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### Module 8: High Energy Astrophysics

high energy photon

Swinburne Online EducationIntroduction to Particle Physics and High Energy Astrophysics

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 non-thermal 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.

- Flux

- Wavelength

- 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 radiation. The wavelength peak of the spectrum depends only of the temperature of the source.

- 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.

To calculate the thermal source temperature we use Wien’s law:

2.898 x106 nm

c

T =

Recall that wavelength and frequency are related via:

=

where c is the speed of light

max

The photon energy and momentum are related to frequency via:

E = h and Momentum = h / c

where h is Planck’s constant

- 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.

This means that when a photon loses energy and momentum, its frequency n 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 range0.001 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

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.

- This type of emission form is called free-free emission, or thermal bremsstrahlung - which is German for “braking radiation”.

- If a negative electron approaches a positive ion, they will be attracted to each other and the strong electric force will alter the trajectory of the electron (i.e. accelerating it), which leads to electromagnetic radiation being emitted:

H+

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

- 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 thermalprocess.

electron

electron

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.

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.

Photon (no change in wavelength)

e-

electron

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.

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.

electronat rest

higher energy electron

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.

lower energy photon

high energy photon

mec2

Dl = l - l =

(1 – cos )

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:

where a 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.

high energy electron

photon gains energy

lower energy photon

Inverse Compton Scattering- In inverse Compton scattering, a high energy electron transfers both energy and momentum to a lower energy scattering photon.

- In astrophysics, inverse Compton scattering is actually more important that Compton scattering.

The Compton effect and the inverse Compton effect are exactly the same process, only the order of energy and momentum transfer is reversed.

Such relativistic electrons are produced in supernovae and active galactic nuclei.

Crab Nebula

PKS 2356-61

- 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.

max / 0

/ 0 arbitrary unit

The Inverse Compton SpectrumIf 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.

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.

e-

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).

- For this to occur, the photon energy (hn) must be at least the rest mass (mc2) of the electron and positron, given by
- hn > 2 mec2 = 2 x 0.51 MeV = 1.02 MeV.

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.

- 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.

helical path

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 calledsynchrotron radiation.

photons

fast-moving electron

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 densityUB(UBB2): P UB , 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.

Beam of radiation

1

Electronvelocity

v

Collimated RadiationSynchrotron 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.

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.

log10n

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 emission that exhibits a typical blackbody spectrum ...

F = flux density

n = frequency

Since synchrotron radiation is strongest at low frequencies, it can be detected with radio telescopes

log10F

This straight line behaviour can be represented by the formula

where is a constant. We say that the flux has a ‘power law dependence’ on frequency: F ~ - .

log10F ~ - log10

log10n

log10F

Sum of individual contributions

log10 / c

Log10/ c

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:

Above the critical frequency, c , the spectrum drops exponentially.

c

Summing the individual contributions of many electrons gives the resulting synchrotron spectrum:

Turn-over

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, known as synchrotron self absorption.

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 non-thermal 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/SAOhttp://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, ATNFhttp://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

- Press the ESC (Escape) key to return to the home page for this Module.

The energy of elementary particles is quoted in electronvolts (eV) where1 eV= 1.602 10-19 Joule = 1.602 10-12erg

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

Physical Constants and UnitsSpeed of light = c = 2.9979 108m/s

Planck’s constant: h = 6.6261 10-34J s

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