Radiation Processes

High Energy Astrophysicsemp@mssl.ucl.ac.uk

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

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.