Transcript Intro to Particle Physics and High Energy Astrophysics

Swinburne Online Education Introduction to Particle Physics and High Energy Astrophysics
Module 8:
High Energy Astrophysics
ehigh energy
photon
Activity 1:
High Energy Processes
© Swinburne University of Technology
Summary
In this Activity we will learn about some of the high
energy processes that both produce high energy
emissions and also high energy interactions that can
occur between photons and elementary particles that are
important in high energy astrophysics. Specifically, we
will learn about:
blackbody radiation;
bremsstralung radiation;
Compton and inverse Compton scattering;
pair production; and
synchrotron radiation.
Introduction
So far in this Unit we have learned a great deal about
particle physics and the detection of elementary particles.
Let’s now apply our new found particle physics knowledge
to study high energy processes in astrophysics.
In this Activity we’ll look at some of the processes that
produce high energy particles - both by thermal and nonthermal processes. We’ll also look at some of the ways
that high energy photons interact with matter.
Then in the next few Modules we’ll look at high energy
processes in the Sun and other stars including white
dwarfs and pulsars, and then move on to X-ray and
gamma ray astronomy.
High Energy Radiation
Electromagnetic radiation is produced whenever a
charged particle is accelerated. The greater the
acceleration, the higher the energy of the emitted photon.
There are two types of electromagnetic radiation: thermal
radiation - which depends on the temperature of the
emitting source - and non-thermal - which does not depend
on the source temperature.
The shape of the spectrum (which is radiation flux plotted
again frequency) allows us to determine the source’s
emission mechanism.
The simplest case of thermal emission is that of a
blackbody - which absorbs all radiation that falls on it and
in turn emits a smooth spectrum of
blackbody spectrum
Flux
radiation. The wavelength peak of
the spectrum depends only of the
temperature of the source.
Wavelength 
Blackbody radiation obeys two important laws:
• Wien’s Law: which relates the peak wavelength to the
source temperature, and basically the hotter the source
the shorter the peak wavelength (the higher the energy).
• Stefan-Boltzmann’s Law: which relates the total amount of
energy emitted per second to the source temperature, and
again, the hotter the source, the more energy produced.
So what sort of temperatures and energies are involved in
high energy thermal radiation? First let’s review a few
equations related to electromagnetic radiation.
To calculate the thermal source T = 2.898 x106 nm
max
temperature we use Wien’s law:
Recall that wavelength and
frequency  are related via:
=
c

where c is the
speed of light
The photon energy and momentum are related to frequency
via:
E = h  and Momentum = h  / c where h is Planck’s constant
This means that when a photon loses energy and
momentum, its frequency  decreases.
Click here to be reminded about the
physical constants and units used.
Armed with these equations, we can now see what thermal
temperatures and energies are involved in high energy
radiation:
• Gamma radiation is generally defined by photons with
 < 0.001 nm, which corresponds
E >1.24 MeV and T >108 K.
Such high energy photons are created in nuclear
reactions and other very high energy processes.
• X-rays are those photons in within the wavelength range
0.001 nm <  < 10 nm, with
124 eV < E < 1.24 MeV and 106 K < T < 108 K.
These high energy photons are created, for example, in
supernovae remnants and the solar corona, as well as in
the hot gas between galaxy clusters.
Types of Thermal Radiation
You will already be familiar with atomic excitation and
de-excitation as a means of producing photons. Thermal
atomic excitation is generally via collisions, which excite
atoms, and as they de-excite, they emit photons. The
hotter the medium, the higher the kinetic energy of the
impacts, and the higher the resulting photon energy.
photon
As well as atomic excitation, another thermal process is
bremsstrahlung radiation, which occurs when free electrons
interact with ions in, for example, the hot atmospheres of
stars.
If a negative electron approaches
a positive ion, they will be
attracted to each other and the
H+
strong electric force will alter the
trajectory of the electron (i.e.
ephoton
accelerating it), which leads to
electromagnetic radiation being
emitted:
This type of emission form is called free-free emission, or
thermal bremsstrahlung - which is German for “braking
radiation”.
The frequency range of the radiation depends on how
much the electron’s trajectory is bent by the interaction
with the positive ion. This depends on several things,
including the relative velocities of the two bodies, which
in turn depends on the temperature of the gas, which is
why free-free emission is a thermal process.
An example of high energy
thermal bremsstrahlung is the
X-ray emission from giant
elliptical galaxies and hot
intercluster gas.
X-ray image of hot
intercluster
gas in Hydra A
Thomson Scattering
As an introduction to particle scattering, let’s begin with
Thomson scattering, which is actually low energy
scattering between a photon and an electron.
electron
e-

Photon (no change in wavelength)
photon
electron
The interaction is elastic, which means that the photon
and electron just both bounce off each other, changing
their direction, but there is no exchange of energy.
Thomson Scattering
As an introduction to particle scattering, let’s begin with
Thomson scattering, which is actually low energy
scattering between a photon and an electron.
electron
e-

Photon (no change in wavelength)
photon
The interaction is elastic, which means that the photon
and electron just both bounce off each other, changing
their direction, but there is no exchange of energy.
Increasing the Energy
If the energy of the scattering photon is increased, then
there will be an exchange of energy, and hence and
frequency change after the interaction.
But as long as the energy of the incident photon is lower
than the rest mass energy of the stationary electron, that
is:
h  << mec2
(in the reference frame of centre of momentum)
then the interaction can always be described as Thomson
scattering.
Ok - let’s now look at what happens if h > mec2.
Compton Scattering
In high energy astrophysics there are many inelastic
photon interactions, whereby the photon energy changes
after the scattering.
In Compton scattering, a photon of high energy collides
with a stationary electron and transfers part of its energy
and momentum to the electron, decreasing its frequency
in the process.
electron
at rest
ehigh energy
photon

lower energy photon
higher energy
electron
This process was discovered first in 1923 by Arthur
Compton, who realised that the wavelength of X-ray
radiation increased after the scattering with stationary
electrons.
The change in wavelength of the photon after Compton
scattering is given by:
h
D=- =
(1 – cos )
2
m ec
where  is the scattering angle of the photon.
In the optical band, this effect is pretty negligible, but in
the X-ray the wavelength shift can be as high as 10.
The increase in wavelength during Compton scattering
results in a corresponding decrease in the the energy of
the photon. The energy is transferred to the electron in
the form of kinetic energy or motion.
Inverse Compton Scattering
In astrophysics, inverse Compton scattering is actually
more important that Compton scattering.
In inverse Compton scattering, a high energy electron
transfers both energy and momentum to a lower energy
scattering photon.
high energy electron
electron loses some energy
photon gains energy
lower energy photon
The Compton effect and the inverse Compton effect are
exactly the same process, only the order of energy and
momentum transfer is reversed.
In astrophysical situation, the inverse Compton effect
occurs when a low energy photon, such as in the cosmic
microwave background, bounces off a relativistic
electron.
Such relativistic electrons are
produced in supernovae and
active galactic nuclei.
Crab Nebula
PKS 2356-61
The Inverse Compton Spectrum
If we plot the spectrum of an inverse Compton source,
we can easily see that it is quite different to a thermal
spectrum.
At low frequencies, the
scattered radiation
increases proportionally
with frequency, while at
high frequencies, it drops
down below a maximum
frequency.
log10I()
arbitrary unit
max / 0
 / 0
arbitrary unit
Relativistic effects become important in inverse Compton
scattering since it involves high energy (and therefore fast
moving) electrons. The maximum energy gained by photons
via inverse Compton scattering is equal to its initial energy
multiplied by the square of twice the Lorentz factor (where
the Lorentz factor squared is given by 2 =1 / [1-(v/c)2] and v
is the electron velocity):
Emax = (h )max  4 2 h 0
In general, the frequency of the scattered photon is
approximately given by   2 0 . In many astronomical
sources there are electrons with  100 –1000, and therefore
inverse Compton scattering is the main radiation process,
scattering low energy photons up to very high energies.
Pair Production
As we have seen in the Activity Lend Me a Lepton, every
particle has an antiparticle, and if they encounter each
other they will annihilate and give off gamma rays.
The reverse of this process can also occur: pair
production is the formation of an electron and position
from a high energy photon (usually in the vicinity of an
atomic nucleus).
e+

e-
For this to occur, the photon energy (h) must be at least
the rest mass (mc2) of the electron and positron, given by
h > 2 mec2 = 2 x 0.51 MeV = 1.02 MeV.
For X-ray and gamma ray energies above 1.02 MeV, pair
production is one of the most important types of
interaction with matter, and one of the principle ways that
gamma rays are absorbed in matter.
If the photon energy is greater than 2 mec2, the excess
energy goes into the kinetic energy of the particle pair.
In the presence of a magnetic field,
the electron-positron pair will follow
curved arcs away from each other.
This is in fact how pair production
was first discovered in 1933.
Electron-positron pairs in
bubble chamber tracks.
Synchrotron Emission
When electrons encounter a magnetic field, they spiral
along the field lines in a helical path. This means that
their direction is constantly changing, and hence they are
accelerating and therefore emit radiation. This radiation
is called synchrotron radiation.
photons
B
fast-moving electron
helical path
Synchrotron radiation is emitted over a wide range of
energies, producing a continuum spectrum. The region of
maximum emission depends on the energy of the electron
and the strength of the magnetic field.
The total power, P, emitted by a particle moving inside a
magnetic field is proportional to the magnetic energy
density UB (UB  B2): P  U B , which means that the
stronger the magnetic field, the stronger the emitted
radiation.
This relation can be reversed and used to determine
the magnetic field strength producing the observed
synchrotron radiation.
Collimated Radiation
Synchrotron radiation is highly collimated in the direction
of the velocity of the charged particles due to relativistic
effects.
Because the electrons are travelling at relativistic
speeds, they don’t escape in all directions. In fact, the
faster the electrons are travelling, the more collimated
the radiation beam.
Source
Electron
v
velocity
Beam of radiation
1

As v c,  increases,
so 1/  decreases and
the beam becomes
more collimated.
Beaming can result in anomalously high radiation. The
strong gamma ray sources that we see, for example,
could either be extremely strong sources of radiation
that emit in all directions equally; or it could simply be
that the charged particle that produce the radiation are
moving towards us and thus the radiation is beamed in
our direction, making it seem a lot stronger than it really
is.
We will return to this idea in the Module of Gamma Ray
Bursts.
Synchrotron Spectrum
Since there will be many electrons with a range of energies
that encounters the magnetic field, the radiation emitted
covers a wide frequency range and so synchrotron
radiation is seen as continuum emission.
The resulting spectrum of synchrotron radiation looks like
this:
… which is very different from thermal
log10F
emission that exhibits a typical
blackbody spectrum ...
F = flux density
 = frequency
log10

log10F
Since synchrotron radiation is strongest
at low frequencies, it can be detected with
radio telescopes
log10

This straight line behaviour can be represented by the
formula
log10F ~ - log10 
where  is a constant. We say that the flux has a ‘power
law dependence’ on frequency: F ~  - .
The shape of the overall spectrum actually comes from the
sum of each electron’s contribution. Individual electrons
spiraling around the magnetic field lines emit a spectrum that
peaks at one particular frequency, c:
log10F
Above the critical frequency,
c , the spectrum drops
exponentially.
log10F
c log10  / c
Summing the individual contributions
of many electrons gives the resulting
synchrotron spectrum:
Sum of
individual
contributions
Log10 / c
Synchrotron Self Absorption
Note that at low frequencies, the flux of the synchrotron
emission does not increase without any limit – the
spiralling electrons begin to re-absorb the photons with
low energies.
This corresponds to a
turn-over in the spectrum, log F
10
known as synchrotron
self absorption.
Turn-over
Log10 / c
Synchrotron radiation can be observed anywhere there are
fast-moving electrons and magnetic fields. This occurs, for
example, in supernova remnants and pulsars, around
planets with strong magnetic fields, in the jets emanating
from active galaxies, and near black holes.
Vela
Supernova
Remnant
M82: outflow of ionised
gas streaming out of
the galaxy
Summary
In this Activity, we have had a look a both thermal and nonthermal processes that produce high energy photons, as
well how these photons interact with matter.
We learnt about free-free emission, Compton and inverse
Compton scattering, as well as pair production and
synchrotron radiation.
Now that we understand some of these high energy
processes, we can look at some specific situations of high
energy astrophysics and explore them in more detail.
In the next Activity, we will investigate high energy
processes in the Sun.
Image Credits
VLT image of the Crab nebula
http://antwrp.gsfc.nasa.gov/apod/image/9911/crab_vlt_big.jpg
Chandra observations of a galactic cluster Hydra A - NASA/CXC/SAO
http://chandra.harvard.edu/photo/0087/index.html
The Milky Way
http://antwrp.gsfc.nasa.gov/apod/image/0006/southerncross_gb.gif
Electron-positron pairs in bubble chamber tracks.
http://teachers.web.cern.ch/teachers/archiv/hst2000/teaching/resource/bubble/gtj/gtj.htm
Radio-Optical Image of radio galaxy PKS 2356-61, ATNF
http://wwwatnf.atnf.csiro.au/research/images/pks2356.html
Vela Supernova Remnant
http://antwrp.gsfc.nasa.gov/apod/image/vela_roe.gif
M82
http://crux.astr.ua.edu/gifimages/m82r.html
End of Activity
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Physical Constants and Units
Speed of light = c = 2.9979  108 m/s
Planck’s constant: h = 6.6261  10-34 J s
The energy of elementary particles is quoted in
electronvolts (eV) where
1 eV = 1.602  10-19 Joule = 1.602  10-12 erg
In high energy astrophysics, we deal with high energy
particles, and the energies may give given in terms of:
1 kiloelectron-volt = 1 KeV = 103 eV
1 megaelectron-volt = 1 MeV = 106 eV
1 gigaelectron-volt = 1 GeV = 109 eV
1 tetraelectron-volt = 1 TeV = 1012 eV
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