# GEAR RT

Warning

The radiative transfer schemes are still in development and are not useable at this moment. This page is currently a placeholder to document new features and requirements as the code grows.

## Compiling for GEAR RT

• To compile swift to be able to run with GEAR RT, you need to configure with --with-rt=GEAR_N where N is the integer number of photon groups that you intend to use in your simulation.

• You need to choose a Riemann solver for the RT equations. You can choose between the GLF and HLL solver. For the time being, I recommend sticking to the GLF solver as the HLL solver is more expensive, but seemingly offers no advantage, although this remains to be confirmed in further testing.

• GEAR RT is only compatible with the Meshless Finite Volume scheme. You’ll need to compile using --with-hydro=gizmo-mfv, which will also require you to select a hydro Riemann solver, e.g --with-riemann-solver=hllc.

• The thermochemistry requires the grackle library version 3.2. Grackle is a chemistry and cooling library presented in B. Smith et al. 2017. Please note that the current implementation is not (yet) as advanced as the GEAR subgrid model grackle cooling, and the parameters listed as available there are not applicable for the grackle cooling in combination with GEAR RT. You can however follow the Grackle installation instructions documented there.

## Compulsory Runtime Parameters

You need to provide the following runtime parameters in the yaml file (which will be further explained below):

GEARRT:
photon_groups_Hz: [3.288e15, 5.945e15, 13.157e15]  # Photon frequency group bin edges in Hz
stellar_spectrum_type: 0                           # Which radiation spectrum to use.
#   0: constant.
#   1: blackbody spectrum.
stellar_luminosity_model: const                    # Which luminosity model to use.
const_stellar_luminosities_LSol: [1., 1., 1.]      # stellar emission rates for each photon
#   frequency bin in units of solar luminosity
#   for the 'const' luminosity model
f_reduce_c: 1e-3                                   # reduce the speed of light by this factor
CFL_condition: 0.9                                 # CFL condition for time integration
hydrogen_mass_fraction:  0.76                      # total hydrogen (H + H+) mass fraction in the
# metal-free portion of the gas

TimeIntegration:
max_nr_rt_subcycles: 128         # maximal number of RT subcycles per hydro step


The photon_groups_Hz need to be N frequency edges (floats) to separate the spectrum into N groups, where N is the same number you configured with using --with_rt=GEAR_N. The edges are lower edges of the bins, and need to be sorted in increasing order. The final upper edge is defined in a different manner, and depends on the stellar spectrum type you assume (see below for more details).

To specify the radiation emitted by stars, there are two main parameters: stellar_luminosity_model defines which model to use to obtain star luminosities, while stellar_spectrum_type determines the spectrum of the radiation. At the moment, the only way to define star emission rates is to use constant stellar luminosities by setting stellar_luminosity_model: const. 3 The constant star emission rates need to be provided in the parameter file and to be defined for each photon frequency group individually using the const_stellar_luminosities_LSol parameter. The luminosities are expected to be in units of solar luminosities. Each star particle will then emit the given luminosities, independent of their other properties, e.g. the stellar age, metallicity, redshift, etc.

When solving the thermochemistry, we need to assume some form of stellar spectrum so we may integrate over frequency bins to obtain average interaction rates. The parameter stellar_spectrum_type is hence required, and allows you to select between:

• constant spectrum (stellar_spectrum_type: 0)
• Assume same energy density for any frequency.

• This choice additionally requires you to provide a maximal frequency for the spectrum after which it’ll be cut off via the stellar_spectrum_const_max_frequency_Hz parameter

• blackbody spectrum (stellar_spectrum_type: 1)
• Assume the spectrum is a blackbody spectrum

• In this case, you need to provide also temperature of the blackbody via the stellar_spectrum_blackbody_temperature_K parameter.

• The assumed maximal considered frequency $$\nu_{max}$$ for this spectrum is equal to 10 times $$\nu_{peak}$$, the frequency at which the blackbody spectrum has its maximum, i.e.

\begin{align}\begin{aligned}\nu_{peak} = 2.82144 \times k_{B} \times T / h_{Planck}\\\nu_{max} = 10 \times \nu_{peak}\end{aligned}\end{align}

Warning

The stellar_spectrum_type parameter also determines the averaged photon interaction cross sections, as they are being computed by integrating a parametrization of the cross section multiplied by the assumed spectrum. See e.g. equations 9 - 11 in Rosdahl et al. 2013.

Finally, you will also need to provide an upper threshold for the number of RT-subcycles w.r.t. a single hydro step via TimeIntegration:max_nr_rt_subcycles. For more details, refer to the subcycling documentation.

## Optional Runtime Parameters

There are several optional parameters which can be set in the GEARRT block in the yaml parameter file:

• f_limit_cooling_time: (Default: 0.6) The cooling time computed by grackle will be multipled by this factor when estimating the particle’s RT time step size. If set to 0.0, the computation of cooling time is turned off.

• skip_thermochemistry: (Default: 0) If set to 1, the entire thermochemistry part of radiative transfer will be skipped. This is intended only for debugging and testing the radiation transport, as it breaks the purpose of RT.

• stars_max_timestep: (Default: -1.) Restrict the maximal timestep of stars to this value (in internal units). Set to negative to turn off.

• grackle_verbose: (Default: 0) set grackle to verbose.

• case_B_recombination: (Default: 1) If 1, use case B recombination rates. Otherwise, case A recombination rates are used.

• max_tchem_recursion: (Default: 0) If set to positive nonzero value, the thermochemistry is computed using a “10% rule” in addition to the ones grackle already uses. If during a thermochemistry step the internal energy :math:u of the gas changes by more than 10%, i.e. $$|u_{new}/u_{old} - 1| > 0.1$$, then the thermochemistry step is repeated twice using half the time step size. This parameter sets the maximal recursion depth of halving the time step size and repeating the entire thermochemistry step.

There are some further optional parameters related to setting up initial ion mass fractions which are detailed in the corresponding section of this documentation.

## Choice of Internal Units

The choice of internal units requires a bit of special attention. Part of the reason is that the exponents of the gas and radiation variables can quickly change by several dozens and cause overflows and other errors. Furthermore, the grackle library may have some other troubles with the units, e.g. when trying to find a converging solution. 2

For this reason, I strongly encourage you to run the Internal Units check for GEAR-RT which you can find in the swiftsim-rt-tools repository under /GEARRTUnitsCheck. The test should take no more than a minute to run, and requires only two yaml parameter files: the yaml parameter file that you intend to run your simulation with, and one that a provided script can extract automatically from the initial conditions hdf5 file. This test can save you a lot of headaches down the line.

## Initial Conditions

### Setting Up Initial Conditions for RT

Optionally, you may want to provide initial conditions for the radiation field and/or the mass fraction of the ionizing species. To do so, you need to add the following datasets to the /PartType0 particle group:

PhotonEnergiesGroup1
PhotonEnergiesGroup2
.
.
.
PhotonEnergiesGroupN
PhotonFluxesGroup1
PhotonFluxesGroup2
.
.
.
PhotonFluxesGroupN
MassFractionHI
MassFractionHII
MassFractionHeI
MassFractionHeII
MassFractionHeIII

• The PhotonEnergies* datasets need to have dimension nparts, while the PhotonFluxesGroup* datasets need to have dimension (nparts, 3), where nparts is the number of hydro particles.

• Note that the GEAR-RT scheme expects the PhotonEnergies* to be total energies, not energy densities.

• If you are writing initial conditions where the fields have units 1, then PhotonEnergies* are expected to have units of energy $$[M L^2 T^{-2}]$$), while the PhotonFluxes* fields should be in units of energy times velocity (i.e. energy per unit time per unit area times volume, $$[M L^3 T^{-3}]$$).

• The MassFraction* datasets need to have dimension nparts as well, and are all unitless.

### Example using Python and swiftsimio

If you are using swiftsimio to write the initial condition files, then the easiest way of adding the RT initial conditions is to first use the swiftsimio routines to write a file, then open it up again and write the additional RT fields again using h5py routines.

Here is an example:

from swiftsimio import Writer
import unyt
import numpy as np
import h5py

# define unit system to use.
unitsystem = unyt.unit_systems.cgs_unit_system

# number of photon groups
nPhotonGroups = 4

# filename of ICs to be generated
outputfilename = "my_rt_ICs.hdf5"

# open a swiftsimio.Writer object
w = Writer(...)

# do your IC setup for gas, gravity etc now
# ...

# write the IC file without doing anything RT related.
w.write(outputfilename)

# Now open file back up again and add RT data.
F = h5py.File(outputfilename, "r+")
parts = F["/PartType0"]

# Create initial photon energies and fluxes. You can leave them unitless,
# the units have already been written down with w.write(). In this case,
# it's in cgs.
for grp in range(nPhotonGroups):
dsetname = "PhotonEnergiesGroup{0:d}".format(grp + 1)
energydata = np.ones((nparts), dtype=np.float32) * some_value_you_want
parts.create_dataset(dsetname, data=energydata)

dsetname = "PhotonFluxesGroup{0:d}".format(grp + 1)
fluxdata = np.zeros((nparts, 3), dtype=np.float32) * some_value_you_want
parts.create_dataset(dsetname, data=fluxdata)

# Create initial ionization species mass fractions.
HIdata = np.ones((nparts), dtype=np.float32) * 0.4
parts.create_dataset("MassFractionHI", data=HIdata)
HIIdata = np.ones((nparts), dtype=np.float32) * 0.1
parts.create_dataset("MassFractionHII", data=HIIdata)
HeIdata = np.ones((nparts), dtype=np.float32) * 0.3
parts.create_dataset("MassFractionHeI", data=HeIdata)
HeIIdata = np.ones((nparts), dtype=np.float32) * 0.15
parts.create_dataset("MassFractionHeII", data=HeIIdata)
HeIIIdata = np.ones((nparts), dtype=np.float32) * 0.05
parts.create_dataset("MassFractionHeIII", data=HeIIIdata)

# close up, and we're done!
F.close()


### Generate Ionization Mass Fractions Using SWIFT

Warning

Using SWIFT to generate initial ionization mass fractions will overwrite the mass fractions that have been read in from the initial conditions.

Optionally, you can use SWIFT to generate the initial mass fractions of the ionizing species. To set the initial mass fractions of all particles to the same value, use the following parameters in the yaml parameter file:

set_initial_ionization_mass_fractions: 1    # (Optional) manually overwrite initial mass fractions
# (using the values you set below)
mass_fraction_HI: 0.76                      # set initial HI mass fractions to this value
mass_fraction_HII: 0.                       # set initial HII mass fractions to this value
mass_fraction_HeI: 0.24                     # set initial HeI mass fractions to this value
mass_fraction_HeII: 0.                      # set initial HeII mass fractions to this value
mass_fraction_HeIII: 0.                     # set initial HeIII mass fractions to this value


Alternatively, you can make SWIFT compute the initial ionization mass fractions for you assuming ionization equilibrium, following Katz, et al. 1996 by setting

set_equilibrium_initial_ionization_mass_fractions: 1    # (Optional) set the initial ionization fractions
# depending on gas temperature assuming ionization
# equilibrium.
hydrogen_mass_fraction:  0.76                           # total hydrogen (H + H+) mass fraction in the
# metal-free portion of the gas


The hydrogen_mass_fraction (which is a compulsory argument in any case) will determine the hydrogen and helium mass fractions, while SWIFT will determine the equilibrium ionizations.

Warning

If you have somewhat sophisticated initial conditions (e.g. proper galaxies etc) it is strongly recommended to set up the initial mass fractions to equilibrium values. Otherwise, the initial states can be too far off for GRACKLE’s thermochemistry to handle it well, leading to all sorts of troubles, including crashes.

## Accessing Output Data

We recommend using swiftsimio to access the RT related snapshot data. The compatibility is being maintained. Here’s an example how to access some specific quantities that you might find useful:

#!/usr/bin/env python3

import swiftsimio
import unyt

# ---------------------------------

# get scheme name: "GEAR M1closure"
scheme = str(meta.subgrid_scheme["RT Scheme"].decode("utf-8"))

# number of photon groups used
ngroups = int(meta.subgrid_scheme["PhotonGroupNumber"])

# get the reduced speed of light that was used. Will have unyts.
reduced_speed_of_light = meta.reduced_lightspeed

# Accessing Photon Data
# ------------------------

# accessing a photon group directly
group_1_photon_energies = data.gas.photon_energies.group1
group_1_photon_fluxes_x = data.gas.photon_fluxes.Group1X
group_1_photon_fluxes_y = data.gas.photon_fluxes.Group1Y
group_1_photon_fluxes_z = data.gas.photon_fluxes.Group1Z

# want to stack all fluxes into 1 array?
group1fluxes = swiftsimio.cosmo_array(
unyt.uvstack(
(group_1_photon_fluxes_x, group_1_photon_fluxes_y, group_1_photon_fluxes_z)
),
group_1_photon_fluxes_x.units,
).T
# group1fluxes.shape = (npart, 3)

# Load all photon energies in a list
photon_energies = [
getattr(data.gas.photon_energies, "group" + str(g + 1)) for g in range(ngroups)
]

# Accessing Ion Mass Fractions
# -------------------------------
fHI = data.gas.ion_mass_fractions.HI
fHII = data.gas.ion_mass_fractions.HII
fHeI = data.gas.ion_mass_fractions.HeI
fHeII = data.gas.ion_mass_fractions.HeII
fHeIII = data.gas.ion_mass_fractions.HeIII


Footnotes

1

To avoid possible confusions, here are some notes and equations regarding this choice of units.

One of the RT equations solved by the GEAR RT is the zeroth moment of the equation of radiative transfer for each photon frequency group $$i$$ :

$$\frac{\partial E_i}{\partial t} + \nabla \cdot \mathbf{F}_i = 0$$

where

• $$E_i$$ : photon energy density; with $$[E_i] = erg / cm^3 = M L^{-1} T^{-2}$$

• $$F_i$$ : radiation flux (energy per unit time per unit surface); with $$[F_i] = erg / cm^2 / s = M T^{-3}$$

and we neglect possible source and sink terms in this footnote.

These dimensions are also used internally when solving the equations. For the initial conditions however, we require these quantities multiplied by the particle volume. The reason for this choice is so that the photon energies for each particle can be set by the users exactly, while the particle volume computation can be left to SWIFT to worry about internally. The addition of the particle volume term for the radiation flux was made so that the initial conditions are compatible with the SPHM1RT conventions, and both methods can run on the exact same ICs.

2

For example, choosing cgs units as the internal units may lead to trouble with grackle. (Trouble like a gas at 10^6K without any heating sources heating up instead of cooling down.) The library is set up to work with units geared towards cosmology. According to Britton Smith (private comm), a decent rule of thumb is density_units ~ proton mass in g, time_units ~ 1 Myr to 1 Gyr in s, length_units ~ 1 kpc to 1 Mpc in cm. This should keep you in a relatively safe range. This is the state of things at 08.2022, with grackle being at version 3.2 (commit a089c837b8649c97b53ed3c51c84b1decf5073d8)

3

Technically there is also the model used for “Test 4” from the I. Iliev et al. 2006 paper, but that is very specialized and shouldn’t have much use in real applications.