El-Gordo from Menanteau et al. (2012)

Physics 514: Radiative Processes
Spring 2023

Tuesdays and Fridays 10:20–11:40 am, Serin 401
Instructor: Saurabh W Jha


Electromagnetic phenomena in astrophysical systems. Radiative transfer. Radiation from moving charges. Emission mechanisms: bremsstrahlung, synchrotron, Compton scattering. Plasma effects. Atomic and molecular structure and spectroscopy.

Contact Information

Prof. Saurabh W Jha (he/him)
Room 315, Serin Physics Building, Busch campus
Email: saurabh[at]physics.rutgers.edu
Phone: 848-445-8962 (email preferred)

Office hours: Thursdays 3:30 to 4:30 pm on Zoom, or by appointment


The required textbook we will use is Radiative Processes in Astrophysics by Rybicki and Lightman. This is not always easy to find, so get your copy early. You may want to search for other formats of this book.

Supplementary textbooks (not required) include An Introduction to Modern Astrophysics, by Carroll & Ostlie, Theoretical Astrophysics, Volume I: Astrophysical Processes, by T. Padmanabhan, and The Physics of Astrophysics, Volume I: Radiation, by Frank H. Shu.


We will have roughly weekly problem sets due on Fridays. In working on the problem sets, you are encouraged to work in groups, though your submitted write-up should be your own. You must list your collaborators on the write-up. You are allowed to consult any outside sources (which, other than the course lecture notes or the textbook, must be cited), except that you may not examine problem set solutions from previous years of Physics 514 or other similar courses online. Any use of AI to assist with the problem sets must be cited, and you have to show me how you did it. Late problem sets will be accepted with a 20% penalty (one day late) or a 50% penalty (two days late). Solutions will be posted after two days, and no late problem sets will be accepted after the solutions are posted. All problem sets are due in PDF format on Canvas.

There will be one in-class midterm exam and a final exam scheduled by the university. There will also be a numerical group project, where you write the code to solve a particular problem, working in groups of 2 or 3 people.

The final grade will be calculated from the problem sets (50%), midterm exam (15%), numerical project (10%), and final exam (25%). The lowest problem set grade will be dropped in calculating the final grade.

Academic Integrity

Students are expected to maintain the highest level of academic integrity. You should be familiar with the university policy on academic integrity. Violations will be reported and enforced according to this policy. See also the department's page on academic integrity for graduate students.

Use of external website resources (such as Chegg.com or others) to obtain solutions to homework assignments or exams is cheating and a violation of the University Academic Integrity policy. Cheating in the course may result in grade penalties, disciplinary sanctions or educational sanctions. Posting homework assignments or exams to external sites without the instructor's permission may be a violation of copyright and may constitute the facilitation of dishonesty, which may result in the same penalties as cheating. 

The Rutgers honor pledge will be included on all major assignments for you to sign: On my honor, I have neither received nor given any unauthorized assistance on this examination/assignment.

Almost all original work is the intellectual property of its authors. In this course, this includes syllabi, lecture slides, recorded lectures, homework problems, exams, and other materials, in either printed or electronic form. You may not copy this work, post it online, or disseminate it in any way without the explicit permission of the instructor. Respect for the author's efforts and for the author’s intellectual property rights is an important value that members of the university community are expected to take seriously.

Schedule: Topics and Assignments

This schedule may be updated as the semester progresses.

Jan 17 (Tue)
radiative transfer
Jan 20 (Fri)
Jan 24 (Tue)
Jan 27 (Fri)
PS 1 due
Jan 31 (Tue)
Feb 03 (Fri)
radiation fields
PS 2 due
Feb 07 (Tue)
Feb 10 (Fri)
radiation from moving charges
PS 3 due
Feb 14 (Tue)
Feb 17 (Fri)
PS 4 due
Feb 21 (Tue)
Feb 24 (Fri)
PS 5 due
Feb 28 (Tue)
Mar 03 (Fri)
PS 6 due
Mar 07 (Tue)
in-class midterm exam
  Mar 10 (Fri)     numerical project description due
Mar 14, 17
spring break
Mar 21 (Tue)
synchrotron radiation
Mar 24 (Fri)
PS 7 due
Mar 28 (Tue)
Compton scattering;
inverse Compton
Mar 31 (Fri)
PS 8 due
Apr 04 (Tue)
plasma effects
Apr 07 (Fri)
atomic structure
PS 9 due
Apr 18 (Tue)
Apr 21 (Fri)
radiative transitions
PS 10 due
Apr 25(Tue)
Apr 21 (Fri)
molecular structure/transitions
PS 11 due
Apr 25 (Tue)
course summary
Apr 28 (Fri)
numerical project presentations
numerical projects due
May 5 (Fri)
take-home final exam due

Detailed Topic List (to be modifed as the semester progresses)

Lectures 1-5. Fundamentals of radiative transfer: specific intensity, radiative transfer, optical depth, thermal radiation, Einstein coefficients, scattering, and diffusion.
Lectures 6, 7. Review of radiation fields: Maxwell's equations, electromagnetic waves, polarization, Stokes parameters, scalar and vector potentials.
Lecture 8, 9, 10. Radiation from moving charges: Lienard-Wiechart potentials, Larmor's formula, dipole approximation, multipole expansion, Thomson scattering.
Lectures 11, 12, 13. Relativistic covariance and kinematics: 4-vectors, relativistic mechanics, emission from relativistic particles, relativistic beaming.
Lecture 14 . Bremsstrahlung: non-relativistic free-free emission and absorption, relativistic bremsstrahlung.
Lectures 15, 16. Synchrotron radiation: spectral energy distribution, polarization, synchrotron self-absorption, cooling. Gamma-ray bursts.
Lectures 17, 18. Compton scattering: cross-section, inverse Compton scattering, spectral energy distribution, multiple scattering, Kompaneets equation, Sunyaev-Zeldovich effect.
Lecture 19. Plasma effects: plasma frequency, dispersion measure, Faraday rotation.
Lectures 20, 21. Atomic structure: one-electron systems, many-electron systems, fine structure, Zeeman effect, hyperfine structure, thermal equlibrium, Saha equation.
Lectures 22, 23. Radiative transitions: oscillator strengths, selection rules, transition rates, hydrogen recombination, line broadening.
Lecture 24. Molecular structure: electronic transitions, rotational transitions, vibrational transitions, combined spectra.
Lecture 25. Course summary; applications of radiative processes in the astrophysical literature.
Lecture 26. Numerical project presentations.


A list of physical and astronomical constants in cgs units.

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Astrophysics at RutgersDepartment of Physics and AstronomyRutgers University

Last updated: April 16, 2023 swj