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Radiative Processes


Admission requirements

Knowledge of calculus, special relativity and electromagnetism at the bachelor’s level is required. In terms of the Leiden curriculum, the prerequisites for this course are Analyse 2 or Analyse 2NA, Introductie Moderne Natuurkunde, Classical Electrodynamics and Introduction to Astrophysics.


The main goal of this course is to understand and recognize the different ways matter and light interact in an astrophysical context, including emission, scattering and absorption. This allows us to physically interpret the light that we observe from astrophysical sources. Throughout the course, we will rely on mathematical derivations to gain a deep understanding of the processes involved.

We will define a number of fundamental concepts necessary to unambiguously discuss radiation. This is followed by the introduction of the basic equation of radiative transfer, which describes how radiation changes as it traverses a medium. In the remainder of the course we will keep coming back to this equation. This part will be concluded with a discussion of a few methods to solve the equation of radiative transfer.

Then we take a step back and examine the relation between the concepts introduced earlier. We will find that radiation can only be generated and changed by accelerating electrical charges, and we will deduce several fundamental relations. We will also investigate how the emission of radiation is changed when the emitting particle is moving relativistically (beaming).

This is followed by a discussion of three important mechanisms to produce continuous radiation, i.e., radiation that changes only weakly with wavelength. All these processes involve freely moving electrons: in an ionized plasma (Bremsstrahlung or free-free emission); in the presence of magnetic fields (cyclotron and synchrotron emission, depending on whether the electrons move non-relativistically or relativistically); and the interaction between relativistic electrons and photons (inverse Compton scattering).

We will conclude the lecture series with the production of radiation at discrete wavelengths, i.e. spectral lines. These processes involve electrons bound to atoms or molecules.

Course objectives

The main objective of this course is to be able to physically interpret a spectrum from an astrophysical source, based primarily on its continuum emission and to a lesser extent on its spectral lines.

Upon completion of this course you will be able to:

  • Describe the physical processes through which radiation is emitted, changed or absorbed

  • Solve the equation of radiative transfer for a range of physical conditions

  • Construct a spectrum for a range of astrophysical sources including isothermal ionized clouds, stars and charged particles moving in magnetic fields

  • Physically interpret continuum spectra including free-free emission, synchrotron emission, inverse Compton radiation and Comptonized blackbody radiation, deducing source properties such as temperature, density and optical depth

  • Physically interpret spectral lines from single charged particles, simple atoms and diatomic molecules.

Soft skills



See Schedules bachelor Astronomy

Mode of instruction

  • Lectures

  • Exercise classes

Assessment method


Blackboard will be used to communicate with students and to share lecture slides, homework assignments, and any extra materials. You must enroll on Blackboard before the first lecture. To have access, you need a student ULCN account.

Reading list

  • Radiative Processes in Astrophysics, Rybicki & Lightman, ISBN 9780471827597 (required)

  • Radiative Processes in High Energy Astrophysics, Ghisellini, ISBN 9783319006123, download here (optional)


Register via uSis. More information about signing up for classes and exams can be found here. Exchange and Study Abroad students, please see the Prospective students website for information on how to register. For a la carte and contract registration, please see the dedicated section on the Prospective students website.

Contact information

Lecturer: Prof. Dr. M (Michiel) Hogerheijde
Assistants: Andrew Barr, Christian Groeneveld