## Trinity College Dublin, The University of Dublin

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# PYU33A06 Statistical Thermodynamics and Astrophysical Spectroscopy

Michaelmas Term – 30 lectures/tutorials – 5 credits (G Cross, B Espey)

Part I: Statistical Thermodynamics
Part II: Astrophysical Spectroscopy

Learning Outcomes
On successful completion of this module, students should be able to:

• Outline the basic concepts of equilibrium statistical thermodynamics
• Describe mathematically the behaviour of physical systems governed by Fermi-Dirac, Bose-Einstein, and Maxwell-Boltzmann statistics
• Determine the partition functions of simple quantum systems
• Distinguish between thermodynamic equilibrium (TE), local thermodynamic equilibrium (LTE), & non-LTE, and how these apply in the case of stellar interiors and surfaces
• Describe the basic phases of the curve-of-growth and illustrate the appearance of the line profiles associated with each stage
• Interpret the multi-dimensional stellar classification system with reference to the Saha and Boltzmann equations

Syllabus

Part I: Statistical Thermodynamics
The purpose of this course is to introduce Statistical Thermodynamics, which provides a microscopic understanding of the macroscopic thermodynamic properties of materials. A simple assumption of equal statistical weights allows the properties of individual quantum particles to be combined together properly to calculate macroscopic thermodynamic quantities, which can be compared with experiment. Topics covered (1) Counting states in classical and quantum systems (2) Fundamental assumption of statistical physics; ensembles (3) Model system of 2-state components (4) Two systems in equilibrium: entropy, temperature and chemical potential (5) Partition functions and their relation to thermodynamic quantities (6) Third Law of Thermodynamics (7) Fermi-Dirac and Bose-Einstein Statistics (8) Quasi-classical statistics: equipartition of energy (9) Application of quantum statistics to photons, gases, and solids.

Part II: Astrophysical Spectroscopy
Spectroscopy across the full EM spectrum is the primary means for determining the properties and characteristics of astronomical objects. Some important parameters which characterize astronomical spectra, and which determine the choice of instrumentation are reviewed, with a brief outline of some examples, focussing on the optical and ultraviolet portions of the spectrum. The underlying physics required for the interpretation of stellar spectra for stellar classification and for the diagnostics of low density plasmas is discussed and applied to some specific, topical examples.

 Assessment Weighting Statistical Thermodynamics examination 50% Astrophysical Spectroscopy examination 40% Astrophysical Spectroscopy Continuous Assessment 10%