petitRADTRANS has an extensive database of line opacities. However, it is very likely that we are missing the one atom / molecule that you want. There are three options for adding external opacities to petitRADTRANS:

1. Importing custom-made opacity tables from the Exomol website. These are already in the petitRADTRANS format and can be used in a plug-and-play fashion. The opacities are available for the low-resolution mode of petitRADTRANS only ($$\lambda/\Delta\lambda=1000$$).
2. Converting cross-section grids from opacity.world.
3. Calculating opacities from line lists yourself, and converting them to the petitRADTRANS format.

These different options are explained in more detail below.

If you add opacities which are not available through the Exomol website with Option 2 or 3, and if you are particularly nice, you can share these opacities with us. We would then make them available to the other petitRADTRANS users via this website, while properly attributing your contribution.

## Importing custom-made opacity tables from the Exomol website¶

The linelists available on the Exomol website were recently converted into opacity tables in the custom format of various retrieval codes, see Chubb et al. (2020). Opacity tables in the petitRADTRANS can be downloaded on this page of the Exomol website. These opacity grids have been calculated for temperatures ranging from 100 to 3400 K ($$\Delta T = 100 \ {\rm K}$$ for $$T \in [100-2000] \ {\rm K}$$ and $$\Delta T = 200 \ {\rm K}$$ for $$T \in [2000-3400] \ {\rm K}$$) and 22 pressure points spaced equidistantly in log-space, from $$10^{-5}$$ to 100 bar. Thermal and pressure broadening have also been included, see Chubb et al. (2020) for more information. If you use petitRADTRANS at pressures and temperatures outside of this grid, petitRADTRANS will use the opacity at the gridpoint closest to the pressure and temperature specified in your calculation. These Exomol grids, in the hdf5 format, can simply be dropped into the opacity folder of petitRADTRANS to use them. This is arguably the easiest option to install external opacities, which we always recommend, if the species of interest is available from Exomol. Note that Exomol tables are available for the low-resolution mode of petitRADTRANS only ($$\lambda/\Delta\lambda=1000$$). The installation is outlined below.

1. In this example we will look at the Exomol POKAZATEL line list for water. Navigate to its entry on the Exomol website and scroll to the bottom of the page to the “POKAZATEL: opacity” section (see screenshot). Click on the link to download the petitRADTRANS opacity table.

2. Navigate to your petitRADTRANS opacity folder, which is the path to input_data/opacities/lines/corr_k/ folder. Make a new folder called, for example, H2O_Chubb and place the 1H2-16O__POKAZATEL__R1000_0.3-50mu.ktable.petitRADTRANS.h5 file inside.

You’re done! pRT will check automatically if an *.h5 file is in the opacity folder, so as long as you keep the .h5 extension, the file in the H2O_Chubb folder can be called whatever you like. The name of the folder, which we chose to be H2O_Chubb here, can also be anything. After dropping the .h5 file in the H2O_Chubb folder, the opacity species H2O_Chubb is now ready for use! Note that also the abundances must be specified for H2O_Chubb when using petitRADTRANS with this opacity table.

## Converting cross-section grids from opacity.world¶

Pre-computed opacities are also available from opacity.world, which have been generated using the method presented in Grimm & Heng (2015) . The website allows to download the cross-section tables as a function of pressure and temperature.

Simply decide on any P-T and wavelength range that you are interested in. Note that their spectral coordinate is wavenumber, in units of $${\rm cm}^{-1}$$.

Then transform the resulting binary files, that you downloaded from opacity.world, like described in the following. This script was developed together with Mantas Zilinskas, for Ziliniskas et al. (2020).

First we load the relevant packages.

import numpy as np
import struct
import os
from scipy.interpolate import interp1d
import math
import sys

Then we define where the input file are and where ouput files are supposed to be put. This example here is for the HDO opacity.

# Paths to opacity world files and output directory (ADJUST ACCORDINGLY)
path_to_files = 'opacity.world.s3/generateddata/1H-2H-16O__VTT_e2b/'
filelist = os.listdir(path_to_files)  # Find all opacity world files in the directory

Opacity.world saves the opacities in units of $${\rm cm}^{2}{\rm g}^{-1}$$, but the petitRADTRANS conversions scripts need $${\rm cm}^{2}$$. So we will have to convert below. For this it is important that the mass of the absorber species is defined, in units of amu. Do not forget to adapt this for every new species!

# Properties of chosen species
species_mass = 19.

""" Read a binary opacity world file.
"""

# Open file
file = open(filename,mode='rb')
file.close()

# The number of bytes per entry is 4
# Get the number of datapoints
points = int(len(cont)/4)
# Create array of the appropriate length
x = np.ones(points)

# Read the binary data into the array
for i in range(int(points)):
test = struct.unpack('f',cont[i*4:(i+1)*4])
x[i] = test[0]

return x

Finally we define the function that reads the binary opacity.world files, and saves them in the format that can be used by the opacity input generating scripts of petitRADTRANS. For this you also need the file that defines the petitRADTRANS wavelength grid, which can be downloaded here: wlen_petitRADTRANS.dat

def convert():

""" Converts opacity.world binary files for further pRT processing
"""

for file in filelist:

# Temp and pressure for naming files
t = file[16:21]
t = t.lstrip('0')
p = file[22:26]
print (t,p)

# Wavenumber points from range given in the file names
wl_start = int(file[4:9])
wl_end = int(file[10:15])
wlen = np.linspace(wl_start, wl_end, len(opa))
# Convert to cm or [micron]
wavelength = 1./wlen#/1e-4

# Invert them to go from a accending wavenumber ordering
# to an accending wavelength ordering.
wavelength = wavelength[::-1]
sigma = opa[::-1]

# OW opacities cm^2/g, convert to cm^2 by *species_mass*amu
sigma = sigma*species_mass*1.66053892e-24

# Interpolate
sig_interp = interp1d(wavelength, sigma,bounds_error=False,fill_value=0.0)
sig_interpolated_petit = sig_interp(wavelength_petit)

# Check if interp values are below 0 or NaN
for i in sig_interpolated_petit:
if i < 0.:
print (i)
elif math.isnan(i):
print (i)

#### SAVING REBINNED #### Around 300 MB per grid point
# New file name is 'sigma_+ temp + .K_ + Pressure + bar.dat'
np.savetxt(path_to_output + 'sigma_' + str(t) + '.K_' + str(p) + 'bar.dat', \
np.column_stack((wavelength_petit, \
sig_interpolated_petit)))

Then you just need to start the conversion:

convert()

Finally, these input files need to be converted to petitRADTRANS k-tables. This is done in an analogous way as explained in Section Preparing ExoCross opacities for petitRADTRANS below. When doing this, note that you can omit the step rebinning the cross-section files to the petitRADTRANS wavelength grid, because this was already done in convert() above!

The opacities can then be installed as described in Section Installing the new opacity files in petitRADTRANS below.

## From line lists to opacities (using ExoCross)¶

Before we can use it, any line list needs to be converted into actual opacities. In this example we will show you how to do this using ExoCross, the open-source opacity calculator of the Exomol database. ExoCross can be downloaded here, is described in Yurchenko et al. (2018) and documented here.

First, download the ExoCross source, go into the folder containing the source and the makefile called “makefile”. Adapt that to your liking. For example, if you have the gfortran compiler, but not ifort, make sure that the flag using ifort is commented out, and that it uses gfortran. The relevant lines in “makefile” should look like this:

#FOR  = ifort
#FFLAGS =  -O3 -qopenmp -traceback  -ip
FOR = gfortran
FFLAGS = -O2 -fopenmp -std=f2008

Then, build ExoCross by typing make in the terminal. Sometimes the compiler will complain that lines within the ExoCross source are too long. Just open the source and introduce a line break there manually, like this:

! This is an example for a line that is too long
DOUBLE PRECISION :: very_long_variable_name_number_one, very_long_variable_name_number_two, very_long_variable_name_number_three

! This is how you introduce line breaks
DOUBLE PRECISION :: very_long_variable_name_number_one, &
very_long_variable_name_number_two, &
very_long_variable_name_number_three

So the & is th line break operator. After fixing this, recompile using make.

In this example we will calculate the opacities of the NaH molecule. All necessary files for calculating opacities can be found on the Exomol website, just click here.

• 23Na-1H__Rivlin.states.bz2
• 23Na-1H__Rivlin.trans.bz2
• 23Na-1H__Rivlin.pf

Please unzip the .bz2 files before use.

Next, make an input file for carrying out the calculations, in this example we call it NaH_input.inp. This is what it looks like:

absorption
voigt
verbose 3
offset 60.
mass 24
temperature 1000.000000
pressure 0.00001
range 39. 91000.
R 1000000
pffile 23Na-1H__Rivlin.pf
output NaH_1000K_1em5bar.out
states 23Na-1H__Rivlin.states
transitions
"23Na-1H__Rivlin.trans"
end
species
0 gamma 0.06 n 0.5 t0 296 ratio 1.
end

This calculates the opacity of NaH with the following settings

• offset  results in a line cutoff of 60 $${\rm cm}^{-1}$$. While being an important effect that also speeds up calculations, the choice of a cutoff is often arbitrary because the physics behind it remain difficult to model, see, for example the discussion in Grimm & Heng (2015)_. Here we use the equivalent width of the line decrease function given by Hartmann et al. (2002), for $$\rm CH_4$$ broadened by $$\rm H_2$$.
• NaH has a mass of 24 (in amu)
• The opacity is calculated at a temperature of 1000 K
• The opacity is calculated at a pressure of $$10^{-5}$$ bar
• The opacity is calculated in the range from 39 to 91000 $${\rm cm}^{-1}$$. This corresponds to a wavelength range from 0.1099 to 256.4103 micron, therefore bracketing the full petitRADTRANS wavelength range (0.11 to 250 micron at low resolution). This large a range is needed. Therefore, do not change this. Note that the opacities in the high-resolution mode of petitRADTRANS ultimately only go from 0.3 to 28 microns.
• The resolution of the calculations carried out here is for a wavelength spacing of $$\lambda/\Delta\lambda=10^6$$.
• The pfile line gives the relative path to the partition function file, that you have already downloaded from Exomol.
• The states line gives the relative path to the states file, that you have already downloaded from Exomol.
• The lines below transitions line give the relative paths to the transition files, that you have already downloaded from Exomol. For NaH this is only one file. For molecules with a lot more lines this can be multiple files.
• The lines below species define the pressure broadening to be used. This pressure boradening (width of the Lorentz profile) is of the form $$\gamma \cdot (T_{0}/T)^n ({\rm ratio}\cdot P/{\rm 1 \ bar})$$, in units of $$\rm cm^{-1}$$. The choice here is a compromise between the various values reported for the broadening by $$\rm H_2/He$$ of various absorbers, e.g. in Amundsen et al. (2014), Gharib-Nezhad & Line (2018). Also see the text around Equation 12 in Sharp & Burrows (2007) for more information. Sometimes more detailed broadening information is available on Exomol, see here.

If more detailed broadening information is avaiable (not for NaH) you can replace the lines below species with something like

species
0 gamma 0.06 n 0.5 t0 296 file path_toH2_broadening_information_file model J ratio 0.860000
1 gamma 0.06 n 0.5 t0 296 file path_toHe_broadening_information_file model J ratio 0.140000
end

The above setting is for a primordial composition atmosphere, where $$\rm H_2$$ and He roughly make up 86 % and 14 % of the atmosphere, respectively (i.e. these are volume mixing ratios, not mass fractions). The $$\gamma$$ and $$n$$ values given before the path to the boradening files are what is used for rotational quantum numbers ($$J$$) not covered by the broadening files.

Finally, the opacities are calculated by running ExoCross from the terminal command line via

./xcross.exe < NaH_input.inp > test_run.out

The resulting wavelength-dependent opacity will be in the “NaH_1000K_1em5bar.out.xsec” file, in our example here. In the end quite a few opacity points need to be calculated for petitRADTRANS (for example at 130 or 200 different pressure-temperature conbinations, see below). This is doable on a local machine for smaller linelists such as NaH, but may require the use of a cluster for much larger linelists. There also exsists the so-called superline treatment (see Yurchenko et al. 2018) , where multiple lines are combined into one, this can speed up calculations a lot, but is not recommended if you want to calculate high-resolution spectra with petitRADTRANS (because line positions will shift if multiple lines are combined into one on a fixed wavelength grid during the superline treatment).

### Preparing ExoCross opacities for petitRADTRANS¶

For creating opacities for use in petitRADTRANS, calculate the molecular opacities from Exomol with ExoCross using the settings outlined above. Change parameters where applicable (temperature, pressure, molecule mass, broadening information…).

The opacities can be calculated on any rectangular pressure temperature grid (the disctance between grid points may be variable, but it must be rectangular for use in petitRADTRANS). An example are the original 130 P-T points of petitRADTRANS which you can find in the file PTgrid.dat. Temeratures go from 80 up to 3000 K, in a log-uniform way. You can also calculate opacities using PTgrid_new.dat, where we have added a few more points at high temperatures (increasing the temperature resolution there) and extend the temperature range to 4000 K (note that currently petitRADTRANS sets $$\kappa(T>3000 K)$$ to $$\kappa(T=3000 K)$$ for the opacity $$\kappa$$ in the old 130-point grid, if temperatures get too high). The new grid has 200 points in total.

Now, let’s turn towards preparing the ExoCross results for petitRADTRANS. We will assume that you have calculated the opacites at all 130 (or 200) pressure-temperature points. The high-resolution wavelength setup between ExoCross and our classical petitCODE/petitRADTRANS opacity calculator is slightly different. ExoCross’ wavelength spacing varies a bit around the user-defined resolution, whereas our routines preparing the opacity files for petitRADTRANS assume that the wavelength spacing is exactly $$\lambda/\Delta\lambda=10^6$$, from 0.11 to 250 microns. Hence we will first have to rebin the ExoCross results to the petitCODE/petitRADTRANS grid. To this end, please download the petitRADTRANS high resolution grid (wlen_petitRADTRANS.dat).

Next, rebin all ExoCross opacity files to that wavelength file, like shown below, using Python, here for simplicity we use the NaH opacity file calculated above.

import numpy as np
from scipy.interpolate import interp1d

# Read the opacity file from ExoCross
dat = np.genfromtxt('NaH_1000K_1em5bar.out.xsec')
wavelength = 1./dat[:,0]
sigma = dat[:,1]

# Invert them to go from a accending wavenumber ordering
# to an accending wavelength ordering.
wavelength = wavelength[::-1]
sigma = sigma[::-1]

# Interpolate the ExoCross calculation to that grid
sig_interp = interp1d(wavelength, sigma)
sig_interpolated_petit = sig_interp(wavelength_petit)

# Save rebinned calculation
np.savetxt('NaH_1000K_1em5bar_petit_grid.dat', \
np.column_stack((wavelength_petit, \
sig_interpolated_petit)))

Now we can create the correlated-k tables (or just “k-tables”) and high-resolution opacity files from these formatted files. Please email us to get the relevant Fortran source to do this, we will send you four files called

• calc_k_g_r1000_ptrad.f90: this converts the opacity data to petitRADTRANS k-tables (these are the opacities for the low-resolution mode of petitRADTRANS, at $$\lambda/\Delta\lambda=1000$$.
• retrieval_NP_16_ggrid.dat: this is the 16-point Gaussian quadrature grid that petitRADTRANS uses as the g-coordinate for the k-tables.
• make_short.f90: this cuts the opacities to the right 0.3 to 28 micron range for the high-resolution calculations $$\lambda/\Delta\lambda=10^6$$.
• short_stream_lambs_mass.dat: input file for make_short.f90.

You do not need to understand anything about k-tables to do this step here, we just wanted to explain what the routines are for.

To start, put the names of all opacity files you want to convert into a file called “sigma_list.ls”. Do not include the paths to these files, just the file names. Hence will have to run the Fortran conversion routines in the folder where the opacity files are. In our simple example (just one NaH file at 1000 K and $$10^{-5}$$ bar, its content looks like this:

NaH_1000K_1em5bar_petit_grid.dat

Let’s start with the k-table calculation, for the low-resolution opacity mode of petitRADTRANS. Open calc_k_g_r1000_ptrad.f90 and modify it to have the correct mass for the molecular species that you are interested in (NaH has 24 amu, so just put 24, like below):

! (c) Paul Molliere 2014

program calc_k_g

implicit none

!-----------------------------------------------------------
!            |||               |||                |||      !
!           \|||/             \|||/              \|||/     !
!             v                 v                  v       !
!----------------------------------------------------------!
!----------------------------------------------------------!
! DO NOT FORGET TO CHANGE THE MASS OF THE MOLECULE
! EVERY TIME!!!
DOUBLE PRECISION, parameter   :: mol_mass_amu = 24d0  !<---!
!----------------------------------------------------------!
!----------------------------------------------------------!
!             ^                 ^                  ^       !
!           /|||\             /|||\              /|||\     !
!            |||               |||                |||      !
!----------------------------------------------------------!

Next, compile the Fortran source:

Lastly, create a folder called kappa_gs_r1000. Now, take care that the opacity files, the compiled Fortran routine, sigma_list.ls, retrieval_NP_16_ggrid.dat and the kappa_gs_r1000 folder are all in the same folder. And that you are in this folder. Type

and all k-tables will be generated and placed into the kappa_gs_r1000 folder.

For the high resolution mode, generate a folder called “short_stream”. Next, open the short_stream_lambs_mass.dat file and adapt its content to have the correct molecule mass. Do not change the wavelength boundary values in this file. For NaH, with mass 24, it should look like this:

# Minimum wavelength in cm
0.3d-4
# Maximum wavelength in cm
28d-4
# Molecular mass in amu
24d0

Next, compile the high-resolution opacity conversion routine:

gfortran -o make_short make_short.f90

Now, again take care that the opacity files, the compiled Fortran routine, sigma_list.ls, short_stream_lambs_mass.dat and the short_stream folder are all in the same folder. And that you are in this folder. Type

./make_short

and all high resolution opacity tables will be generated and placed into the short_stream folder.

### Installing the new opacity files in petitRADTRANS¶

The new opacity files are now ready to be installed. Before that create a file called “molparam_id.txt” with the following content

#### Species ID (A2) format
06
#### molparam value
1.0

Simply leave the “06” two-digit integer unchanged, this is not needed for the custom opacities calculated here. Also the molparam value should not be changed. Copy the “molparam_id.txt” file to the short_stream and kappa_gs_r1000 folders. Now we are ready for installation. In the folder where petitRADTRANS is installed, there also is a input_data folder. To install a new species (e.g. NaH), create a folder called NaH in the input_data/opacities/lines/corr_k/ and input_data/opacities/lines/line_by_line folders. Copy the contents of the kappa_gs_r1000 and short_stream folders to the NaH folders in the corr_k and line_by_line folders, respectively. The opacities are now almost installed and ready for use, just carry out this last step below (almost there…).

### Using arbitrary (but rectangular) P-T opacity grids in petitRADTRANS¶

For the new opacity grid of a species that is not defined on the “classical” petitRADTRANS grid (13x10 T-P points) and/or uses another opacity file naming convention, simply add a PTpaths.ls file to its opacity folder. petitRADTRANS will be looking for this file, and will try the usual (old) grid and naming scheme if this file is missing. So, if you don’t put this file in the folder containing opacities petitRADTRANS will crash!

PTpaths.ls lines contain (without a header):

• 1st column: pressure (in bar) where opacity file is defined
• 2nd column: temperature (in K) where opacity file is defined
• 3rd column: name of file (can be anything) that contains the opacities at this P-T grid point, in the usual petitRADTRANS format.

The order of the lines of entries of PTpaths.ls can be whatever you like (e.g. random, sorted by pressure, sorted by temperature), it does not matter. petitRADTRANS will sort them by pressure and temperature internally. The only important criterion is that the grid must be rectangular: the delta T or delta P spacing is allowed to vary, but for every T value all P values must exist.

In your petitRADTRANS calculations you can combine species with different P-T grids, for different species, petitRADTRANS will simply interpolate within the species’ respective T-P grid. If the atmospheric T and P leave the respective grid, it will take the opacity of that species at the values of the nearest grid boundary point.