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AS4011   The Physics of Nebulae and Stars 1

Academic year(s): 2019-2020

Key information

SCOTCAT credits : 15

ECTS credits : 7

Level : SCQF Level 10

Semester: 1

Availability restrictions: Not automatically available to General Degree students

Planned timetable: 11.00 am Mon, Tue, Thu

This module introduces the physics of astrophysical plasmas, as found in stars and interstellar space, where interactions between matter and radiation play a dominant role. A variety of absorption, emission, and scattering processes are introduced to describe exchanges of energy and momentum, which link up in various contexts to control the state and motion of the matter, to regulate the flow of light through the matter, and to impress fingerprints on the emergent spectrum. The theory is developed in sufficient detail to illustrate how astronomers interpret observed spectra to infer physical properties of astrophysical plasmas. Applications are considered to photo-ionise nebulae, interstellar shocks, nova and supernova shells, accretion discs, quasar-absorption-line clouds, radio synchrotron jets, radio pulsars, and x-ray plasmas. Monte-Carlo computational techniques are introduced to model radiative transfer.

Relationship to other modules

Pre-requisite(s): Before taking this module you must ( pass AS2001 or pass AS2101 ) and pass PH2011 and pass PH2012 and ( pass MT2001 or pass MT2501 and pass MT2503 ) and pass PH3081 or pass PH3082 or pass MT2003 or ( pass MT2506 and pass MT2507 )

Anti-requisite(s): You cannot take this module if you take AS4023 or take AS3015

Learning and teaching methods and delivery

Weekly contact: 3 lectures occasionally replaced by whole-group tutorials.

Scheduled learning hours: 32

Guided independent study hours: 118

Assessment pattern

As used by St Andrews: 2-hour Written Examination = 75%, Coursework = 25%

As defined by QAA
Written examinations : 75%
Practical examinations : 0%
Coursework: 25%

Re-assessment: Oral Re-assessment, capped at grade 7


Module coordinator: Dr K Wood
Module teaching staff: Dr K Wood

Additional information from school


The gas that lies between the stars takes many forms. From the dense, cold molecular clouds in which stars are conceived to the rarefied ionized plasma of HII regions, escaping photons carry information about their nature to distant parts of the Universe, a few of which contain astronomers. Astronomers unravel the nature of these gas clouds by catching photons whose last physical interaction was usually with an atom or ion in the cloud itself. The material with which the radiation last interacted imprints clues to its physical nature on this radiation. To find out the temperature, density, chemical abundance and ionization state of the cloud we must understand how matter behaves in a radiation field: how photons and inter-particle collisions can trigger transitions between different excitation and ionization states in atoms and molecules, and how these transitions create or destroy the photons that we eventually see.


Aims & Objectives

To present an introductory account of radiation transfer and its application to gaseous astrophysical systems, including


  • The definitions of the basic radiant quantities and the equation of radiation transfer.
  • The use of the Boltzmann and Saha equations to compute level populations and ionization equilibria - The Einstein relations and their role in computing line opacities and emissivities,
  • The Planck function and its properties,
  • The various types of atomic and molecular line transitions and broadening mechanisms encountered in nebulae,
  • The application of these theories to molecular clouds, HII regions and planetary nebulae.


Learning Outcomes

By the end of the module, students will have a comprehensive knowledge of the topics covered in the lectures and will be able to:


  • Define and use the basic radiant quantities such as specific intensity, mean intensity, flux and radiation pressure of a radiation field;
  • Differentiate and integrate the Planck function to obtain Wien’s Law and the Stefan- Boltzmann Law,
  • Use the Boltzmann equation, the Saha equation and the Einstein relations to determine level populations and ionization balance both in and out of thermodynamic equilibrium,
  • Use the equation of radiative transfer to solve for simple geometries how the emergent intensity of a beam of radiation is modified by emitting and absorbing material along its path,
  • Define the photon mean free path and optical depth, and distinguish between optically thick and optically thin media,
  • Distinguish between radiatively and collisionally induced transitions, and state their importance in relation to the global energy balance of a body of gas,
  • Distinguish between natural, collisional and thermal broadening mechanisms in spectral lines,
  • State the importance of ionization fronts, use the jump conditions to distinguish between R- and D-type fronts, and understand their importance in the evolution of an HII region.
  • Distinguish between recombination-spectrum formation in Case A and Case B, and use Balmer-line fluxes and line ratios to determine total ionizing flux and interstellar extinction in Case B,
  • Use simple atomic theory to demonstrate the usefulness of transitions between low-lying levels of common collisionally-excited species as density and temperature diagnostics in emission-line nebulae,
  • Use radio brightness temperatures of a background source and foreground nebula to determine nebular temperature,
  • Distinguish the various types of transition for simple molecules, and recognise their importance as coolants in star-forming regions,
  • Understand basic principles behind Monte Carlo radiation transfer scattering codes including sampling for direction of emission, optical depths, and scattering angles,
  • Outline a Monte Carlo scattering code and develop Monte Carlo estimators for the intensity moments of the radiation field showing how they relate to formal definitions.



Definitions of basic radiant quantities. Opacity and emissivity. The equation of radiative transfer. Source function and optical depth. Black-body radiation and the diffusion approximation. Atomic and molecular processes: bound-bound, bound-free and free-free transitions, electron scattering, Boltzmann and Saha laws, the Einstein coefficients and their relation to emission and absorption coefficients and to blackbody radiation. Masers. Line-broadening mechanisms. Stromgren spheres, protoplanetary discs. Derivation of jump conditions across ionization fronts using conservation of mass, momentum and energy. Thermal equilibrium between ionization and cooling via photon escape in nebulae. Collisional cooling and detailed balance; hydrogen recombination spectrum in Case A and Case B; common line-ratio and radio diagnostics for nebular temperature and density. Rotational and vibrational spectra and selection rules in molecules. Monte Carlo radiation transfer, sampling from probability distributions, estimators for intensity moments of the radiation field, scattering codes.


Additional information on continuous assessment etc

Please note that the definitive comments on continuous assessment will be communicated within the module.  This section is intended to give an indication of the likely breakdown and timing of the continuous assessment. 


The 25% continuous assessment is expected to take the form of writing Monte Carlo radiation transfer computer programs, building on what is taught in class. This homework will be issued around week 5 with a deadline around two weeks later.


Accreditation Matters

This module may not contain material that is part of the IOP “Core of Physics”, but does contribute to the wider and deeper learning expected in an accredited degree programme.  The skills developed in this module, and others, contribute towards the requirements of the IOP “Graduate Skill Base”.


Recommended Books

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General Information

Please also read the general information in the School's honours handbook that is available via