Astronomy 2:
Theoretical Astrophysics
  Dr G. Woan

This course concentrates on how the motions of particles, and the details of their radiation processes, affect observed astrophysical spectra. The emphasis is on the astrophysics of spectral line broadening, and the physical processes that can be probed using observations of these lines. The course covers a range of thermal effects in astrophysics, including thermal equilibrium and non-equilibrium, particle speed distributions and planetary atmospheres.

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Course details
Copies of lecture notes will appear here as the course proceeds. They are for reference only, and should not be used to replace your own lecture notes. You will find the course much harder if you don't create your own written version, so please do not print these notes out in quantity.


Spectral lines
The definition of a spectral line in term of a power spectrum. Time and frequency domains and the basic idea of a Fourier transform. Loss of information in a power pesctrum. The Doppler effect. Broadening of spectral lines as a consequence of an ensemble of emitters. Doppler broadening. Rotational broadening and its spectrum. Examples of the Sun, and Galaxy rotation curves. The velocity mapping of the Galaxy in H I.The H I line (1420 MHz) as an example of radio spectral line.
lecture notes:  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Pictures: [ Dopplergram of the Sun | HI map of the Milky Way | Galactic rotation geometry ]
Handouts:[ ]
Websites: [Fourier applet 1, Fourier applet 2, MDI homepage ]

Natural line widths
The spectrum of a classical damped harmonic oscillator as a function of its decay time. Spectral width and Lorentzian profiles. Quantum mechanical interpretation of natural width as the lifetime of an excited state, and its conection with the Heisenberg energy-time uncertainty relation. Oscillator strangths, allowed and forbidded transitions. Einstein A coefficient as a spontaneous emission rate. Line cooling from clouds.

lecture notes:  1 2 3 4 5 6 7 8
Pictures: [ ]
Handouts:[ ]

 Collision and pressure broadening
Coherence time and its connection with spectral width. Mean free path of particles in an ideal gas. Collision broadening width derived from mean free path. Pressure broadening due to local perturbations of the atom.
lecture notes:  1 2 3 4 5 6 7
Pictures: [ ]
Handouts:[ ]

Thermal astrophysics and 1-D velocity distributions
The definition of a 'system' and a quantum 'state'. The statistical definition of temperature. Derivation of the Boltzmann factor. Examples of non-degererate and degenerate 2-level systems. Non-ionising atomic transitions. One dimensional velocity distribution of particles in thermal equilibrium. Doppler broadening of spectral lines, and the Gaussian profile. Comparisons with pressure/collisional broadening and Voigt profiles.
lecture notes:  Slides used for introduction (8) 1 2 3 4 5 6 7 8 9 10 11 12
Pictures: [  ]
Handouts:[ Thermal astrophysics -- a non-examinable introduction  ]

3-D particle velocity distributions
State degeneracy in three dimensions. The Maxwellian speed distribution function. Moments of the speed. The Maxwell tail. Astrophysical examples.
lecture notes:  1 2 3 4 5 6 7 8
Pictures: [ ]
Handouts:[ some useful maths ]

The Planck function
Blackbody radiation as a consequence of thermal population of modes. Oscillator statistics. The Planck function. Wien and Rayleigh-Jeans approximations. Planetary temperatures: Extension of A1 treatment. Factors influencing planetary temperature
lecture notes:  1 2 3 4 5 6 7 8 9 10 11 12 13 14
Pictures: [ ]
Handouts:[blackbody curves and equations]


Books
The recommended textbook for A2 is An Introduction to Modern Astrophysics, B W Carroll and D A Ostlie, Addison Wesley .  If you are a physicist you will find that your thermal physics textbooks will help too!