Postgraduate Lectures - Course PY5013: Introduction to Quantitative Spectroscopy and Radiative Transfer

Lecturer: Dr. Graham Harper

Rationale:
To provide a theoretical and practical foundation for the analysis of astrophysical and laboratory plasma spectra under general non-equilibrium conditions.
To provide best practice guidelines for solving and analysing radiative transfer problems.

Module Aims:
To provide an overview how the concepts of atomic physics, statistical equilibrium, and the propagation of radiation can be integrated to analyze spectra in a research context. This is a graduate level course.
 
Module Learning Outcomes: On successful completion of this module, students will be able to:
1) Understand the concepts of non- Local Thermodynamic Equilibrium
2) Construct appropriate rate equations for plasma diagnostics
3) Solve the non-LTE problem exactly and in approximate form
4) Appreciate best practices for solving the radiative transfer problems
5) Locate atomic data resources and public radiative transfer codes
6) Construct simple code to solve a two-level atom problem

Teaching and Learning Methods, including contact hours:  
Frontal Teaching: 14 hrs
Individual Reading: 64 hrs
Problem sets:  4 assignments of 4 hours each (16 hrs)
Computer laboratory sessions: 4 hours (2 sessions of 2 hours)

Syllabus:
An appreciation of spectra: emission and absorption, line and continuum.
The Equation of Radiative Transfer
Atomic Processes: collisional and radiative, bound-bound, bound-free, and free-free
Opacity and emissivity: the source function and optical depth.
Local Thermodynamic Equilibrium
Rate (statistical) equilibrium equations, advection
Applications I: optically thin electron density and temperature diagnostics
Source functions: different descriptions of two-level atoms, Equivalent-Two-Level-Atom
Solving the radiative transfer problem: long and short characteristics, Feautrier’s method
Solution to some simple transfer problems: kernel functions, thermalization depths
Numerical techniques I: numerical solutions for absorption spectra
Applications II: escape probabilities, correcting for opacity effects in traditional diagnostics
Advanced topics I: geometry, velocity fields, partial redistribution
Advanced topics II: time dependent solutions for rate equations
Advanced topics III: line formation and the multi-level atom
Numerical techniques II: testing codes and discrete ordinates

Assessment:
Continuous assessment: 4 open-book assignments (30%), 2 numerical laboratory projects (10%). Final examination (60%)

Evaluation of the module:
Pre- and post-course concept questionnaires. Post-course evaluation of class assessment.

Indicative Reading and Resources:
Radiative Transfer in Stellar Atmospheres, 2003, R. J. Rutten (8th edition) publically available.
The Physics of Astrophysics Vol 1: Radiation, 1991 F. H. Shu, University Science Books
Stellar Atmospheres, 1978, D. Mihalas (2nd edition)
Radiation Hydrodynamics, 2004, J. Castor, Cambridge Univ. Press
Foundations of Radiation Hydrodynamics, 1999, Mihalas, D. And Weibel-Mihalas, B., Dover Publications, Inc. Mineola, New York
Astrophysics of Gaseous Nebulae and Active Galactic Nuclei (Osterbrock & Ferland)
(Review) Escape Probabilities, G. Rybicki, 1984, in Method in Radiative Transfer. Ed. W. Kalkofen, Cambridge University Press
(Resource) NIST Atomic and Molecular Database, TopBase (atomic data)
(Resource) StarCAT (T. R. Ayres) – stellar ultraviolet spectral library
(Resource) MULTI – a radiative transfer code for 1-D problems (planar-spherical)
(Resource) CHIANTI – atomic data and optically thin solutions (high temperature plasmas)