11/15/18

1

Lecturer: Eline Tolstoyetolstoy@astro.rug.nl

http://www.astro.rug.nl/~etolstoy/radproc/

Electrodynamics of Radiation Processes

Tutorials: Roland Timmermantimmerman@astro.rug.nl

Main book: Radiative Processes in Astrophysics, Rybicki & Lightman

also use: High Energy Astrophysics, Longair (3rd edition)

Course update

No Lecture OR Tutorial on Monday 19th November

Instead Lecture on Tuesday 20th November 13-15 (room KB 5419.0161)

Tutorial tomorrow 9-11, in room KB 5419.0161

Next week:

2. Thermal Radiation

Electrodynamics of Radiation Processes

Chapter 1: Rybicki&LightmanSections 1.5. 1.6

Radiative Transferradiation passing through matter, energy maybe absorbed, emitted and/or scattered and the intensity will not in general remain constant.

combining emission and absorption

The RTE takes a particularly simple form if we replace path length, s by optical depth, τν

Equilibrium

Maxwell-Boltzmann LawWhen particles interact suff iciently they spread the available energy around and an equilibrium distribution evolves which means that the velocities of particles in thermodynamic equilibrium in a hot gas are distributed with a Maxwellian velocity distribution.

T

Black-Body Radiation

A photon gas in perfect thermal equilibrium at temperature T will exhibit an energy spectrum of specific amplitude and shape known as a blackbody spectrum. The spectrum peaks at a frequency proportional to its temperature.

if a material absorbs well at some wavelength it will also radiate well at the same wavelength (Kirchoff 1859)

11/15/18

2

Specific intensity emitted by black body: spectrum

Hotter black bodies emit more total energy

Area under curves obeyStefan-Boltzmann

Wien’s law

Hotter black bodies have peak f lux at shorter λ

Wien’s approx.

Rayleigh-Jeans approx

The Einstein A,B CoefficientsProbability coefficient for changes in energy levels from upper (2) to lower (1) separated by energy h𝞶.

spontaneous emission

absorption

stimulated emission

=j⌫↵⌫

Planck’s law

Boltzmann’s Eqn

=j⌫↵⌫

Characteristic Temperature

Brightness at a certain frequency by giving it the temperature a blackbody would have at same brightness and frequency

Brightness Temperature, Tb

In the Wien region of the Planck law the concept of brightness temperature is not so useful because of the rapid decrease in Bν with ν, and because it is not possible to formulate a RTE linear in brightness temperature.

The RTE for thermal emission takes a particularly simple form in terms of brightness temperature in the Rayleigh-Jeans limit:

when T is constant,

thus if the optical depth is large the brightness temperature, Tb of the radiation approaches the temperature of the material, T

Rayleigh-Jeans – applicable at low frequencies – like radio astronomy

Colour Temperature, Tc

We can deduce the characteristic temperature from the shape of the spectrum - measuring the flux at a range of frequencies and determining which of the possible planck curves a source lies on, ie., estimating the peak of the spectrum and applying Wien’s displacement law:

Characteristic Temperature

Effective Temperature, Teff

A bolometer provides the total flux density F integrated over all frequencies but without any detailed frequency distribution information. Can deduce Teffif the size of the source, dΩ is known by equating the actual flux F to the flux of a blackbody at temperature Teff.

11/15/18

3

The Energy Distribution of the Sun Different Stars

T~30000K

T~20000K

T~8000K

T~6000K

T~5500K

T~4500K

T~3000K