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AS 713 Spectroscopy in Astrophysics Fall 2014 Monday 9:30 - 11:00, Wednesday 2:00 – 3:30 Astronomy Conference Room CAS 502 Prof. James Jackson CAS 605 353-6499 [email protected] Office Hours: MWF 11-12 Overview: This course presents the physical basis for spectroscopic measurements in astronomy. We will therefore cover elementary quantum mechanics, to see where the energy levels come from, and statistical mechanics, to see what determines the strength of a spectral line. Armed with our copious knowledge, we will then learn how to measure physical quantities (temperature, density, column density, composition...) from spectroscopic measurements. Finally, we will review current instrumentation used for spectroscopic measurements. Grading: problem sets 40 % midterm 30 % final 30 % Midterm: The midterm exam will be held on Wednesday, October 15 in class. Final: There will be an oral final during finals week. Late Work: I do not accept late work except under extraordinary circumstances. Please contact me if you foresee an extraordinary circumstance to make arrangements. Collaboration: I encourage collaboration on problem sets, but please do not copy. Discussions about how to solve a problem are fine, but exchanging papers is unacceptable. Academic Conduct: Each of you should adhere to the Graduate School’s policies on academic conduct. Do not cheat, plagiarize, or copy another student’s work. Drops: The last day to drop classes without a “W” is February 14, and with a “W” is March 7. Textbooks: No single text covers all the material in this course. You are not required to purchase any texts. For the first part of the course, a good elementary text on quantum mechanics is best (e.g., Anderson, Cohen-Tannoudji...). For the second part of the course, there are a few good texts, such as: Shu, The Physics of Astrophysics, Vol. 1, Radiation Rybicki and Lightman, Radiative Processes in Astrophysics Spitzer, Physics of the Interstellar Medium Townes and Schawlow, Microwave Spectroscopy COURSE OUTLINE I. Review of Quantum Mechanics A. Wave Functions B. Dispersion relations C. Schrödinger's equation D. Stationary states E. Eigenvalues and quantization F. Operators G. Simple one-dimensional potentials 1. example: constant potentials 2. example: The simple harmonic oscillator H. Central Potentials I. Spherical Harmonics II. Atoms A. The hydrogen atom B. Angular momentum and spin C. Electronic orbitals and notation D. More complicated atoms III. Molecules A. Rotation B. Vibration C. Linear molecules D. Symmetric rotors E. Asymmetric rotors IV. Time Independent Perturbation Theory A. Two level systems ex 1. H I fine structure ex 2. NH$_3$ inversion splitting B. N-level systems ex 1. Zeeman splitting ex 2. Nuclear quadrupole hyperfine splitting V. Time Dependent Perturbation Theory A. Electric Dipole B. Magnetic Dipole C. Electric Quadrupole VI. Atomic Spectral Lines A. Electronic Orbital B. Fine structure VII. Molecular Spectral Lines A. Rotational B. Lambda doubling C. Vibrational D. Inversion E. Hyperfine VIII. Review of Statistical Mechanics A. Thermal Equilibrium B. Maxwell-Boltzmann distribution C. Connection to thermodynamics D. Partition Function E. The Saha equation IX. Atomic and Molecular Excitation A. Collisional excitation B. Radiative excitation C. Detailed balance D. The rate equations E. Critical density and excitation temperature F. Examples 1. Two level system 2. Multi-level system G. Local Thermodynamic Equilibrium (LTE) H. Non-LTE Excitation 1. Subthermal excitation 2. Masers X. Physical Parameters from Lines A. Temperature B. Column Density C. Density D. Radiation Fields E. Kinematics XI. Line Shapes A. Natural broadening B. Thermal broadening C. Pressure broadening D. Doppler broadening XII. Spectrometers A. Prisms B. Gratings C. Circular Variable Filters D. Echelles E. Fabry-Perots F. Filterbanks G. Autocorrelators H. Acousto-Optical Spectrometers