Eline Tolstoyhttp://www.astro.rug.nl/~etolstoy/astroa07/

7. Radiation Processes,starting Bremsstrahlung

Radiative Processesin Astrophysics

Chapter 1,2,3 & 4 - Rybicki & Lightman -Fundamentals of Radiative Transfer & Radiation processes

Important Themes we covered so far

1. Basic Definitions, Specific Intensity2. Radiative Transfer, Opacity3. Black-Body Radiation, Planck Spectrum4. Maxwell’s Equations, Radiation Spectrum5. Polarisation & Stokes Parameters6. Dipole Approximation7. Liénard-Wiechart Potentials8. Larmor’s Formula9. Thomson (electron) scattering10. Fields of a Uniformly Moving Charge11. Emission from Relativistic Particles

Radiation Processes:two main radiation types: thermal & non-thermal.

Thermal - Maxwell-Boltzmann thermo-dynamic equilibrium conditions forparticle velocities, relating to the temperature of the emitting gas

black-body; bremsstrahlung

Non-Thermal - any other kind of process which encourages particles tomove and radiate.

synchrotron, inverse-compton

Radiation Processes in this course:

2. Bremsstrahlung free electrons decelerating in the field of an ion

4. Thomson & Compton scattering electron scattering processes

3. Cylotron & Synchrotron radiation acceleration of electrons spirallingaround magnetic field lines

1. Thermal or Blackbody radiation radiation from a heated body

Bremsstrahlung

Bremsstrahlung originates from the acceleration of a charge (e.g., anelectron) in coulomb collisions with other charges (e.g., ions or nuclei).The most common situation is the emission from a hot gas as theelectrons collide with the nuclei due to their random thermal motions.

Chapter 5 R&L (from p. 155)

Synchrotron Radiation Particles accelerated by a magnetic field will radiate. Synchrotronradiation is caused by the acceleration of electrons as they spiralaround magnetic field lines. The electrons radiate photons of acharacteristic energy, corresponding to the radius of the circular motionabout the field lines.

Chapter 6 R&L (from p. 167)

Compton Scattering

This process scatters photons from lower to higher energies (or vice-versa) in interactions with electrons of higher (or lower) energies.

A common example is, low energy photons (e.g., UV, optical) scatterwith relativistic electrons, making X-rays and/or gamma-rays.

The non-relativistic version is called Thomson scattering.

Chapter 7 R&L (from p. 195)

the physical interpretation ofastronomical obserations

Active Galactic Nuclei / Quasars Radio Galaxies

The planet Jupiter

X-ray Clusters of Galaxies

Young Stars

Forming Stars

Jupiter - Spectral Energy Distribution

Centaurus A

a nearby radio galaxy

it contains dust lanes, neutral gas, ionised gas, thermal emission,non-thermal emission, radio jets, x-ray emission (diffuse andpoint-like), an active nucleus with a black-hole at the centre.

i.e., to understand this object we need to understand radiationprocesses very well (and more besides).

CenA - Optical (~500nm)

Thermal emission fromstars and gas,i.e., bremsstrahlung (free-free radiation), lineemission, dustscattering,. . . )

CenA - Near-Infra Red

Thermal emission, mainly fromstars, similar to optical, but dustless apparent. The opacity of dustin IR is smaller.

2 micron

CenA - Radio

Neutral Hydrogen(HI) gas

VLA Observations at 21cm

CenA - Radio

Synchrotron radiationfrom jets and black hole.

VLA Observations at 6cm

CenA - X-ray

Synchrotron radiationfrom jet, Comptonizedphotons from black hole,Thermal radiation fromstars.

Chandra High resolution Observations at 2-20 keV

CenA - Multi-wavelength

Spectral Energy Distribution

Active Galactic Nuclei

emit radiation from radio to !-rays

Virgo clusters is filled with hot gasradiating strongly at 2keV (severalbillion degrees).

Virgo Cluster - X-ray Image

BREMSSTRAHLUNG !!

Quantifying this process will allowus to obtain physical insights intowhat is being seen in this image.

e.g., mass, temperature, density...

most of the baryonic mass in the Universe is in this form and isradiating via Bremsstrahlung

BremsstrahlungProduced by collisions between particles in hot ionized plasmas

predominantly from collisions between electrons and ions

In an electron-ion collision we can take the ion to be unaccelerated

1. compute radiation power spectrum from a single collision with givenelectron velocity & impact parameter.

2. Integrate over impact parameter to get the emission from a singlespeed electron component

3. Integrate over a thermal distribution of electron velocities to obtainthermal bremsstrahlung emissivity

4. Consider thermal bremsstrahlung absorption & emission from aplasma with relativistic electron velocities

Dipole Radiation

The Fourier transform of d(t) :

from lecture 4DIPOLEAPPROXIMATION

Consider an electron of charge -e moving past an ion of charge Ze withimpact parameter b:

Radiation from a single collision

"# << 1

"# >> 1

Since path is almost linear, velocity means integrating component ofacceleration along the path

thus for small angle scatterings, the emission from a single collision:

a single collision

to determine the spectrum for a medium with an ion density, ni an electrondensity, ne and a fixed electron speed, v the flux of electrons (electrons perunit area per unit time) incident on one ion is simply nev and the elementof area is 2!bdb about a single ion.

add the ion density, for a fixed electron speed

the integral requires the full range of impact parameters, however it turnsout to be a good approximation using only low frequency (b<<v/") form

Total emission

bmax is a value of b beyond where b<<v/" is applicable and the contributionof the integral becomes negligible, so it is of order v/"

limits on the integrationA possible value for the lower limit on the integration is the value of bmin

for which the “straight-line” approximation ceases to be valid, this occurswhen $v~v

when bvmin >> bq

min then a classical description of scattering is valid andbv

min is the appropriate choice for bmin.

this occurs when where

When bvmin<< bq

min or equivalently 1/2mv2 >> Z2Ry then the uncertaintyprinciple plays a big role and the classical calculation cannot strictly be used,but using bq

min gives results of the correct order of magnitude.

another option is quantum in nature, and treats collision process in termsof classical orbits

The Gaunt FactorFor any regime the exact results are conveniently stated in terms of acorrection factor, or Gaunt factor gff(v,").

Thermal Bremsstrahlung Let’s consider a more realistic plasma than single speed electrons

the limits of the integration should account for the fact that at frequency % theincident velocity must be such that

because otherwise the photon of energy h% could not be created.

A plasma in thermal equilibrium means that the electrons have a Maxwell-Boltzmann velocity distribution:

M-B means, the probability dP that a particle has a velocity in range d3v is

Now we have to integrate

over this distribution.

thus, in CGS units (erg s-1 cm-3 Hz-1), we have for the emission

Thermal bremsstrahlung

the total power per unit volume emitted by bremsstrahlung comes fromintegrating the above over frequency (erg s-1 cm-3) is:

T-1/2 comes from dW/dVdtdw & v-1 and <v> & T1/2

exp(-h%/kT) comes from lower limit cut off in the velocity integration due tophoton discreteness and the Maxwellian shape of the velocity distribution

Bremsstrahlung spectrum

Bremsstrahlungvs. Blackbody