Title: Optical properties and radiative transfer
Lecturers: Ciska Kemper & Alvaro Sanchez-Monge
Context: ICE summer school 2023 -- Life Cycle of Dust
Date: 4 July 2023 -- 14:00-18:00

In order to calculate the absorption and scattering efficiencies, we will be using a software package called optool¹²³⁴, available from https://github.com/cdominik/optool, and developed by Carsten Dominik, based on the routines written by Michiel Min and Ryo Tazaki. This package allows the conversion from $n$ and $k$ values to absorption and scattering efficiencies (including a full scattering matrix) for different grain shapes, including Mie theory, hollow spheres, fractal grains, and continuous distribution of ellipsoids. It also allows for the combination of different materials in one grain, including vacuum, to represent porosity.

optool calculates the mass absorption coefficients $\kappa$, rather than $Q$, as this is more meaningful for the general, e.g. non-spherical case. $\kappa$ gives the extinction cross-section (in cm$^2$) per mass (in g) of material. Derive that for the spherical case, $\kappa$ and $Q$ are related as:

$$ \kappa = \frac{3}{4} \frac{1}{\rho_\mathrm{d}} \frac{Q}{a} $$

where $a$ is the radius of the grain, and $\rho_{\mathrm{d}}$ the bulk density.

First, we will install optool and check the (existing) installation

Download optool into a directory other than your ~/bin/ directory, for instance in a specially created directory for this session:

mkdir ~/handsonI
cd ~/handsonI  # or other directory of your choice
git clone https://github.com/cdominik/optool.git

enter the code directory and compile optool with multicode support:

cd optool
make multi=true

copy the executables to your binary path:

make install bindir=~/bin/

You should now have the following executables in your binary path: optool, optool2tex, and optool-complete. You can now run the program by typing ./optool in the command line while in the directory where the executable is stored, or simply optool, if it is in your binary path.

In order to test the installation run optool with the following options in the command line:

optool -c pyr 0.87 -c c 0.13 -p 0.25

which mixes 87% of pyroxene with 13% of carbon, to which a 25% volume fraction of vacuum is added to simulate porosity. A full description of the options are given in the user guide, which can be downloaded from https://github.com/cdominik/optool/blob/master/UserGuide.pdf

Optional: There is also a python module, which can be installed by typing

pip install -e .

while in the optool code directory. It is generally a good idea to activate a python environment, prior to installing and using python module, e.g.

source ~/python-virtual-environments/env/bin/activate.csh

For more information on python environments, see e.g. https://realpython.com/python-virtual-environments-a-primer/

optool comes with the optical properties of a number of different bulk materials built. In order to list the built-in optical properties, type

optool -c

and study the output. From this we can deduce that our previous command optool -c pyr 0.87 -c c 0.13 -p 0.25 uses pyroxene of the composition Mg${0.7}$Fe${0.3}$SiO$_3$⁵, and amorphous carbon⁶.

Now we will print the optical constants for the pyroxene and carbon used, and also the resulting output.

Use your favorite plotting routine, for instance in python, to plot the $n$ and $k$ values of the pyroxene and carbon used, as a function of wavelength, and also plot the resulting $\kappa_{\mathrm{abs}}$ and $\kappa_{\mathrm{sca}}$ values as a function of wavelength.

The built-in optical constants can be found in ~/handsonI/optool/lnk_data. The resulting $\kappa$ values can be found in the working directory, in file dustkappa.dat.

Now that we know how to run optool, we can play with different grain models. For instance:

• vary compositions: change the ratio between carbon and pyroxene in the example above, and see how the resulting $\kappa$ spectrum changes. Make a plot where you go from pure pyroxene grains to pure carbon grains, with steps of 20%.

• vary porosity: now for the default composition above, change the porosity, in steps of 25%.

You can also try some other species from the built-in library. However, the built-in library has its limitations, and you may be interested in trying some other species.

• alternative optical properties:

  • Start with the extended optool library, which can be found in a separate repository: https://github.com/cdominik/optool-additional-refind-data Inspect the carbonates, and create a dust grain that contains 10% carbonates in addition to 90% pyroxene.
  • You can also read in your own choice of optical properties, for instance Mg$\mathrm{0.5}$Fe$\mathrm{0.5}$O⁷ from https://www.astro.uni-jena.de/Laboratory/OCDB/mgfeoxides.html. Be aware that you may need to edit the lnk file to be readable by optool, please consult the User's Manual.

• vary grain sizes: to study the effect of grain sizes we will use amorphous olivine grains of the MgFeSiO$_4$ composition (abbreviated as ol in optool). We do not mix this with another material and also do not add any porosity.

  • Use the -a option in optool to calculate the opacities for grains of 0.1 $\mu$m and 0.2 $\mu$m in size (separately), and compare the appearance over the 8-13 $\mu$m wavelength range in a plot.
  • Look up the details of the MRN grain size distribution⁸, and model the opacity of grains of standard composition (see above) with this grain size distribution.

• vary grain shapes: The effect of grain shapes is best studied with a material that has many sharp resonances, such as forsterite (Mg-rich crystalline olivine), which is abbreviated in the built-in dust library as for. Do not use any other dust species or vacuum. Use a single grain size of 0.1 micron. Over the 5-50 micron range, plot the resulting opacities for spherical (Mie) grains, hollow spheres, a continuum distribution of ellipsoids (CDE) and fractal particles (MMF) in a single plot. What do you conclude?

Radiative transfer is the physical phenomenon of energy transfer in the form of electromagnetic radiation. The propagation of radiation through a medium is affected by absorption, emission and scattering processes. The equation of radiative transfer describes these interactions mathematically. In astrophysics, radiative transfer allows to better understand the medium through which radiation travels from stars to us. In our particular context, by solving the equation of radiative transer we can investigate the effect of dust in the emission that we detect.

During the last decades, several softwares have been developed to solve the radiative transfer in multiple astrophysical environments (galaxies, clouds, disks, stars, ...). Some of them are RADMC-3D, LIME, MCFOST, hyperion. In this hands-on session we will use SKIRT developed at the Astronomical Observatory of the Ghent University (Belgium).

SKIRT can be installed in Linux/Unix and MacOS. The installation guide provides additional support and requirements if you encouter problems. We will install SKIRT in the directory that we created before for this session handsonI:

cd ~/handsonI  # or the directory of your choice
mkdir SKIRT
cd SKIRT
mkdir release run git

This will create three directories: release, run, and git, that will be used later. We can now transfer the code from its git repository:

cd ~/handsonI/SKIRT
git clone https://github.com/SKIRT/SKIRT9.git git

To build SKIRT for the first time, using default build options, enter the following commands:

cd ~/handsonI/SKIRT/git
./makeSKIRT.sh

You may need to make configSKIRT.sh and makeSKIRT.sh exectuable using chmod +rw

If thins go well, you should see an output similar to this:

Using /usr/local/bin/cmake to generate build files

-- The C compiler identification is AppleClang 8.0.0.8000042
-- The CXX compiler identification is AppleClang 8.0.0.8000042
...
[  0%] Built target timestamp
[  0%] Building CXX object SMILE/build/CMakeFiles/build.dir/BuildInfo.cpp.o
[  0%] Linking CXX static library libbuild.a
...
[ 98%] Building CXX object SKIRT/core/CMakeFiles/skirtcore.dir/ZubkoSilicateGrainSizeDistribution.cpp.o
[ 99%] Linking CXX static library libskirtcore.a
[ 99%] Built target skirtcore
[ 99%] Building CXX object SKIRT/main/CMakeFiles/skirt.dir/SkirtCommandLineHandler.cpp.o
[ 99%] Building CXX object SKIRT/main/CMakeFiles/skirt.dir/SkirtMain.cpp.o
[100%] Linking CXX executable skirt
[100%] Built target skirt

Because of size limitations in GitHub repositories, the resource data files needed by the SKIRT code are hosted elsewhere on the Ghent University and must be downloaded separately. For this, you have to do:

cd ~/handsonI/SKIRT/git
./downloadResources.sh

The script will ask confirmation before starting the download of a resource package that has not yet been installed. Always answer yes for the "Core" resource package (you can skip the other resource packages, and download them later simply by running the script again)

Do you want to download and install SKIRT9_Resources_Core version 6? [y/n] y

Downloading SKIRT9_Resources_Core_v6.zip ...
------------------------------------------------
--2023-06-30 14:46:08--  https://sciences.ugent.be/skirtextdat/SKIRT9/Resources/SKIRT9_Resources_Core_v6.zip
...
inflating: SKIRT9_Resources_Core/SingleGrain/MeanPascucciBenchmarkOpticalProps.stab  
------------------------------------------------

To provide easy access to the executables in the SKIRT code, we recomment that you edit your login script (.profile, .bashrc, .bash_profile or equivalent) to add the appropriate SKIRT executable paths to your system path. For example, add the following line:

export PATH="${HOME}/handsonI/SKIRT/release/SKIRT/main:${PATH}"

To verify your installation of the SKIRT code, open a new terminal window and execute:

skirt

If the SKIRT code has been successfully installed, you should see an output similar to this:

30/06/2023 14:51:46.743   Welcome to SKIRT v9.0 (git 587faab built on 30/06/2023 at 14:37:18)
30/06/2023 14:51:46.744   Running on dune.local for asanchez
30/06/2023 14:51:46.750   Interactively constructing a simulation...
30/06/2023 14:51:46.750 ? Enter the name of the ski file to be created: 

The User Guide of SKIRT is a comprehensive document describing the main components and usage of SKIRT as well as some hands-on tutorials of different levels.

As first steps with SKIRT, we will follow the recommendations of the SKIRT User Guide and start with the simplest case: "Monochromatic simulation of a dusty galaxy" to get to know better the code and how to generate input files and first results. For this, follow the instructions at https://skirt.ugent.be/root/_tutorial_basics_mono.html

IMPORTANT.- Note that some of the interactive menus are slightly different between the current version of SKIRT and the one listed in the User Guide (this is because new options have been implemented in the code).

Once you ave defined all your conditions for your model, you should see in the terminal:

Successfully created ski file 'MonoDisk.ski'.
To run the simulation use the command: skirt MonoDisk

To actually run the simulation, enter the following command (within the same directory where the MonoDisk.ski file is located):

skirt MonoDisk

Once solving the radiative transfer is finished you will have some output files:

MonoDisk_log.txt            # containing the progress log as it was written in the terminal
MonoDisk_parameters.xml     # containing a copy of the ski file

MonoDisk_cut_dust_t_xy.fits # t ("theoretical") single-frame FITS data iles providing the theoretical dust density
MonoDisk_cut_dust_t_xz.fits #

MonoDisk_cut_dust_g_xy.fits # g ("gridded") single-frame FITS data files of the grid-discretized dust density in a coordinate plane
MonoDisk_cut_dust_g_xz.fits #

MonoDisk_i88_total.fits     # FITS file containing the data cube with the total surface brightness for the defined instrument
                            # since the simulation has only one wavelength, there is only a single frame in the output file

In order to visualize the results, you can open FITS files using softwares such as SAOImage DS9

There is no need to go through the lengthy interactive process to re-run a simulation with slightly adjusted parameters. You can manually edit the ski file instead. Let's do some tests.

Duplicate the file MonoDisk.ski to a new file named MonoDisk2.ski and open it with a text editor. This is an xml file with all the parameters that were defined previously. You can make the following changes:

• increase the number of photon packets by a factor of five (replace 1e6 by 5e6)
• add a second instrument by duplicating the <FrameInstrument .../> element
• change the new instrument's name to i84 and adjust its inclination to 84 degrees

Save the changes and execute the adjusted simulation using the command

skirt MonoDisk2

Note that the simulation will now be substantially slowed because it is launching more photon packets and because there are more instruments.

Look at the differences between output files

• MonoDisk_i88_total.fits vs MonoDisk2_i88_total.fits
• MonoDisk2_i84_total.fits vs MonoDisk2_i88_total.fits

The potential of SKIRT is huge, as demonstrated by the multiple scientific publications that make use of it to explain and reproduce their observations. In this hands-on tutorial we can not explore all of it, but we can suggest some directions to play with:

• How does the monochromatic galaxy that we simulated look like at different wavelengths? Explore how the images look like in the ultraviolet, in the near-infrared, far-infrared and even (sub)millimetric wavelengths
• How does the emission at different wavelengths look like if we completely change the angle from close edge-on (90 degrees) to close face-on (0 degrees)?
• We can generate a multi-wavelength (pan-chromatic) simulation following the instructions of the second tutorial: https://skirt.ugent.be/root/_tutorial_basics_pan.html