
02424
0 75.010103.0exp FFF
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 Scatteringlow-E photon scattered by electron -
Thomson cross-section is given by -
helectron h
2
3
8er mre
151082.2 , where
2291065.6 me
Thomson scattering cont.
If N = number of particles per 3m
1m
1m
then fraction of area blocked by a square metre of path =
mN /1065.6 29
NR291065.6
exp0FF
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
0h
cos111
20
cm
h
e
frequency change
h
Compton scattering cont.
On average, 20
0
cm
h
e
20 cm
h
e
Electron-positron pair production-ray
e-/e+ photon
Two photons, one of which must be a -ray, collide and create an electron-positron (e-/e+)
pair. This is therefore a form of -ray absorption.
x
y
e+
e-
Minimum -ray energy required
Must first demonstrate that is a relativistic invariant.
22 pcE
2mcE Rest energy of particle,
0mm
2
2
1
1
cv
Thus, from and ,2mcE mvcpc
22
22220
22
20
22
220
/1/1/1 cv
vccm
cv
vcm
cv
cm
420
2
22
22220 cm
cvc
vccm
And this is a relativistic invariant
Total initial momentum,
thus
pppp
222 cpcppc yx
22 sincos cpcpcp pp
222222 cos cpcp p
2222 sincos2 cpcpp pp
cos2 22222 cppcpcp pp
But since ,
and -
Ecp
cos2222pp EEEEpc
222 ][ pinitial EEpcE
cos222pp EEEE
cos12 pEE
Calculating the minimum energy
Assuming e+ and e- have no momentum…
and since ,
2222 2][ cmpcE efinal
cos12 pEE
cos12
222
p
e
E
cmE
Which gives us this expression for the energy of the -ray photon
And this is...found by simply making the denominator as
large as possible, ie when cos()=-1, ie when =180 degrees.
-ray e-/e+ photon
p
e
E
cmE
22
min
And the minimum -ray energy is given by:
Minimum energy for mm-wave photon
-ray photon interacts with mm-wave
First converting to eV :
=1.2mm corresponds to h=10 eV-3
3
2622
min 10
105.0
p
e
E
cmE
eV14105.2
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 -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 densityeg., for 3K -wave background photons -
eVhE 4103 35314 103105 eVmJmU ph
Corresponding to about 10 photons / m9 3
No of nuclei in space is about 10 / m6 3
Synchrotron Self-Absorption
e-
e-
Relativistic electrons moving in a magnetic field
Synchrotron SpectrumFlux emitted as a function of frequency:
ccm
eB
cmE e
e 1.
2~ 2
2
1
E
logF
log
Blackbody turnoverAssume power-law cut off, , 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
43
2
max 2 cm
eBE
e
On the Rayleigh-Jeans side...
logF
log
synchrotronR-J
impossible
Rayleigh-Jeans approximation to blackbody...
dc
kTdI 2
2
2
blackbody
Total flux at Earth...So total energy flux at Earth is given by:
22
2 c
EIF
2
1538
Be
me
SSA spectrum
logF
log
SSA
Optically-thick regime
a
Optically-thin
lies at the point where the observed synchrotron flux equals the blackbody limit.
a
Source distance
For d=source distance and R=source size,
d
R
2
2
d
R
… and SSA frequencySubstituting for then:
2
22/1538
d
R
Be
mF e
and
4/54/12/117103 dBFR
SSA in Compact X-ray sources
X-ray frequency, =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 to be
observable in the X-ray band).
- but a neutron star diameter is 10 to 20km -
18
-29 -2 -1
8
a
Radiation processes (summary)
• Thermal - Bremsstrahlung electron energies ~ photon energies to produce X-rays, = 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,
PHUB
0
2
2162 105~ S
-10
Inverse Compton Scattering
Consider starlight: <h> ~ 2eV (~6000A)
or 3K background photons, <h> ~3x10 eV
then
= for stars
= for the 3K background, to produce X-rays. We need cosmic rays!!!
h
keVIC
82
31047103
-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
2
3
)(
EEN
Power radiated in the two processes is about equal in the case of equipartition of energy
ie when
ie an electron with a given 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.
phUB
0
2
2
Ratio of IC to Synchrotron Xrays
For example:
Galactic X-rays require (stars)
(3K)
but for synchrotron
32 104IC7103
162 105S
Ratio IC to Synchrotron (cont.)
Ratio = (no of electrons with )
(no of electrons with )
But:
ICS 2
2
S
IC
S
IC
S
IC
N
N2
2
2
3
2
3
S
IC
S
IC
S
IC
E
E
N
N
Ratio IC to Synchrotron (cont.)
Thus:
So which is more important for producing
X-rays via IC; starlight or 3K background?
2
1
2
32
S
IC
S
ICR
X-rays from IC scattering
(no. X-rays produced from starlight per )
(no. X-rays produced from 3K per )
3m3m
K
OPT
K
OPT
K
OPT
N
N
U
U
3
2
33
2
1
33
2
32
33
K
OPT
K
OPT
K
OPT
K
OPT
U
U
U
U
IC - starlight versus 3K
We know that
and
Thus ie 3K photons more important!
27
3
3
353
36
10103
104
103
10
K
OPT
K
OPT
eVmU
eVmU
3
1'R
IC or synchrotron for X-rays?
Remember
assuming for :
thus synchrotron dominates over IC in Galaxy
2
1
S
ICR
K3 IC
32
1
16
7
105105
103
R
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 whetherthere are enough electrons to produce IC.