Ruprecht-Karls-Universität Heidelberg

Radiative transfer in astrophysics (Master/PhD Course)

Wintersemester, 2017

For the moment, see the lecture web page of 2013 if you want to read some of the lecture material used the last time this lecture was held. Some new material may be added, and some may be dropped..

C.P. Dullemond


Radiative transfer is one of the cornerstones of astronomy. Any radiation we receive from an astrophysical object has been processed by that object through radiative transfer. Therefore, in order to interpret observations in terms of the geometry, temperature, dynamics and composition of that object, we must be able to calculate how this radiative transfer process works.

Unfortunately, radiative transfer can be rather complicated, both physically as well as technically. In practice this often means that not all information that is encoded in observations is being retrieved. The goal of this lecture is to learn more about radiative transfer, its difficulties and the methods and computer codes to solve radiative transfer problems. A particular emphasis will be on hands-on exercises using a radiative transfer code.

Topics to be covered (provided it fits in the time):

  • learn about basics of radiative transfer theory and the problem of non-locality: LTE versus non-LTE.
  • learn more about radiative processes, beyond the basics what one typically learns in a course on theoretical astrophysics:
    • Dust continuum radiative transfer (emission, absorption, scattering; Mie scattering, Rayleigh scattering)
    • Gas line radiative transfer (LTE, non-LTE; atomic, forbidden, recombination, molecular rovibrational, molecular rotational)
    • Photoionizing radiation, photodissociating radiation
    • Thompson scattering, compton scattering
    • Polarized radiation
    • Quantum-heating of tiny particles
  • learn about the different kinds of transfer problems these processes lead to, and what their difficulties are (typically related to the non-locality of these problems)
  • learn about numerical methods for solving LTE and non-LTE radiative transfer problems:
    • Methods for integrating the formal transfer equation, including subtleties with complex gridding
    • Methods for solving non-LTE transfer problems (Monte Carlo versus discrete ordinate methods; Lambda Iteration, Accelerated Lambda Iteration, Ng-acceleration)
    • Approximate methods (Escape probability, Large Velocity Gradient)
  • learn to work with an actual radiative transfer code. We will use the RADMC-3D code for that:
    • Basics of the code
    • How to set up problems
    • How to gather the required opacities and atomic/molecular data
    • How to create spectra, images, visibilities (for interferometers) etc.
    • How to post-process these and compare to observations
  • learn about various astrophysical applications:
    • Stellar / planetary atmospheres
    • Molecular clouds
    • HII regions
    • Protoplanetary disks


This course will be given in English. It consists of 2 hours per week of lecture and 2 hours per week of exercises, most of which will be actual computer exercises in which you will use a radiative transfer code to solve "real" problems and compare with real observed data.

Time and venue

The lecture takes place on Fridays, from 14:15-16:00 in the kleine-Hoersaal in Philosophenweg 12. The exercise class takes place on the same day, 16:15-18:00 in the same room. Note: These times were changed (it used to be planned for earlier in the day but I decided to change it to the above mentioned time).


Basics of theoretical astrophysics are desireable. You must have basic experience with using computers on the linux/unix command line, compiling programs in C or fortran and making plots with any graphical software of your chosing (e.g. gnuplot, IDL, Python), and programming simple programs or scripts.

Lecture notes

Here the script will appear as we go (the order of topics may change!).

You can also have a look at the previous lecture script of this course in SS2013.

Exercises + Computer Problems

Here the exercises and computer exercises will be published. Please bring your own laptop to the exercise class. During the first exercise class we will install some of the required software for the course.


The lecture will not require additional literature. But good companion literature is:

  • Rybicki and Lightman, "Radiative Processes in Astrophysics"
  • Rob Rutten's: lecture notes on radiative transfer
  • Sara Seager, "Exoplanet Atmospheres"
  • Erika Boehm-Vitense, "Stellar Astrophysics Vol 2: Stellar Atmospheres"
  • Wendisch and Yang, "Theory of Atmospheric Radiative Transfer"
  • Dmitry Mihalas, "Stellar Atmospheres"
  • Mihalas and Mihalas, "Radiation hydrodynamics"

Verantwortlich: Cornelis Petrus Dullemond, letzte Änderung am 17.11.2017 13:43 CET
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