# 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 comfirmed 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. 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:

GEARRT:
photon_groups_Hz: [3.288e15, 5.945e15, 13.157e15]  # Photon frequency group bin edges in Hz
use_const_emission_rates: 1
star_emission_rates_LSol: [1., 1., 1., 1.]         # stellar emission rates for each photon
# frequency bin in units of solar luminosity
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

stellar_spectrum_type: 0                           # Which radiation spectrum to use. 0: constant. 1: blackbody spectrum.


The photon_groups need to be N - 1 frequency edges (floats) to separate the spectrum into N groups. The outer limits of zero and infinity are assumed.

At the moment, the only way to define star emission rates is to use constant star emission rates that need to be provided in the parameter file. The star emission rates need to be defined for each photon frequency group individually. The first entry of the array is for the photon group with frequency [0, <first entry of photon_groups_Hz>). Each star particle will then emit the given energies, independent of their other properties.

Furthermore, even though the parameter use_const_emission_rates is intended to be optional in the future, for now it needs to be set to 1., and it requires you to manually set the stellar emission rates via the star_emission_rates_LSol parameter.

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

## 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.

## 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.