Astronomy 601: Fall 2017

Ionization from First Galaxies (Ricotti 2002) 

"Radiative Processes"

The production and propagation of radiation and its application in a variety of astrophysical contexts.


    Instructor:  Massimo Ricotti
    Class:       room ATL 0201
    Lectures:    Tuesday and Thursday 
                 12:30pm to 1:45pm
    First class: Tu Aug 28
    Last  class: Th Dec 7

Contact info and Notes

I will keep a copy of the lecture notes (hand written notes kindly provided by Eve Ostriker) in the mail room. Please return the notes after you are done with them so that other students will be able to use them too. If you need help or have questions you can reach me here:

Course Description

The emission, absorption and scattering of radiation by matter with astrophysical applications. Emphasis on basic theory and problem-solving.

  1. Radiative transfer: specific intensity, transfer equation, opacity, diffusion, scattering.
  2. Statistical mechanics of matter and radiation: LTE, level populations, rate equations.
  3. Electrodynamics: Maxwell equations, spectra of radiation, polarization, dipole and multipole radiation, Thompson scattering.
  4. Plasma radiation: bremsstrahlung and synchrotron emission, Compton scattering, EM wave propagation in plasmas.
  5. Atomic and molecular radiation: energy levels, Einstein coefficients, oscillator strengths, line broadening.
  6. Textbooks and Notes

    The Physics of Astrophysics Volume I: Radiation by F.H. Shu
    Radiative Processes in Astrophysics by G. Rybicki and A. Lightman

    In addition, I will post the lecture notes I use to teach on ELMS or hand out hardcopies.

    Course Grading

    • Homework 50%
    • Midterm Exam 20%
    • Final Exam 30%

    There will be one in-class Midterm exam (tentatively scheduled on Oct 24th) and an in-class Final (on Monday, Dec 18 1:30pm-3:30pm, see Final Exam Schedule Fall 2017. Class participation is strongly encouraged. Class attendance is instead required.

    Policies and course outline

    The Syllabus for this course is available in pdf format on ELMS and here: ASTR601_Syl17.pdf

    You can find updated information on Course Related Policies at:

    Tentative Course Outline - 28 lectures & 2 exams
    A. Radiative transfer - 9 lectures

    1. Tu Aug 29: Course Syllabus. Radiation definitions; specific intensity, photon distribution function, occupation number, energy density, flux, momentum flux, radiation pressure (Shu Ch. 1; R-L § 1.1-1.3)
    2. Th Aug 31: Radiation definitions cont..
    3. Tu Sept 5: Equation of radiative transfer; emissivity and opacity. (Shu Ch. 1; R-L § 1.4)
    4. Th Sept 7: Blackbody radiation: radiation thermodynamics, Stefan-Boltzmann law; Bose-Einstein statistics; Planck spectrum; Rayleight-Jeans and Wien limits, radiation constant, effective temperature, color temperature and brightness temperature (Shu Ch. 1,2; R-L § 1.5)
    5. Tu Sept. 12 : Moment equations; radiative diffusion approximation, Rosseland mean opacity, scattering and random walks (Shu Ch. 2; R-L § 1.7, 1.8)
    6. Th Sept. 14: Moment equations cont.
    7. Tu Sept 19: General solution of radiative transfer equation; source function; optically-thick and -thin limits; LTE; line formation: absorption and emission spectra, limb darkening (Shu Ch. 3; R-L § 1.4)
    8. Th Sept 22: General solution of radiative transfer equation cont.
    9. Tu Sept 26: Plane-parallel atmospheres: radiative equilibrium, grey opacity, Eddington approximation (Shu Ch. 4; R-L § 1.8)

    B. Thermodynamics and Statistical Mechanics - 4 lectures

    1. Th Sept 28: Statistical mechanics: definitions of entropy, temperature, chemical potential, pressure, grand canonical partition function (Gibbs sum); Thermodynamics: thermodynamic identity, grand potential, entropy (Shu Ch. 6; R-L § 1.5)
    2. Tu Oct 3: Quantum statistical mechanics: Fermion and Boson partition functions, grand potentials, occupation numbers (Shu Ch. 6; R-L § 1.5)
    3. Th Oct 5:Statistical equilibria: reaction equilibrium, Boltzmann law for internal level populations, Saha equation for ionization state populations; free particle partition functions (Shu Ch. 7; R-L § 9.5)
    4. Tu Oct 10: Rate equations and detailed balance; Einstein A and B coefficients, relations to emissivity, absorption opacity, cross-section, oscillator strength; collisional processes (Shu Ch. 8; R-L § 1.6)

    C. Electrodynamics - 5 lectures

    1. Th Oct 12: Maxwell equations; vacuum electromagnetic wave equations; plane parallel waves; EM energy and momentum flux [Poynting vector and Maxwell stress tensor] (Shu Ch. 11; R-L § 2.1-2.2)
    2. Tu Oct 17: Fourier spectra of radiation; Stokes parameters and polarization (Shu Ch. 12; R-L § 2.3-2.4)
    3. Th Oct 19: EM wave equation with sources; scalar and vector potentials; gauge transformations; retarded potentials; Green's function solutions for inhomogeneous wave equations, single particle (Lienard-Wiechert) retarded potential (Shu Ch. 13; R-L § 2.5, § 3.1-3.2)
    4. Tu Oct 24: Midterm exam
    5. Th Oct 26: Wave zone; electric dipole radiation; radiation reaction; Thomson scattering Rayleigh scattering (Shu Ch. 14; R-L § 3.3-3.6)
    6. Tu Oct 31: Multipole radiation: magnetic dipole, electric quadrupole, permitted and forbidden transitions (Shu Ch. 15; R-L § 3.3))

    D. Plasma radiation and transfer - 5 lectures

    1. Th Nov 2: Thermal Bremsstrahlung (Shu Ch. 15; R-L Ch. 5)
    2. Tu Nov 7: Compton scattering (R-L Ch. 7)
    3. Th Nov 9: Radiation from relativistic charges (Shu Ch. 16, 17; R-L Ch. 4)
    4. Tu Nov 14: Synchrotron radiation (Shu Ch. 18, 19; R-L Ch. 6)
    5. Th Nov 16: EM waves in plasmas; dispersion; Faraday rotation (Shu Ch. 20; R-L Ch. 8)

    E. Atomic and molecular structure and radiation (QED) - 5 lectures

    1. Tu Nov 21: Electromagnetic Hamiltonian (Shu Ch. 21; R-L § 10.1)
    2. Th Nov 23: Thanksgiving holiday
    3. Tu Nov 28: Semiclassical theory of radiative transitions: quantum matter/radiation interaction Hamiltonian, theory vector potential, E and B fields, semiclassical radiation energy density, absorption and emission Hamiltonians (Shu Ch. 22; R-L § 10.1)
    4. Th Nov 30: Time dependent perturbation theory; propagator; one- and two- photons transitions; transition probabilities and rates for absorption/emission [Fermi's golden rule] (Shu Ch. 22; R-L § 10.1)
    5. Tu Dec 5: Dipole approximation; bound-bound transition rates and cross-sections; oscillator strengths; matrix elements; Einstein A and B coefficients for bound-bound transitions (Shu Ch. 23; R-L § 10.2, 10.3, 10.5)
    6. Th Dec 7: Bound-free transitions in the Born approximation; photoionization and recombination rates and cross-sections; Einstein-Milne relations; linewidth and natural broadening (Shu Ch. 23; R-L § 10.5, 10.6)
    7. Monday Dec 18 (1:30pm-3:30pm): Final exam

    Lecture homework

    Homework will be assigned roughly every other week. Their due dates will be announced at the time they are assigned. On the due date the students will be expected to turn in their homework in class. The homework turned in will be graded and returned to the students.

    I will post the homework assignements, solutions and grades on ELMS

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    Past Midterm and Final Exams


    • Cole Miller's lecture NOTES for ASTR601