APS 5110: INTERNAL PROCESSES 1

Schedule

Course Description

Syllabus

Problem Sets

Fall 2002

Instructor: Phil Maloney
Email: maloneyącasa.colorado.edu
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Schedule: MWF 10:00-10:50, in G1B39

This course (IP-1) is designed for first-year graduate students in astrophysics and planetary science, as well as interested physics students. It provides a survey of theory and applications of the processes that determine the physical characteristics of stars, planets, galaxies, and gas in the interplanetary, interstellar, and intergalactic medium. The primary reason for this course is to understand "Spectrum Formation in Astrophysical and Planetary Sciences". This naturally introduces the need to cover such topics as: Applied Quantum Mechanics; Radiative, Thermal, & Ionization Processes; Atomic and Molecular Spectroscopy; Radiative Transfer; and Statistical Mechanics. In the spring semester, the continuation of this course (IP-2) covers more statistical physics, kinetic theory, radiative transport, and fluid dynamics, with specific applications to astrophysics and planetary science.

Highlights:

• Introduction and Review of Quantum Mechanics
• Multi-electron spectroscopy
• Ionization, Excitation, Radiative Cooling
• Radiative Transitions and Opacities
• Molecular Physics and Spectroscopy
• Introduction to Radiative Transfer
• Statistical Mechanics (Micro-Canonical, Canonical, Grand Canonical Ensembles)
• Quantum Statistics

A stunning image of the Rosette Nebula in Monoceros, taken by Travis Rector and collaborators using the Mosaic Camera on the 0.9m telescope on Kitt Peak. The hot blue stars in the center are responsible for ionizing the gas and clearing the central hole (through the action of stellar winds). Red, blue, and green correspond to emission from hydrogen, sulfur, and oxygen, respectively.

Introduction and Review of Quantum Mechanics:

• Operators, Schroedinger Equation, Angular Momentum
• Relationships to Classical Mechanics (orbits, angular momentum, etc.)
• Perturbation Theory (time-independent, time-dependent)
• Hydrogen atom and its spectroscopy
• Central potentials: wavefunctions and spherical harmonics
• Spin, magnetic moments, fine structure, hyperfine structure, Zeeman effect

Multi-electron spectroscopy:

• Single-electron orbitals (shells, sub-shells)
• Hamiltonian with perturbation terms
• L-S coupling (configurations, terms, levels)
• Isoelectronic sequences and Generalized Pauli Principle
• Angular momentum coupling, "raising & lowering" operators, Clebsch-Gordan coefficients
• Radiative selection rules: allowed, forbidden, semi-forbidden, fine-structure lines

Ionization, Excitation, Radiative Cooling

• Ionization Equilibrium (coronal, photoionization, Saha models)
• Processes and rate coefficients (collisional ionization, radiative and dielectronic recombination)
• Collisional excitation/de-excitation and detailed balance
• (2-level atom, collision strengths, line quenching)
• Radiative cooling function and plasma diagnostics (density, temperature, abundances, etc.)
• Thermal equilibrium and thermal instability

Radiative Transitions and Opacities

• Blackbody spectrum, quantum oscillators (second quantization)
• Two-level atom, Einstein "A and B relations", stimulated emission, maser action
• Absorption and emission processes, optical depth, curve of growth
• Line profile functions (Doppler, Lorentz, Voigt profiles)
• Radiative transfer equation, emissivity and absorption coefficients
• Non-LTE, 2-level atom
• Opacity processes (continuum and lines; radio/IR through UV/X-ray/gamma-ray)

Molecular Physics and Spectroscopy

• Molecular orbitals: bonding and anti-bonding, Born-Oppenheimer approximation
• Rigid rotator, harmonic oscillator, and departures
• Electronic, vibrational, and rotational spectra
• Effects of nuclear spin: homonuclear molecules (H₂, N₂, O₂, etc.)
• Nuclear motion, Franck-Condon principle, Lambda-doubling
• Molecule formation, destruction, pre-dissociation

Introduction to Radiative Transfer

• Definitions (specific intensity, mean intensity, flux moments, etc.)
• Equation of transfer in simple cases (pure emission, pure absorption)
• Source function and formal solution
• Gaussian quadratures, Eddington approximation, two-stream approximation
• Grey atmosphere (Milne solution) and emergent intensity
• Radiative equilibrium; effects of absorption and scattering
• Line formation; redistribution function; escape probability; diffusion approximation
• Mean opacities (flux-weighted, Rosseland, Planck, Absorption means)

Introduction to Transport Phenomena

• Random walk, Binomial distributions, and diffusion
• Transport coefficients, mean-free-paths, collision times
• Scattering and absorption, line escape formalisms
• Langevin and Fokker-Planck equations; applications

Review of Undergraduate Thermodynamics

• Three laws of thermodynamics
• State variables, mathematical theorems, Maxwell relations, Legendre transformations
• Phase diagrams, latent heats, adiabatic processes, isothermal processes
• Heat transport processes (conduction, radiation, etc.)

Introduction to Statistical Mechanics

• Microstates and macrostates, phase space
• Statistical definitions of temperature, entropy, chemical potential
• Enthalpy, Helmholtz and Gibbs Free Energies
• N-dimensional phase space, entropy of mixing, Gibbs paradox
• Review of Hamiltonian mechanics and phase-space trajectories
• Poincare invariant theorem, Poisson brackets, Liouville's Theorem

Micro-Canonical and Canonical Ensembles

• Phase-space density function and ensemble averages
• Derivation of thermodynamic functions, equipartition theorem
• Boltzmann statistics, partition functions, and applications
• Paramagnetism (classical and quantum versions; spin-1/2 and general spin)
• Ideal gases (classical), harmonic oscillator (classical and quantum)
• Thermal equilibrium (Gibbs function, chemical potentials, Saha equation)

Grand Canonical Ensemble

• Grand partition function, fugacity
• Derivation of thermodynamic variables
• Applications: ideal gases, Fermi-Dirac & Bose-Einstein statistics
• Equation of state derived from Grand Partition Function

Quantum Statistics (Fermi-Dirac, Bose-Einstein)

• Derivation of FD and BE statistics from micro-canonical ensemble
• Properties of FD and BE distributions (Fermi level, BE condensation)
• Equations of state (relativistic and non-relativistic ideal gases)
• Photon (BE) and neutrino (FD) statistics
• Critical temperatures and Bose-Einstein phase transitions

• Problem Set 1 (LaTeX; gzip'd PostScript)
• Problem Set 2 (LaTeX; gzip'd PostScript)
• Problem Set 3 (LaTeX; gzip'd PostScript)
• Problem Set 4 (LaTeX; gzip'd PostScript)
• Problem Set 5 (LaTeX; gzip'd PostScript)
• Problem Set 6 (LaTeX; gzip'd PostScript)
• Problem Set 7 (LaTeX; gzip'd PostScript)
• Problem Set 8 (TeX; gzip'd PostScript)