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AS4012   The Physics of Nebulae and Stars 2

Academic year(s): 2019-2020

Key information

SCOTCAT credits : 15

ECTS credits : 7

Level : SCQF Level 10

Semester: 2

Availability restrictions: Not automatically available to General Degree students

Planned timetable: 12 noon odd Mon, 3.00 pm even Tue, 12 noon Wed & Fri

This module develops the physics of stellar interiors and atmospheres from the basic equations of stellar structure introduced in AS2001/AS2101 using the radiative transfer concepts developed in Nebulae and Stars I. Topics include: the equation of state that provides pressure support at the high temperatures and densities found in normal and white-dwarf stars; the interaction of radiation with matter, both in terms of radiation-pressure support in super-massive stars and in terms of the role of opacity in controlling the flow of energy from the stellar interior to the surface; the equation of radiative transfer and the effects of local temperatures, pressures and velocity fields on the continuum and line absorption profiles in the emergent spectrum. Computer-aided tutorial exercises illustrate the computational schemes that represent one of the triumphs of late twentieth-century physics, in their ability to predict the observable properties of a star from its radius and luminosity, which in turn are determined by its mass, age and chemical composition.

Relationship to other modules

Pre-requisite(s): Before taking this module you must pass AS4011

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 P Woitke
Module teaching staff: Dr P Woitke

Additional information from school

Aims & Objectives

Develop a deeper understanding of all physical processes that are important in the atmospheres and interiors of stars to explain their observed spectra, their internal structure and their evolution.


Learning Outcomes

By the end of the module the students will be able to:


  • Solve the equation of radiation transfer for static, plane parallel model atmospheres in the gray atmosphere approximation, both analytically and numerically.
  • Explain limb darkening in stellar atmospheres, and continuum and spectral line
  • Understand the concept of LTE and the conditions where it applies.
  • Understand the concept of the curve of growth and its significance for measuring stellar properties and element
  • Be able to define and calculate Jeans' masses and densities.
  • Be able to write down and explain the terms in the equations of stellar structure and solve them using simple numerical techniques.
  • Understand the equation of state that provides pressure support in stellar interiors.
  • Understand what is meant by a homologous model and apply it to solve the equations of stellar
  • Understand and describe nuclear burning in stars including CNO cycle and pp-chain.
  • Understand and describe stellar properties on the main sequence and explain post main sequence evolution and the fate of stars.



The course is organised in two parts: stellar atmospheres (11 lectures) and stellar interiors (12 lectures). There are six additional workshop sessions taking place in the lecture room with exam-like questions. There are two assessed computational homework exercises to self-compute simple models for the emergent spectrum and the inner structure of solar-like stars using PYTHON, which count with 12.5% each towards to module grade.


Additional information on workshops and continuous assessment

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 six workshops develop exam-style problem-solving skills. The questions will be distributed about one week prior to the sessions. Students will then be subdivided into small groups in the workshops to discuss and compare their solutions. Complete solutions of all exam-style questions will be made available to the students afterwards on Moodle.  


The deadlines for submitting the assessed computational homework are likely to be towards the end of weeks 5 and 11.


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