JH ASTRONOMY AND ASTROPHYSICS: AS 3015
Nebulae: Sample exam questions
1. Distinguish between the terms natural,thermal and collisional broadening of spectral
lines. Write down formulae that represent the profiles of spectral lines broadened
by these processes, defining all terms that are used, and sketch the form of the
spectral lines. Explain clearly how the pressure affects the relative importance of
the different processes.
(15 marks)
Write down the equation of radiative transfer, and its formal solution, for radiation
passing through a medium. If the source function is constant along a path through
the medium, derive an expression for the emergent specific intensity.
(15 marks)
Use this result to explain why some sources display absorption line spectra, and
others emission line spectra. Give one example of each.
(10 marks)
2. Define the three Einstein coefficients A21,B12 and B21.
(6 marks)
Explain what is meant by the principle of detailed balance and the Boltzmann law.
Hence, derive an expression for the mean intensity of radiation in thermal equilib-
rium in terms of the Einstein coefficients.
(12 marks)
By requiring that the expression derived above equal the Planck function at all
frequencies, derive the Einstein relations between the coefficients.
(10 marks)
Two energy levels have statistical weights g1(for the lower level) and g2, and popula-
tions n1and n2. The frequency of a photon emitted or absorbed during a transition
between them is ν. At temperature Twhat ratio between n1and n2do you expect
(i) when local thermodynamic equilibrium applies, (ii) out of LTE, and (iii) in a
maser source?
(12 marks)
