El-Gordo from Menanteau et al. (2012)

Physics 514: Radiative Processes
Spring 2022

Tuesdays and Thursdays 3:50–5:10 pm
now: online via Canvas
later: 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 after class, 5:15–6:15 pm, 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.

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. 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.

Technological Requirements

As our class begins in an online/virtual format, you will need a computer or tablet and good Internet access to connect. A mobile phone may not be large enough to show slides and equations clearly, and will be difficult to use for the numerical problems that require computation. A phone camera with an app such as Adobe Scan, Office Lens, Apple Notes, or something similar will be useful to convert pictures of your completed assignments into PDF format for upload and submission to Canvas. Please visit the Rutgers Student Tech Guide page for resources available to all students. If you do not have the appropriate technology for financial reasons, please email the Dean of Students for assistance. If you are facing other financial hardships, please visit the Office of Financial Aid.

Schedule: Topics and Assignments

This schedule may be updated as the semester progresses.

Jan 18 (Tue)
online via Zoom
radiative transfer
Jan 20 (Thu)
online via Zoom
Jan 25 (Tue)
online via Zoom
Jan 27 (Thu)
online via Zoom
PS 1 due Friday Jan 28
Feb 01 (Tue)
Feb 03 (Thu)
radiation fields
PS 2 due Friday Feb 04
Feb 08 (Tue)
Feb 10 (Thu)
radiation from moving charges
PS 3 due Friday Feb 11
Feb 15 (Tue)
Feb 17 (Thu)
PS 4 due Friday Feb 18
Feb 22 (Tue)
Feb 24 (Thu)
PS 5 due Friday Feb 25
Mar 01 (Tue)
Mar 03 (Thu)
PS 6 due Friday Mar 04
Mar 08 (Tue)
in-class midterm exam
15 Mar 10 (Thu)     numerical project description due Mar 11
Mar 15, 17
spring break
Mar 22 (Tue)
synchrotron radiation
Mar 24 (Thu)
PS 7 due Friday Mar 25
Mar 29 (Tue)
Compton scattering;
inverse Compton
Mar 31 (Thu)
PS 8 due Friday Apr 01
Apr 05 (Tue)
plasma effects
Apr 07 (Thu)
atomic structure
PS 9 due Friday Apr 08
Apr 12 (Tue)
Apr 14 (Thu)
radiative transitions
PS 10 due Friday Apr 15
Apr 19 (Tue)
Apr 21 (Thu)
molecular structure/transitions
PS 11 due Friday Apr 22
Apr 26 (Tue)
course summary
Apr 28 (Thu)
numerical project presentations
numerical projects
due Apr 29
final exam to be scheduled

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.
Lectures 14, 15. Bremsstrahlung: non-relativistic free-free emission and absorption, relativistic bremsstrahlung.
Lectures 16, 17. Synchrotron radiation: spectral energy distribution, polarization, synchrotron self-absorption, cooling. Gamma-ray bursts.
Lectures 17, 18, 19. Compton scattering: cross-section, inverse Compton scattering, spectral energy distribution, multiple scattering, Kompaneets equation, Sunyaev-Zeldovich effect.
Lecture 20. Plasma effects: plasma frequency, dispersion measure, Faraday rotation.
Lectures 21, 22. Atomic structure: one-electron systems, many-electron systems, fine structure, Zeeman effect, hyperfine structure, thermal equlibrium, Saha equation.
Lectures 23, 24. Radiative transitions: oscillator strengths, selection rules, transition rates, hydrogen recombination, line broadening.
Lecture 25. Molecular structure: electronic transitions, rotational transitions, vibrational transitions, combined spectra.
Lecture 26. Course summary; applications of radiative processes in the astrophysical literature.
Lecture 27. 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: January 12, 2022 swj