# Radiative transfer in astrophysics (Master/PhD Course)

### Summersemester, 2012

### C.P. Dullemond

## Introduction

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

## Organization

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.

If you wish to participate, please sign up on the moodle for this lecture. The password is radtrans.

## Time and venue

The lecture takes place on Mondays, 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 Seminarraum 1, Albert Ueberlestr 3-5, which is very close to the place where the lecture takes place.

## Requirements

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!).

- Chapter 1: Introduction
- Chapter 2: Radiative quantities
- Chapter 3: Formal transfer equation
- Chapter 4: Why radiative transfer is difficult, and methods to solve it
- Chapter 5: Radiative transfer in dusty media
- Chapter 6: Scattering of light off dust particles
- Chapter 7: Line transfer (first part of this chapter)
- Chapter 7: Line transfer (second part of this chapter)
- Chapter 8: Radiative transfer in circumstellar/interstellar media
- Chapter 9: Radiative transfer in planetary atmospheres

## 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.

- Exercise sheet 1, plus a test program to check if your gfortran compiler works.
- Exercise sheet 2
- Exercise sheet 3
- Exercise sheet 4 and the program twostream.f90
- Exercise sheet 5, the program problem_setup.f90 and the opacity file dustkappa_silicate.inp
- Exercise sheet 6
- Exercise sheet 7, the program problem_setup_2.f90, the opacity file dustkappa_silicate_2.inp, the .BMP-making program image_to_bmp.f90 (thanks to Keiji Hayashi from Stanford!) and, if you like, a nice color table ct.inp
- Voluntary addition to Exercise 7
- Exercise sheet 8, the program make_ca_cs_g.f90 and the Makefile.
- Exercise sheet 9
- Voluntary addition to Exercise 9
- Exercise sheet 10
- Exercise sheet 11

## Exam

You can have a look at this year's exam held on Monday, July 23, 2012, the formula sheet, and the solutions to the exam questions.## Literature

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"