doc/RTD/source/SubgridModels/AGNSpinJets/variable_heating_temperatures.rst

+.. AGN spin and jet model
+   Filip Husko, 26 September 2023
+
+.. AGN_spin_jet:
+
+Variable AGN heating temperature model
+--------------------------------------
+
+As part of this AGN model we also introduce an option of using variable AGN heating temperatures, as opposed to a constant value. This can be turned on by setting ``AGN_heating_temperature_model`` to ``AGN_heating_temperature_local``. In this scheme, we use three different criteria, all of which are applied simultaneously, and all of which are numerically motivated. These are: 1) the `Dalla Vecchia & Schaye (2012) <https://ui.adsabs.harvard.edu/abs/2012MNRAS.426..140D/abstract>`_ to prevent numerical overcooling, 2) a replenishment condition to make sure that the BH smoothing kernel can be replenished at a rate similar to the rate of evacuation due to heating and 3) a crossing condition that ensures a sufficient separation of heating events in time such that the kernel is never expected to contain more than a single heated particle.
+
+We implement the `Dalla Vecchia & Schaye (2012) <https://ui.adsabs.harvard.edu/abs/2012MNRAS.426..140D/abstract>`_ condition using Eqn. (18) from the paper. We invert it to obtain the minimum heating temperature:
+
+.. math::
+    \Delta T_\mathrm{DV}= 1.8\times10^6\hspace{0.5mm}\mathrm{K}\hspace{0.5mm}\times\bigg(\frac{N_\mathrm{ngb}m_\mathrm{g}}{60\times10^6\hspace{0.5mm}\mathrm{M}_\odot} \bigg)^{1/3}\bigg(\frac{n_\mathrm{H}}{0.1\hspace{0.5mm}\mathrm{cm}^{-3}} \bigg)^{2/3},
+
+where :math:`N_\mathrm{ngb}` is the number of neighbours in the BH kernel, :math:`m_\mathrm{g}` the average neighbour mass and :math:`n_\mathrm{H}` the number density of gas in the BH kernel.
+
+We derive the second condition by comparing the time-scales of replenishment onto the kernel and evacuation out of it on account of gas heating. The evacuation time-scale is the time required to evacuate the entire kernel of gas, and it is given by :math:`t_\mathrm{evac}=m_\mathrm{g}N_\mathrm{ngb}/\dot{M}`, where :math:`\dot{M}` is the mass flux associated with feedback. It can be expressed using the feedback power :math:`P` and internal energy per unit mass :math:`e` as :math:`\dot{M}=P/e`, where :math:`e=3k_\mathrm{B}\Delta T/2\mu m_\mathrm{p}`, :math:`\Delta T` is the heating temperature, :math:`m_\mathrm{p}` the proton mass and :math:`\mu\approx0.6` the mean molecular weight for ionized gas.
+
+The replenishment time-scale is given by :math:`t_\mathrm{repl}=h/v_\mathrm{repl}`, where :math:`v_\mathrm{repl}` is an effective velocity with which gas can flow inwards to replenish the kernel. Given this formulation, we can set the two time-scales (of evacuation and replenishment) equal to each other and solve for a heating temperature that ensures timely replenishment:
+
+.. math::
+    \Delta T_\mathrm{repl} = \frac{2\mu m_\mathrm{p}}{3 k_\mathrm{B}}\frac{hP}{N_\mathrm{ngb}m_\mathrm{g}v_\mathrm{repl}}.
+
+Finally, we calculate the replenishment velocity :math:`v_\mathrm{repl}` as follows. We assume that gas can replenish the kernel under the effects of either gas turbulence or pressure. We thus express the replenishment velocity as :math:`v_\mathrm{repl} = \max(\sigma,\Tilde{c}_\mathrm{s})`, where :math:`\sigma` is the velocity dispersion of gas and :math:`\Tilde{c}_\mathrm{s}` an effective sound speed, which we calculate by assuming that there is always some ISM exherting its pressure on gas near the BH, even if all of the gas in the kernel is cold. We choose the form :math:`\Tilde{c}_\mathrm{s}=\max(c_\mathrm{s,hot},\hspace{0.5mm}10\hspace{0.5mm}\mathrm{km}\mathrm{s}^{-1})`, where :math:`c_\mathrm{s,hot}` is the kernel-weighted average sound speed of all particles that have a temperature :math:`T>10^4` K and :math:`10` km :math:`\mathrm{s}^{-1}` is the sound speed of the ISM assuming a typical temperature of :math:`T=10^4` K.
+
+The third and final condition we use is based on the time it takes a single heated particle to cross and exit the kernel before the next one is heated. The time-interval between two heating events is :math:`\Delta = m_\mathrm{g}/\dot{M}`, while the time required for a heated particle to cross the kernel is :math:`\Delta t_\mathrm{cross}= h/c_\mathrm{s,\Delta T}`, where :math:`c_\mathrm{s,\Delta T} = \sqrt{\gamma(\gamma-1)e} = \sqrt{5k_\mathrm{B}\Delta T/3\mu m_\mathrm{p}}` is the sound speed of the heated gas. Equating these two time-scales, we obtain the final heating temperature:
+
+.. math::
+    \Delta T_\mathrm{cross} = \frac{\mu m_\mathrm{p}}{k_\mathrm{B}}\bigg(\frac{2hP}{\sqrt{15}m_\mathrm{g}}\bigg)^{2/3}.
+
+The final heating temperature scheme we use can be written as:
+
+.. math::
+    \Delta T = \max[\xi \max(\Delta T_\mathrm{DV}, \Delta T_\mathrm{repl}, \Delta T_\mathrm{cross}), \Delta T_\mathrm{min}],
+
+where :math:`\Delta T_\mathrm{min}` is an additional temperature floor meant to prevent very-low temperature heating events, and :math:`\xi` is an additional free parameter that can be used to rescale heating temperatures from all three conditions to higher values, which may be necessary to correctly calibrate the simulations. Specifically, one may use the hot gas fractions to choose a value of :math:`\xi` if :math:`\Delta T_\mathrm{min}` is set to a low value of :math:`\approx10^{7.5}` K, or one may set :math:`\xi=1`, thus using the numerical conditions exactly as derived, and instead calibrate the simulations by varying :math:`\Delta T_\mathrm{min}`.
+

doc/RTD/source/SubgridModels/AGORA/index.rst

+.. AGORA sub-grid model
+   Yves Revaz 04.2023
+
+.. _agora:
+
+AGORA model
+===========
+
+AGORA's model corresponds to the subgrid model adopted by the 
+`AGORA Project <https://sites.google.com/site/santacruzcomparisonproject/>`_ (High-resolution Galaxy Simulations Comparison Project).
+Details of the model is described in 
+`Kim \& al. 2014 <https://ui.adsabs.harvard.edu/link_gateway/2014ApJS..210...14K/PUB_PDF>`_
+and
+`Kim \& al. 2016 <https://ui.adsabs.harvard.edu/link_gateway/2016ApJ...833..202K/PUB_PDF>`_.
+
+
+
+This model can be selected with the configuration option ``--with-subgrid=AGORA`` and run with the option ``--agora``. 
+A few examples exist and can be found in ``examples/AGORA``. 
+
+.. _agora_grackle_cooling:
+
+Gas cooling/heating: Grackle
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+The AGORA model uses the Grackle cooling library which is also used by the :ref:`GEAR model <gear_grackle_cooling>`.
+
+
+
+
+.. _agora_star_formation:
+
+Star formation
+~~~~~~~~~~~~~~
+
+The AGORA model uses the :ref:`GEAR model <gear_star_formation>` scheme, however with the 
+``GEARStarFormation:star_formation_mode`` parameter set to ``agora``. Instead of requiring the gas
+density to reach the pressure floor, we simply require it to be denser than a density
+threshold defined by ``GEARStarFormation:density_threshold_Hpcm3``.
+
+
+Recommended parameters for the AGORA model should be:
+
+
+.. code:: YAML
+
+  GEARStarFormation:
+    star_formation_mode: agora            
+    star_formation_efficiency: 0.01   
+    maximal_temperature_K:  1e10
+    n_stars_per_particle: 1
+    min_mass_frac: 0.5
+    density_threshold_Hpcm3:   10
+
+
+
+.. _agora_feedback_and_chemistry:
+
+Stellar Feedback and Chemistry
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+In the current implementation, only two `elements`, iron (Fe) and the sum of all elements heavier than helium (metallicity)
+are considered.
+Only stellar feeback from core collapse supernovae (CCSNe) is considered.
+The model assumes that a number ``AGORAFeedback:ccsne_per_solar_mass`` of CCSNe per solar mass will form out of 
+each stellar particle. Those supernovae will all explode after a time 
+``AGORAFeedback:supernovae_explosion_time_myr`` after the birth of the stellar particle.
+At this time, each stellar particle will expel:
+
+  - ``AGORAFeedback:ejected_mass_in_solar_mass_per_CCSN`` amount of gas (in solar mass), per CCSN formed
+  - ``AGORAFeedback:ejected_Fe_mass_in_solar_mass_per_CCSN`` amount of iron (in solar mass), per CCSN formed
+  - ``AGORAFeedback:ejected_metal_mass_in_solar_mass_per_CCSN`` amount of metals (in solar mass), per CCSN formed
+
+In addition stellar particles will release energy:
+
+  - ``AGORAFeedback:energy_in_erg_per_CCSN`` erg per CCSN formed
+
+The energy released effectively into surrounding gas particles can be mitigated with the 
+parameter ``AGORAFeedback:supernovae_efficiency``, used as a simple factor to ``AGORAFeedback:energy_in_erg_per_CCSN``.
+
+Both energy and mass are ejected into the surrounding gas according to the SPH kernel.
+
+The mass fraction of elements received by gas particles will be smoothed (smoothed metallicity scheme)
+by using the SPH kernel. Note that this scheme does not exchange any material between particles. 
+Snapshots can store both the smoothed metallicity (``SmoothedMetalMassFractions``)
+and/or the non-smoothed one (``MetalMassFractions``), i.e., the mass fraction of elements effectively received
+by the gas particles.
+
+
+The initial metallicity of the gas can be defined by the parameter ``AGORAChemistry:initial_metallicity``.
+A value less than 0 forces the code to take the gas metallicity from the initial condition file (snapshot).
+Instead, if ``AGORAChemistry:scale_initial_metallicity`` is different than 0, the initial mass fraction
+of elements will be set to:
+
+  - ``AGORAChemistry:initial_metallicity`` time ``AGORAChemistry:solar_abundance_Metals`` for the iron
+  - ``AGORAChemistry:initial_metallicity`` time ``AGORAChemistry:solar_abundance_Metals`` for the metals
+
+
+Instead, they will be set to:
+
+  - ``AGORAChemistry:initial_metallicity`` for the iron
+  - ``AGORAChemistry:initial_metallicity`` for the metals
+
+
+
+Recommended parameters for the AGORA model should be:
+
+.. code:: YAML
+
+   AGORAChemistry:
+    initial_metallicity: 1  
+    scale_initial_metallicity: 1            
+    solar_abundance_Fe: 0.001771
+    solar_abundance_Metals: 0.02  
+    
+
+.. code:: YAML
+   
+   AGORAFeedback:
+    energy_in_erg_per_CCSN: 1e51
+    supernovae_efficiency: 1
+    supernovae_explosion_time_myr: 5
+    ccsne_per_solar_mass : 0.010989
+    ejected_mass_in_solar_mass_per_CCSN : 14.8
+    ejected_Fe_mass_in_solar_mass_per_CCSN : 2.63
+    ejected_metal_mass_in_solar_mass_per_CCSN : 2.63
+
+
+
+.. _agora_pressure_floor:
+
+Pressure Floor
+~~~~~~~~~~~~~~
+
+The AGORA model uses precisely the same pressure floor than the :ref:`GEAR model <gear_pressure_floor>`.
+
+
+.. _agora_initial_conditions:
+
+Initial Conditions
+~~~~~~~~~~~~~~~~~~
+
+Note that if in the initial conditions, the time of formation of a stellar particle is given (``BirthTime``)
+and set to a negative value, the stellar particle will provide no feedback.
+A similar behavior will be obtained if the parameter ``overwrite_birth_time`` is set to 1 and
+``birth_time`` to -1. 

doc/RTD/source/SubgridModels/Basic/index.rst

@@ -5,6 +5,25 @@
 Basic model (others)
 ====================
 
+Sinks: Simple Bondi-Hoyle accretion
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
+
+The ``Basic`` sink model provides a foundation on which new sink implementations could be built. It includes a prescription for Bondi-Hoyle gas accretion, and a method for sink-sink mergers that is a slightly simplified version of the implementation used in GEAR.
+
+No other physics is implemented for this model. Sinks cannot form - to use this model, sink particles must already be present in the initial conditions. They also cannot spawn stars from the gas they accrete.
+
+Bondi-Hoyle accretion can be done in one of two ways:
+
+ * Gas particles within the sink's kernel are stochastically swallowed entirely, with a probability set by the Bondi-Hoyle rate. Specifically, the probability is set by the current difference between the sink's subgrid mass (determined by the accretion rate) and its dynamical mass (which tracks the number of particles/sinks actually swallowed). This mode is equivalent to the EAGLE black hole accretion model.
+ * Gas particles within the sink's kernel are "nibbled" down to some minimal mass, which can be specified by the user. This method is equivalent to the black hole accretion model of Bahe et al. 2022.
+
+This model has only two parameters that must be specified in your parameter ``yml`` file:
+
+ * ``BasicSink:use_nibbling``: determines whether accretion is done by "nibbling" or by swallowing outright.
+ * ``BasicSink:min_gas_mass_for_nibbling_Msun``: if using "nibbling", the minimum mass to which gas particles can be nibbled. A good default is half the original particle mass.
+
+For an even more bare-bones starting point, the ``Default`` sink model contains no physics at all, and is a totally blank canvas on which to build your sink model.
+
 
 Cooling: Analytic models
 ~~~~~~~~~~~~~~~~~~~~~~~~

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doc/RTD/source/SubgridModels/EAGLE/index.rst

@@ -33,7 +33,7 @@ used to prevent the fragmentation of high-density gas into clumps that
 cannot be resolved by the coupled hydro+gravity solver. The two limits are
 sketched on the following figure.
 
-.. figure:: EAGLE_entropy_floor.svg
+.. figure:: EAGLE_entropy_floor.png
     :width: 400px
     :align: center
     :figclass: align-center
@@ -443,7 +443,7 @@ designed such that star formation threshold decreases with increasing
 metallicity. This relationship with the YAML parameters defining it is shown on
 the figure below.
 
-.. figure:: EAGLE_SF_Z_dep.svg
+.. figure:: EAGLE_SF_Z_dep.png
     :width: 400px
     :align: center
     :figclass: align-center
@@ -470,7 +470,7 @@ densities. Note that unlike the entropy floor, this is applied at *all*
 densities and not only above a certain threshold. This equation of state with
 the relevant YAML parameters defining it is shown on the figure below.
     
-.. figure:: EAGLE_SF_EOS.svg
+.. figure:: EAGLE_SF_EOS.png
     :width: 400px
     :align: center
     :figclass: align-center
@@ -537,6 +537,15 @@ Note that the star formation rates are expressed in internal units and not in
 solar masses per year as is the case in many other codes. This choice ensures
 consistency between all the fields written to the snapshots.
 
+Finally, the star formation model can also create more than one star particle
+per gas particle in a star formation event. The number of particles generated is
+controlled by a runtime parameter. All the stars generated share the same
+properties. They are slightly displaced from each others using a random vector
+of magnitude :math:`0.1h` added to the position of the gas particle. If only
+one star is formed (as is the default), no displacement is added. If N stars are
+formed per gas particle, each star is born with a mass of 1/N of the gas
+particle's mass.
+
 For a normal EAGLE run, that section of the parameter file reads:
 
 .. code:: YAML
@@ -559,7 +568,8 @@ For a normal EAGLE run, that section of the parameter file reads:
      threshold_max_density_H_p_cm3:     10.0      # Maximal density of the metal-dependant density threshold for star formation in Hydrogen atoms per cm^3.
      min_over_density:                  57.7      # Over-density above which star-formation is allowed.
      EOS_entropy_margin_dex:            0.5       # (Optional) Logarithm base 10 of the maximal entropy above the EOS at which stars can form.
-
+     num_of_stars_per_gas_particle:     1         # (Optional) The number star particles to form per gas particle converted to stars. (Defaults to 1. Must be > 0)
+     
 
 Alternatively, the code can also use a simple Schmidt law for the SF rate
 :math:`\dot{m}_* = \epsilon_{ff} \times m_g \times \frac{3 \pi} {32 G

doc/RTD/source/SubgridModels/EAGLE/plot_EAGLE_SF_EOS.py

+import os
+
+if os.path.exists("EAGLE_SF_EOS.png"):
+    # do not generate plot again
+    exit()
+
 import matplotlib
 
 matplotlib.use("Agg")
@@ -75,4 +81,4 @@ xlim(3e-8, 3e3)
 ylim(20.0, 2e5)
 
 
-savefig("EAGLE_SF_EOS.svg", dpi=200)
+savefig("EAGLE_SF_EOS.png", dpi=200)

doc/RTD/source/SubgridModels/EAGLE/plot_EAGLE_SF_Z_dep.py

+import os
+
+if os.path.exists("EAGLE_SF_Z_dep.png"):
+    # do not generate plot again
+    exit()
+
 import matplotlib
 
 matplotlib.use("Agg")
@@ -96,4 +102,4 @@ ylabel("SF threshold number density $n_{\\rm H, thresh}$ [cm$^{-3}$]", labelpad=
 xlim(1e-7, 1.0)
 ylim(0.0002, 50)
 
-savefig("EAGLE_SF_Z_dep.svg", dpi=200)
+savefig("EAGLE_SF_Z_dep.png", dpi=200)

doc/RTD/source/SubgridModels/EAGLE/plot_EAGLE_entropy_floor.py

+import os
+
+if os.path.exists("EAGLE_entropy_floor.png"):
+    # do not generate plot again
+    exit()
+
 import matplotlib
 
 matplotlib.use("Agg")
@@ -89,9 +95,16 @@ text(
     fontsize=5.5,
     family="monospace",
 )
-text(5e-8, 8800, "Cool_temperature_norm_K", va="bottom", fontsize=5.5, family="monospace")
 text(
-    5e-8, 4400, "Jeans_temperature_norm_K", va="bottom", fontsize=5.5, family="monospace"
+    5e-8, 8800, "Cool_temperature_norm_K", va="bottom", fontsize=5.5, family="monospace"
+)
+text(
+    5e-8,
+    4400,
+    "Jeans_temperature_norm_K",
+    va="bottom",
+    fontsize=5.5,
+    family="monospace",
 )
 fill_between([1e-5, 1e5], [10, 10], [8000, 8000], color="0.9")
 fill_between([1e-1, 1e5], [4000, 400000], color="0.9")
@@ -102,4 +115,4 @@ ylabel("Temperature $T$ [K]", labelpad=2)
 xlim(3e-8, 3e3)
 ylim(20.0, 2e5)
 
-savefig("EAGLE_entropy_floor.svg", dpi=200)
+savefig("EAGLE_entropy_floor.png", dpi=200)

doc/RTD/source/SubgridModels/GEAR/chemistry.rst

+.. GEAR sub-grid model chemistry
+   Darwin Roduit, 30th March 2025
+
+.. gear_chemistry:
+
+.. _gear_chemistry:
+
+Chemistry
+=========
+
+Feedback mechanisms such as supernova feedback transfer metals to the nearby gas particles. There is no mass exchange (mass advection) in SPH methods, as in grid-based or moving-mesh hydrodynamics solvers. As a result, the metals received by the gas particles are locked in these particles. Grid or moving-mesh codes have mass advection and often implement passive scalar advection of metals to model metal mixing. GEAR implements different methods to model metal mixing.
+
+.. _gear_smoothed_metallicity:
+
+Smoothed metallicity
+--------------------
+
+The smoothed metallicity scheme consists in using the SPH to smooth the metallicity of each particle over the neighbors. It is worth to point the fact that we are *not exchanging* any metals but only smoothing it. The parameter ``GEARChemistry:initial_metallicity`` set the (non smoothed) initial mass fraction of each element for all the particles and ``GEARChemistry:scale_initial_metallicity`` use the feedback table to scale the initial metallicity of each element according the Sun's composition. If ``GEARChemistry:initial_metallicity`` is negative, then the metallicities are read from the initial conditions.
+
+For this chemistry scheme the parameters are:
+
+.. code:: YAML
+
+   GEARChemistry:
+    initial_metallicity: 1         # Initial metallicity of the gas (mass fraction)
+    scale_initial_metallicity: 1   # Should we scale the initial metallicity with the solar one?
+

doc/RTD/source/SubgridModels/GEAR/feedback.rst

+.. GEAR sub-grid model feedback and stellar evolution
+   Loic Hausammann, 17th April 2020
+   Darwin Roduit, 30th March 2025
+
+.. _gear_stellar_evolution_and_feedback:  
+
+Stellar evolution and feedback
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+The feedback is composed of a few different models:
+  - The initial mass function (IMF) defines the quantity of each type of stars,
+  - The lifetime of a star defines when a star will explode (or simply die),
+  - The supernovae of type II (SNII) defines the rates and yields,
+  - The supernovae of type Ia (SNIa) defines the rates and yields,
+  - The energy injection that defines how to inject the energy / metals into the particles.
+
+Most of the parameters are defined inside a table (``GEARFeedback:yields_table``) but can be override with some parameters in the YAML file.
+I will not describe theses parameters more than providing them at the end of this section.
+Two different models exist for the supernovae (``GEARFeedback:discrete_yields``).
+In the continuous mode, we integrate the quantities over the IMF and then explodes a floating point number of stars (can be below 1 in some cases).
+In the discrete mode, we avoid the problem of floating points by rounding the number of supernovae (using a floor and randomly adding a supernovae depending on the fractional part) and then compute the properties for a single star at a time.
+
+Initial mass function
+^^^^^^^^^^^^^^^^^^^^^
+
+GEAR is using the IMF model from `Kroupa (2001) <https://ui.adsabs.harvard.edu/abs/2001MNRAS.322..231K/abstract>`_.
+We have a difference of 1 in the exponent due to the usage of IMF in mass and not in number.
+We also restrict the mass of the stars to be inside :math:`[0.05, 50] M_\odot`.
+Here is the default model used, but it can be easily adapted through the initial mass function parameters:
+
+.. math::
+  \xi(m) \propto m^{-\alpha_i}\, \textrm{where}\,
+  \begin{cases}
+   \alpha_0 = 0.3,\, & 0.01 \leq m / M_\odot < 0.08, \\
+   \alpha_1 = 1.3,\, & 0.08 \leq m / M_\odot < 0.50, \\
+   \alpha_2 = 2.3,\, & 0.50 \leq m / M_\odot < 1.00, \\
+   \alpha_3 = 2.3,\, & 1.00 \leq m / M_\odot,
+  \end{cases}
+
+
+Lifetime
+^^^^^^^^
+
+The lifetime of a star in GEAR depends only on two parameters: first its mass and then its metallicity.
+
+.. math::
+   \log(\tau(m)) = a(Z) \log^2(m) + b(Z) \log(m) + c(Z) \\ \\
+   a(Z) = -40.110 Z^2 + 5.509 Z + 0.7824 \\
+   b(Z) = 141.929 Z^2 - 15.889 Z - 3.2557 \\
+   c(Z) = -261.365 Z^2 + 17.073 Z + 9.8661
+
+where :math:`\tau` is the lifetime in years, :math:`m` is the mass of the star (in solar mass) and Z the metallicity of the star.
+The parameters previously given are the default ones, they can be modified in the parameters file.
+
+Supernovae II
+^^^^^^^^^^^^^
+
+The supernovae rate is simply given by the number of stars massive enough that end their life at the required time.
+
+.. math::
+   \dot{N}_\textrm{SNII}(t) = \int_{M_l}^{M_u} \delta(t - \tau(m)) \frac{\phi(m)}{m} \mathrm{d}m
+
+where :math:`M_l` and :math:`M_u` are the lower and upper mass limits for a star exploding in SNII, :math:`\delta` is the Dirac function and :math:`\phi` is the initial mass function (in mass).
+
+The yields for SNII cannot be written in an analytical form, they depend on a few different tables that are based on the work of `Kobayashi et al. (2000) <https://ui.adsabs.harvard.edu/abs/2000ApJ...539...26K/abstract>`_ and `Tsujimoto et al. (1995) <https://ui.adsabs.harvard.edu/abs/1995MNRAS.277..945T/abstract>`_.
+
+Supernovae Ia
+^^^^^^^^^^^^^
+
+The supernovae Ia are a bit more complicated as they involve two different stars.
+
+.. math::
+  \dot{N}_\textrm{SNIa}(t) = \left( \int_{M_{p,l}}^{M_{p,u}} \frac{\phi(m)}{m} \mathrm{d}m \right) \sum_i b_i \int_{M_{d,l,i}}^{M_{d,u,i}}
+  \delta(t-\tau(m)) \frac{\phi_d(m)}{m}\mathrm{d}m
+
+.. math::
+   \phi_d(m) \propto m^{-0.35}
+
+where :math:`M_{p,l}` and :math:`M_{p,u}` are the mass limits for a progenitor of a white dwarf, :math:`b_i` is the probability to have a companion and
+:math:`M_{d,l,i}` and :math:`M_{d,u,i}` are the mass limits for each type of companion.
+The first parenthesis represents the number of white dwarfs and the second one the probability to form a binary.
+
++------------------+--------------------+-------------------+------------------+
+| Companion        |  :math:`M_{d,l,i}` | :math:`M_{d,u,i}` | :math:`b_i`      |
++==================+====================+===================+==================+
+| Red giant        |   0.9              |    1.5            |    0.02          |
++------------------+--------------------+-------------------+------------------+
+| Main sequence    |   1.8              |    2.5            |    0.05          |
++------------------+--------------------+-------------------+------------------+
+
+The yields are based on the same papers than the SNII.
+
+Supernova energy injection
+^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+When a star goes into a supernova (type II and Ia), the stellar evolution determines how much energy (``GEARFeedback:supernovae_energy_erg`` TO BE CHECKED), mass and metals are released during the explosion. The energy can be ditributed as internal/thermal energy or as momentum. Thus, we need to distribute internal energy, momentum, mass and metals to the gas particles.  We will group all these in the “fluxes” term. 
+
+We have two models for the distribution of these fluxes and the subgrid modelling of the supernovae : GEAR model and GEAR mechanical model. We describe the two schemes in the  :ref:`gear_sn_feedback_models` page.
+
+
+Generating a new table
+^^^^^^^^^^^^^^^^^^^^^^
+
+The feedback table is an HDF5 file with the following structure:
+
+.. graphviz:: feedback_table.dot
+
+where the solid (dashed) squares represent a group (a dataset) with the name of the object underlined and the attributes written below. Everything is in solar mass or without units (e.g. mass fraction or unitless constant).
+In ``Data``, the attribute ``elts`` is an array of string with the element names (the last should be ``Metals``, it corresponds to the sum of all the elements), ``MeanWDMass`` is the mass of the white dwarfs
+and ``SolarMassAbundances`` is an array of float containing the mass fraction of the different element in the sun.
+In ``IMF``, ``n + 1`` is the number of part in the IMF, ``as`` are the exponent (``n+1`` elements), ``ms`` are the mass limits between each part (``n`` elements) and
+``Mmin`` (``Mmax``) is the minimal (maximal) mass of a star.
+In ``LifeTimes``, the coefficient are given in the form of a single table (``coeff_z`` with a 3x3 shape).
+In ``SNIa``, ``a`` is the exponent of the distribution of binaries, ``bb1``  and ``bb2`` are the coefficient :math:`b_i` and the other attributes follow the same names than in the SNIa formulas.
+The ``Metals`` group from the ``SNIa`` contains the name of each elements (``elts``) and the metal mass fraction ejected by each supernovae (``data``) in the same order. They must contain the same elements than in ``Data``.
+Finally for the ``SNII``, the mass limits are given by ``Mmin`` and ``Mmax``. For the yields, the datasets required are ``Ej`` (mass fraction ejected [processed]), ``Ejnp`` (mass fraction ejected [non processed]) and one dataset for each element present in ``elts``. The datasets should all have the same size, be uniformly sampled in log and contains the attributes ``min`` (mass in log for the first element) and ``step`` (difference of mass in log between two elements).
+
+.. code:: YAML
+
+  GEARFeedback:
+    supernovae_energy_erg: 0.1e51                            # Energy released by a single supernovae.
+    yields_table: chemistry-AGB+OMgSFeZnSrYBaEu-16072013.h5  # Table containing the yields.
+    discrete_yields: 0                                       # Should we use discrete yields or the IMF integrated one?
+  GEARInitialMassFunction:
+    number_function_part:  4                       # Number of different part in the IMF
+    exponents:  [0.7, -0.8, -1.7, -1.3]            # Exponents of each part of the IMF
+    mass_limits_msun:  [0.05, 0.08, 0.5, 1, 50]    # Limits in mass between each part of the IMF
+  GEARLifetime:
+   quadratic:  [-40.1107, 5.50992, 0.782432]  # Quadratic terms in the fit
+   linear:  [141.93, -15.8895, -3.25578]      # Linear terms in the fit
+   constant:  [-261.366, 17.0735, 9.86606]    # Constant terms in the fit
+  GEARSupernovaeIa:
+    exponent:  -0.35                      # Exponent for the distribution of companions
+    min_mass_white_dwarf_progenitor:  3   # Minimal mass of a progenitor of white dwarf
+    max_mass_white_dwarf_progenitor:  8   # Maximal mass of a progenitor of white dwarf
+    max_mass_red_giant:  1.5              # Maximal mass for a red giant
+    min_mass_red_giant:  0.9              # Minimal mass for a red giant
+    coef_red_giant:  0.02                 # Coefficient for the distribution of red giants companions
+    max_mass_main_sequence:  2.6          # Maximal mass for a main sequence star
+    min_mass_main_sequence:  1.8          # Minimal mass for a main sequence star
+    coef_main_sequence:  0.05             # Coefficient for the distribution of main sequence companions
+    white_dwarf_mass:  1.38               # Mass of a white dwarf
+  GEARSupernovaeII:
+  interpolation_size:  200                # Number of elements for the interpolation of the data

doc/RTD/source/SubgridModels/GEAR/gear_model.rst

+.. GEAR sub-grid model
+   Loic Hausammann, 17th April 2020
+   Darwin Roduit, 30th March 2025
+
+.. _gear_pressure_floor:
+
+Pressure Floor
+~~~~~~~~~~~~~~
+
+In order to avoid the artificial collapse of unresolved clumps, a minimum in pressure is applied to the particles.
+This additional pressure can be seen as the pressure due to unresolved hydrodynamics turbulence and is given by:
+
+.. math::
+    P_\textrm{Jeans} = \frac{\rho}{\gamma} \frac{4}{\pi} G h^2 \rho N_\textrm{Jeans}^{2/3}
+
+where :math:`\rho` is the density, :math:`\gamma` the adiabatic index, :math:`G` is the gravitational constant,
+:math:`h` the kernel support and :math:`N_\textrm{Jeans}` (``GEARPressureFloor:jeans_factor`` in the parameter file) is the number of particle required in order to resolve a clump.
+
+
+This must be directly implemented into the hydro schemes, therefore only a subset of schemes (Gadget-2, SPHENIX and Pressure-Energy) have the floor available.
+In order to implement it, you need equation 12 in `Hopkins 2013 <https://arxiv.org/abs/1206.5006>`_:
+
+.. math::
+   m_i \frac{\mathrm{d}v_i}{\mathrm{d}t} = - \sum_j x_i x_j \left[ \frac{P_i}{y_i^2} f_{ij} \nabla_i W_{ij}(h_i) + \frac{P_j}{y_j^2} f_{ji} \nabla_j W_{ji}(h_j) \right]
+
+and simply replace the :math:`P_i, P_j` by the pressure with the floor (when the pressure is below the floor).
+Here the :math:`x, y` are simple weights that should never have the pressure floor included even if they are related to the pressure (e.g. pressure-entropy).
+
+.. code:: YAML
+
+   GEARPressureFloor:
+    jeans_factor: 10.       # Number of particles required to suppose a resolved clump and avoid the pressure floor.
+
+
+.. _gear_star_formation:
+
+
+Star formation
+~~~~~~~~~~~~~~
+
+The star formation is done in two steps: first we check if a particle is in the star forming regime and then we use a stochastic approach to transform the gas particles into stars.
+
+A particle is in the star forming regime if:
+ - The velocity divergence is negative (:math:`\nabla\cdot v < 0`),
+ - The temperature is lower than a threshold (:math:`T < T_t` where :math:`T_t` is defined with ``GEARStarFormation:maximal_temperature_K``),
+ - The gas density is higher than a threshold (:math:`\rho > \rho_t` where :math:`\rho_t` is defined with ``GEARStarFormation:density_threshold_Hpcm3``)
+ - The particle reaches the pressure floor (:math:`\rho > \frac{\pi}{4 G N_\textrm{Jeans}^{2/3} h^2}\frac{\gamma k_B T}{\mu m_p}` where :math:`N_\textrm{Jeans}` is defined in the pressure floor).
+
+If ``GEARStarFormation:star_formation_mode`` is set to ``agora``, the condition on the pressure floor is ignored. Its default value is ``default``.
+
+A star will be able to form if a randomly drawn number is below :math:`\frac{m_g}{m_\star}\left(1 - \exp\left(-c_\star \Delta t / t_\textrm{ff}\right)\right)` where :math:`t_\textrm{ff}` is the free fall time, :math:`\Delta t` is the time step of the particle and :math:`c_\star` is the star formation coefficient (``GEARStarFormation:star_formation_efficiency``), :math:`m_g` the mass of the gas particle and :math:`m_\star` the mass of the possible future star. The mass of the star is computed from the average gas mass in the initial conditions divided by the number of possible stars formed per gas particle (``GEARStarFormation:n_stars_per_particle``). When we cannot have enough mass to form a second star (defined with the fraction of mass ``GEARStarFormation:min_mass_frac``), we fully convert the gas particle into a stellar particle. Once the star is formed, we move it a bit in a random direction and fraction of the smoothing length in order to avoid any division by 0.
+
+Currently, only the following hydro schemes are compatible: SPHENIX, Gadget2, minimal SPH, Gasoline-2 and Pressure-Energy.
+Implementing the other hydro schemes is not complicated but requires some careful thinking about the cosmological terms in the definition of the velocity divergence (comoving vs non comoving coordinates and if the Hubble flow is included or not).
+
+.. code:: YAML
+
+  GEARStarFormation:
+    star_formation_efficiency: 0.01   # star formation efficiency (c_*)
+    maximal_temperature_K:  3e4       # Upper limit to the temperature of a star forming particle
+    density_threshold_Hpcm3:   10     # Density threshold (Hydrogen atoms/cm^3) for star formation
+    n_stars_per_particle: 4           # Number of stars that an hydro particle can generate
+    min_mass_frac: 0.5                # Minimal mass for a stellar particle as a fraction of the average mass for the stellar particles.
+
+Initial Conditions
+++++++++++++++++++
+
+Note that if in the initial conditions, the time of formation of a stellar particle is given (``BirthTime``)
+and set to a negative value, the stellar particle will provide no feedback.
+A similar behavior will be obtained if the parameter ``Stars:overwrite_birth_time`` is set to 1 and
+``Stars:birth_time`` to -1.
+
+
+.. _gear_grackle_cooling:
+
+Cooling: Grackle
+~~~~~~~~~~~~~~~~
+   
+Grackle is a chemistry and cooling library presented in `B. Smith et al. 2017 <https://ui.adsabs.harvard.edu/abs/2017MNRAS.466.2217S>`_ 
+(do not forget to cite if used).  Four different modes are available:
+equilibrium, 6 species network (H, H\\( ^+ \\), e\\( ^- \\), He, He\\( ^+ \\)
+and He\\( ^{++} \\)), 9 species network (adds H\\(^-\\), H\\(_2\\) and
+H\\(_2^+\\)) and 12 species (adds D, D\\(^+\\) and HD).  Following the same
+order, the swift cooling options are ``grackle_0``, ``grackle_1``, ``grackle_2``
+and ``grackle_3`` (the numbers correspond to the value of
+``primordial_chemistry`` in Grackle).  It also includes some metal cooling (on/off with ``GrackleCooling:with_metal_cooling``), self-shielding
+methods and UV background (on/off with ``GrackleCooling:with_UV_background``).  In order to use the Grackle cooling, you will need
+to provide a HDF5 table computed by Cloudy (``GrackleCooling:cloudy_table``).
+
+Configuring and compiling SWIFT with Grackle
+++++++++++++++++++++++++++++++++++++++++++++
+
+In order to compile SWIFT with Grackle, you need to provide the options ``with-chemistry=GEAR`` and ``with-grackle=$GRACKLE_ROOT``
+where ``$GRACKLE_ROOT`` is the root of the install directory (not the ``lib``). 
+
+.. warning::
+    (State 2023) Grackle is experiencing current development, and the API is subject
+    to changes in the future. For convenience, a frozen version is hosted as a fork
+    on github here: https://github.com/mladenivkovic/grackle-swift .
+    The version available there will be tried and tested and ensured to work with
+    SWIFT.
+
+    Additionally, that repository hosts files necessary to install that specific 
+    version of grackle with spack.
+
+To compile it, run
+the following commands from the root directory of Grackle:
+``./configure; cd src/clib``.
+Update the variables ``LOCAL_HDF5_INSTALL`` and ``MACH_INSTALL_PREFIX`` in
+the file ``src/clib/Make.mach.linux-gnu``.
+Finish with ``make machine-linux-gnu; make && make install``.
+Note that we require the 64 bit float version of Grackle, which should be the default setting. 
+(The precision can be set while compiling grackle with ``make precision-64``).
+If you encounter any problem, you can look at the `Grackle documentation <https://grackle.readthedocs.io/en/latest/>`_
+
+You can now provide the path given for ``MACH_INSTALL_PREFIX`` to ``with-grackle``.
+
+Parameters
+++++++++++
+
+When starting a simulation without providing the different element fractions in the non equilibrium mode, the code supposes an equilibrium and computes them automatically.
+The code uses an iterative method in order to find the correct initial composition and this method can be tuned with two parameters. ``GrackleCooling:max_steps`` defines the maximal number of steps to reach the convergence and ``GrackleCooling:convergence_limit`` defines the tolerance in the relative error.
+
+In the parameters file, a few different parameters are available.
+
+- ``GrackleCooling:redshift`` defines the redshift to use for the UV background (for cosmological simulation, it must be set to -1 in order to use the simulation's redshift).
+
+- ``GrackleCooling:provide_*_heating_rates`` can enable the computation of user provided heating rates (such as with the radiative transfer) in either volumetric or specific units.
+
+- Feedback can be made more efficient by turning off the cooling during a few Myr (``GrackleCooling:thermal_time_myr``) for the particles touched by a supernovae.
+
+- The self shielding method is defined by ``GrackleCooling:self_shielding_method`` where 0 means no self shielding, > 0 means a method defined in Grackle (see Grackle documentation for more information) and -1 means GEAR's self shielding that simply turn off the UV background when reaching a given density (``GrackleCooling:self_shielding_threshold_atom_per_cm3``).
+
+- The initial elemental abundances can be specified with ``initial_nX_to_nY_ratio``, e.g. if you want to specify an initial HII to H abundance. A negative value ignores the parameter. The complete list can be found below.
+
+A maximal (physical) density must be set with the ``GrackleCooling:maximal_density_Hpcm3 parameter``. The density passed to Grackle is *the minimum of this density and the gas particle (physical) density*. A negative value (:math:`< 0`) deactivates the maximal density, i.e. there is no maximal density limit.
+The purpose of this parameter is the following. The Cloudy tables provided by Grackle are limited in density (typically to  :math:`10^4 \; \mathrm{hydrogen \; atoms/cm}^3`). In high-resolution simulations, particles can have densities higher than :math:`10^4 \; \mathrm{hydrogen \; atoms/cm}^3`. This maximal density ensures that we pass a density within the interpolation ranges of the table, should the density exceed it.
+It can be a solution to some of the following errors (with a translation of what the values mean):
+
+.. code:: text
+
+	  inside if statement solve rate cool:           0           0
+	  MULTI_COOL iter >        10000  at j,k =           1           1
+	  FATAL error (2) in MULTI_COOL
+	  dt =  1.092E-08 ttmin =  7.493E-12
+	  2.8E-19    // sub-cycling timestep
+	  7.5E-12    // time elapsed (in the sub-cycle)
+	  2.2E+25    // derivative of the internal energy
+	  T
+
+.. note::
+   This problem is particularly relevant with metal cooling enabled. Another solution is to modify the tables. But one is not exempted from exceeding the table maximal density value, since Grackle does not check if the particle density is larger than the table maximal density.
+
+
+Complete parameter list
+-----------------------
+
+Here is the complete section in the parameter file:
+
+.. code:: YAML
+
+  GrackleCooling:
+    cloudy_table: CloudyData_UVB=HM2012.h5       # Name of the Cloudy Table (available on the grackle bitbucket repository)
+    with_UV_background: 1                        # Enable or not the UV background
+    redshift: 0                                  # Redshift to use (-1 means time based redshift)
+    with_metal_cooling: 1                        # Enable or not the metal cooling
+    provide_volumetric_heating_rates: 0          # (optional) User provide volumetric heating rates
+    provide_specific_heating_rates: 0            # (optional) User provide specific heating rates
+    max_steps: 10000                             # (optional) Max number of step when computing the initial composition
+    convergence_limit: 1e-2                      # (optional) Convergence threshold (relative) for initial composition
+    thermal_time_myr: 5                          # (optional) Time (in Myr) for adiabatic cooling after a feedback event.
+    self_shielding_method: -1                    # (optional) Grackle (1->3 for Grackle's ones, 0 for none and -1 for GEAR)
+    self_shielding_threshold_atom_per_cm3: 0.007 # Required only with GEAR's self shielding. Density threshold of the self shielding
+    maximal_density_Hpcm3:   1e4                 # Maximal density (in hydrogen atoms/cm^3) for cooling. Higher densities are floored to this value to ensure grackle works properly when interpolating beyond the cloudy_table maximal density. A value < 0 deactivates this parameter.
+    HydrogenFractionByMass : 1.                  # Hydrogen fraction by mass (default is 0.76)
+
+    use_radiative_transfer : 1                   # Arrays of ionization and heating rates are provided
+    RT_heating_rate_cgs    : 0                   # heating         rate in units of / nHI_cgs 
+    RT_HI_ionization_rate_cgs  : 0               # HI ionization   rate in cgs [1/s]
+    RT_HeI_ionization_rate_cgs : 0               # HeI ionization  rate in cgs [1/s]
+    RT_HeII_ionization_rate_cgs: 0               # HeII ionization rate in cgs [1/s]
+    RT_H2_dissociation_rate_cgs: 0               # H2 dissociation rate in cgs [1/s]
+
+    volumetric_heating_rates_cgs: 0              # Volumetric heating rate in cgs  [erg/s/cm3]
+    specific_heating_rates_cgs: 0                # Specific heating rate in cgs    [erg/s/g]
+    H2_three_body_rate : 1                       # Specific the H2 formation three body rate (0->5,see Grackle documentation)
+    H2_cie_cooling : 0                           # Enable/disable H2 collision-induced emission cooling from Ripamonti & Abel (2004)
+    H2_on_dust: 0                                # Flag to enable H2 formation on dust grains
+    local_dust_to_gas_ratio : -1                 # The ratio of total dust mass to gas mass in the local Universe (-1 to use the Grackle default value). 
+    cmb_temperature_floor : 1                    # Enable/disable an effective CMB temperature floor
+
+    initial_nHII_to_nH_ratio:    -1              # initial nHII   to nH ratio (number density ratio). Value is ignored if set to -1.
+    initial_nHeI_to_nH_ratio:    -1              # initial nHeI   to nH ratio (number density ratio). Value is ignored if set to -1.
+    initial_nHeII_to_nH_ratio:   -1              # initial nHeII  to nH ratio (number density ratio). Value is ignored if set to -1.
+    initial_nHeIII_to_nH_ratio:  -1              # initial nHeIII to nH ratio (number density ratio). Value is ignored if set to -1.
+    initial_nDI_to_nH_ratio:     -1              # initial nDI    to nH ratio (number density ratio). Value is ignored if set to -1.
+    initial_nDII_to_nH_ratio:    -1              # initial nDII   to nH ratio (number density ratio). Value is ignored if set to -1.
+    initial_nHM_to_nH_ratio:     -1              # initial nHM    to nH ratio (number density ratio). Value is ignored if set to -1.
+    initial_nH2I_to_nH_ratio:    -1              # initial nH2I   to nH ratio (number density ratio). Value is ignored if set to -1.
+    initial_nH2II_to_nH_ratio:   -1              # initial nH2II  to nH ratio (number density ratio). Value is ignored if set to -1.
+    initial_nHDI_to_nH_ratio:    -1              # initial nHDI   to nH ratio (number density ratio). Value is ignored if set to -1.
+
+.. note::
+   A simple example running SWIFT with Grackle can be find in ``examples/Cooling/CoolingBox``. A more advanced example combining heating and cooling (with heating and ionization sources) is given in ``examples/Cooling/CoolingHeatingBox``. ``examples/Cooling/CoolingWithPrimordialElements/`` runs a uniform cosmological box with imposed abundances and let them evolve down to redshift 0.

doc/RTD/source/SubgridModels/GEAR/index.rst

@@ -6,260 +6,16 @@ GEAR model
 ===========
 
 GEAR's model are mainly described in `Revaz \& Jablonka <https://ui.adsabs.harvard.edu/abs/2018A%26A...616A..96R/abstract>`_.
-This model can be selected with the configuration option ``--with-subgrid=GEAR`` and run with the option ``--gear``. A few examples exist and can be found in ``examples/GEAR``. 
+This model can be selected with the configuration option ``--with-subgrid=GEAR`` and run with the option ``--gear``. A few examples exist and can be found in ``examples/GEAR``, ``examples/SinkParticles`` or ``IsolatedGalaxy/IsolatedGalaxy_multi_component``.
 
-Pressure Floor
-~~~~~~~~~~~~~~
 
-In order to avoid the artificial collapse of unresolved clumps, a minimum in pressure is applied to the particles.
-This additional pressure can be seen as the pressure due to unresolved hydrodynamics turbulence and is given by:
+.. toctree::
+   :caption: Table of Contents
 
-.. math::
-    P_\textrm{Jeans} = \frac{\rho}{\gamma} \frac{4}{\pi} G h^2 \rho N_\textrm{Jeans}^{2/3}
+   gear_model
+   chemistry
+   feedback
+   supernova_feedback
+   sinks/index
+   output
 
-where :math:`\rho` is the density, :math:`\gamma` the adiabatic index, :math:`G` is the gravitational constant,
-:math:`h` the kernel support and :math:`N_\textrm{Jeans}` (``GEARPressureFloor:jeans_factor`` in the parameter file) is the number of particle required in order to resolve a clump.
-
-
-This must be directly implemented into the hydro schemes, therefore only a subset of schemes (Gadget-2, SPHENIX and Pressure-Energy) have the floor available.
-In order to implement it, you need equation 12 in `Hopkins 2013 <https://arxiv.org/abs/1206.5006>`_:
-
-.. math::
-   m_i \frac{\mathrm{d}v_i}{\mathrm{d}t} = - \sum_j x_i x_j \left[ \frac{P_i}{y_i^2} f_{ij} \nabla_i W_{ij}(h_i) + \frac{P_j}{y_j^2} f_{ji} \nabla_j W_{ji}(h_j) \right]
-
-and simply replace the :math:`P_i, P_j` by the pressure with the floor (when the pressure is below the floor).
-Here the :math:`x, y` are simple weights that should never have the pressure floor included even if they are related to the pressure (e.g. pressure-entropy).
-
-.. code:: YAML
-
-   GEARPressureFloor:
-    jeans_factor: 10.       # Number of particles required to suppose a resolved clump and avoid the pressure floor.
-
-
-
-Cooling: Grackle
-~~~~~~~~~~~~~~~~
-   
-Grackle is a chemistry and cooling library presented in `B. Smith et al. 2016 <https://arxiv.org/abs/1610.09591>`_ 
-(do not forget to cite if used).  Four different modes are available:
-equilibrium, 6 species network (H, H\\( ^+ \\), e\\( ^- \\), He, He\\( ^+ \\)
-and He\\( ^{++} \\)), 9 species network (adds H\\(^-\\), H\\(_2\\) and
-H\\(_2^+\\)) and 12 species (adds D, D\\(^+\\) and HD).  Following the same
-order, the swift cooling options are ``grackle_0``, ``grackle_1``, ``grackle_2``
-and ``grackle_3`` (the numbers correspond to the value of
-``primordial_chemistry`` in Grackle).  It also includes some metal cooling (on/off with ``GrackleCooling:with_metal_cooling``), self-shielding
-methods and UV background (on/off with ``GrackleCooling:with_UV_background``).  In order to use the Grackle cooling, you will need
-to provide a HDF5 table computed by Cloudy (``GrackleCooling:cloudy_table``).
-
-When starting a simulation without providing the different element fractions in the non equilibrium mode, the code supposes an equilibrium and computes them automatically.
-The code uses an iterative method in order to find the correct initial composition and this method can be tuned with two parameters. ``GrackleCooling:max_steps`` defines the maximal number of steps to reach the convergence and ``GrackleCooling:convergence_limit`` defines the tolerance in the relative error.
-
-In order to compile SWIFT with Grackle, you need to provide the options ``with-chemistry=GEAR`` and ``with-grackle=$GRACKLE_ROOT``
-where ``$GRACKLE_ROOT`` is the root of the install directory (not the ``lib``).
-
-You will need a Grackle version later than 3.1.1. To compile it, run
-the following commands from the root directory of Grackle:
-``./configure; cd src/clib``.
-Update the variables ``LOCAL_HDF5_INSTALL`` and ``MACH_INSTALL_PREFIX`` in
-the file ``src/clib/Make.mach.linux-gnu``.
-Finish with ``make machine-linux-gnu; make && make install``.
-If you encounter any problem, you can look at the `Grackle documentation <https://grackle.readthedocs.io/en/latest/>`_
-
-You can now provide the path given for ``MACH_INSTALL_PREFIX`` to ``with-grackle``.
-
-In the parameters file, a few different parameters are available.
-``GrackleCooling:redshift`` defines the redshift to use for the UV background (for cosmological simulation, it must be set to -1 in order to use the simulation's redshift) and ``GrackleCooling:provide_*_heating_rates`` can enable the computation of user provided heating rates (such as with the radiative transfer) in either volumetric or specific units.
-
-For the feedback, it can be made more efficient by turning off the cooling during a few Myr (``GrackleCooling:thermal_time_myr``) for the particles touched by a supernovae.
-
-The self shielding method is defined by ``GrackleCooling:self_shielding_method`` where 0 means no self shielding, > 0 means a method defined in Grackle (see Grackle documentation for more information) and -1 means GEAR's self shielding that simply turn off the UV background when reaching a given density (``GrackleCooling:self_shielding_threshold_atom_per_cm3``).
-
-.. code:: YAML
-
-  GrackleCooling:
-    cloudy_table: CloudyData_UVB=HM2012.h5       # Name of the Cloudy Table (available on the grackle bitbucket repository)
-    with_UV_background: 1                        # Enable or not the UV background
-    redshift: 0                                  # Redshift to use (-1 means time based redshift)
-    with_metal_cooling: 1                        # Enable or not the metal cooling
-    provide_volumetric_heating_rates: 0          # (optional) User provide volumetric heating rates
-    provide_specific_heating_rates: 0            # (optional) User provide specific heating rates
-    max_steps: 10000                             # (optional) Max number of step when computing the initial composition
-    convergence_limit: 1e-2                      # (optional) Convergence threshold (relative) for initial composition
-    thermal_time_myr: 5                          # (optional) Time (in Myr) for adiabatic cooling after a feedback event.
-    self_shielding_method: -1                    # (optional) Grackle (1->3 for Grackle's ones, 0 for none and -1 for GEAR)
-    self_shielding_threshold_atom_per_cm3: 0.007 # Required only with GEAR's self shielding. Density threshold of the self shielding
-
-
-
-Star formation
-~~~~~~~~~~~~~~
-
-The star formation is done in two steps: first we check if a particle is in the star forming regime and then we use a stochastic approach to transform the gas particles into stars.
-
-A particle is in the star forming regime if:
- - The velocity divergence is negative (:math:`\nabla\cdot v < 0`),
- - The temperature is lower than a threshold (:math:`T < T_t` where :math:`T_t` is defined with ``GEARStarFormation:maximal_temperature``),
- - The particle reaches the pressure floor (:math:`\rho > \frac{\pi}{4 G N_\textrm{Jeans}^{2/3} h^2}\frac{\gamma k_B T}{\mu m_p}` where :math:`N_\textrm{Jeans}` is defined in the pressure floor).
-
-A star will be able to form if a randomly drawn number is below :math:`\frac{m_g}{m_\star}\left(1 - \exp\left(-c_\star \Delta t / t_\textrm{ff}\right)\right)` where :math:`t_\textrm{ff}` is the free fall time, :math:`\Delta t` is the time step of the particle and :math:`c_\star` is the star formation coefficient (``GEARStarFormation:star_formation_efficiency``), :math:`m_g` the mass of the gas particle and :math:`m_\star` the mass of the possible future star. The mass of the star is computed from the average gas mass in the initial conditions divided by the number of possible stars formed per gas particle (``GEARStarFormation:n_stars_per_particle``). When we cannot have enough mass to form a second star (defined with the fraction of mass ``GEARStarFormation:min_mass_frac``), we fully convert the gas particle into a stellar particle. Once the star is formed, we move it a bit in a random direction and fraction of the smoothing length in order to avoid any division by 0.
-
-Currently, only the following hydro schemes are compatible: SPHENIX and Gadget2.
-Implementing the other hydro schemes is not complicated but requires some careful thinking about the cosmological terms in the definition of the velocity divergence (comoving vs non comoving coordinates and if the Hubble flow is included or not).
-
-.. code:: YAML
-
-  GEARStarFormation:
-    star_formation_efficiency: 0.01   # star formation efficiency (c_*)
-    maximal_temperature:  3e4         # Upper limit to the temperature of a star forming particle
-    n_stars_per_particle: 4           # Number of stars that an hydro particle can generate
-    min_mass_frac: 0.5                # Minimal mass for a stellar particle as a fraction of the average mass for the stellar particles.
-
-
-Chemistry
-~~~~~~~~~
-
-In the chemistry, we are using the smoothed metallicity scheme that consists in using the SPH to smooth the metallicity of each particle over the neighbors. It is worth to point the fact that we are not exchanging any metals but only smoothing it. The parameter ``GEARChemistry:initial_metallicity`` set the (non smoothed) initial mass fraction of each element for all the particles and ``GEARChemistry:scale_initial_metallicity`` use the feedback table to scale the initial metallicity of each element according the Sun's composition.
-
-.. code:: YAML
-
-   GEARChemistry:
-    initial_metallicity: 1         # Initial metallicity of the gas (mass fraction)
-    scale_initial_metallicity: 1   # Should we scale the initial metallicity with the solar one?
-
-Feedback
-~~~~~~~~
-
-The feedback is composed of a few different models:
-  - The initial mass function (IMF) defines the quantity of each type of stars,
-  - The lifetime of a star defines when a star will explode (or simply die),
-  - The supernovae of type II (SNII) defines the rates and yields,
-  - The supernovae of type Ia (SNIa) defines the rates and yields,
-  - The energy injection that defines how to inject the energy / metals into the particles.
-
-Most of the parameters are defined inside a table (``GEARFeedback:yields_table``) but can be override with some parameters in the YAML file.
-I will not describe theses parameters more than providing them at the end of this section.
-Two different models exist for the supernovae (``GEARFeedback:discrete_yields``).
-In the continuous mode, we integrate the quantities over the IMF and then explodes a floating point number of stars (can be below 1 in some cases).
-In the discrete mode, we avoid the problem of floating points by rounding the number of supernovae (using a floor and randomly adding a supernovae depending on the fractional part) and then compute the properties for a single star at a time.
-
-Initial mass function
-^^^^^^^^^^^^^^^^^^^^^
-
-GEAR is using the IMF model from `Kroupa (2001) <https://ui.adsabs.harvard.edu/abs/2001MNRAS.322..231K/abstract>`_.
-We have a difference of 1 in the exponent due to the usage of IMF in mass and not in number.
-We also restrict the mass of the stars to be inside :math:`[0.05, 50] M_\odot`.
-Here is the default model used, but it can be easily adapted through the initial mass function parameters:
-
-.. math::
-  \xi(m) \propto m^{-\alpha_i}\, \textrm{where}\,
-  \begin{cases}
-   \alpha_0 = 0.3,\, & 0.01 \leq m / M_\odot < 0.08, \\
-   \alpha_1 = 1.3,\, & 0.08 \leq m / M_\odot < 0.50, \\
-   \alpha_2 = 2.3,\, & 0.50 \leq m / M_\odot < 1.00, \\
-   \alpha_3 = 2.3,\, & 1.00 \leq m / M_\odot,
-  \end{cases}
-
-
-Lifetime
-^^^^^^^^
-
-The lifetime of a star in GEAR depends only on two parameters: first its mass and then its metallicity.
-
-.. math::
-   \log(\tau(m)) = a(Z) \log^2(m) + b(Z) \log(m) + c(Z) \\ \\
-   a(Z) = -40.110 Z^2 + 5.509 Z + 0.7824 \\
-   b(Z) = 141.929 Z^2 - 15.889 Z - 3.2557 \\
-   c(Z) = -261.365 Z^2 + 17.073 Z + 9.8661
-
-where :math:`\tau` is the lifetime in years, :math:`m` is the mass of the star (in solar mass) and Z the metallicity of the star.
-The parameters previously given are the default ones, they can be modified in the parameters file.
-
-Supernovae II
-^^^^^^^^^^^^^
-
-The supernovae rate is simply given by the number of stars massive enough that end their life at the required time.
-
-.. math::
-   \dot{N}_\textrm{SNII}(t) = \int_{M_l}^{M_u} \delta(t - \tau(m)) \frac{\phi(m)}{m} \mathrm{d}m
-
-where :math:`M_l` and :math:`M_u` are the lower and upper mass limits for a star exploding in SNII, :math:`\delta` is the Dirac function and :math:`\phi` is the initial mass function (in mass).
-
-The yields for SNII cannot be written in an analytical form, they depend on a few different tables that are based on the work of `Kobayashi et al. (2000) <https://ui.adsabs.harvard.edu/abs/2000ApJ...539...26K/abstract>`_ and `Tsujimoto et al. (1995) <https://ui.adsabs.harvard.edu/abs/1995MNRAS.277..945T/abstract>`_.
-
-Supernovae Ia
-^^^^^^^^^^^^^
-
-The supernovae Ia are a bit more complicated as they involve two different stars.
-
-.. math::
-  \dot{N}_\textrm{SNIa}(t) = \left( \int_{M_{p,l}}^{M_{p,u}} \frac{\phi(m)}{m} \mathrm{d}m \right) \sum_i b_i \int_{M_{d,l,i}}^{M_{d,u,i}}
-  \delta(t-\tau(m)) \frac{\phi_d(m)}{m}\mathrm{d}m
-
-.. math::
-   \phi_d(m) \propto m^{-0.35}
-
-where :math:`M_{p,l}` and :math:`M_{p,u}` are the mass limits for a progenitor of a white dwarf, :math:`b_i` is the probability to have a companion and
-:math:`M_{d,l,i}` and :math:`M_{d,u,i}` are the mass limits for each type of companion.
-The first parenthesis represents the number of white dwarfs and the second one the probability to form a binary.
-
-+------------------+--------------------+-------------------+------------------+
-| Companion        |  :math:`M_{d,l,i}` | :math:`M_{d,u,i}` | :math:`b_i`      |
-+==================+====================+===================+==================+
-| Red giant        |   0.9              |    1.5            |    0.02          |
-+------------------+--------------------+-------------------+------------------+
-| Main sequence    |   1.8              |    2.5            |    0.05          |
-+------------------+--------------------+-------------------+------------------+
-
-The yields are based on the same papers than the SNII.
-
-Energy injection
-^^^^^^^^^^^^^^^^
-
-All the supernovae (type II and Ia) inject the same amount of energy into the surrounding gas (``GEARFeedback:supernovae_energy_erg``) and distribute it according to the hydro kernel.
-The same is done with the metals and the mass.
-
-
-Generating a new table
-^^^^^^^^^^^^^^^^^^^^^^
-
-The feedback table is an HDF5 file with the following structure:
-
-.. graphviz:: feedback_table.dot
-
-where the solid (dashed) squares represent a group (a dataset) with the name of the object underlined and the attributes written below. Everything is in solar mass or without units (e.g. mass fraction or unitless constant).
-In ``Data``, the attribute ``elts`` is an array of string with the element names (the last should be ``Metals``, it corresponds to the sum of all the elements), ``MeanWDMass`` is the mass of the white dwarfs
-and ``SolarMassAbundances`` is an array of float containing the mass fraction of the different element in the sun.
-In ``IMF``, ``n + 1`` is the number of part in the IMF, ``as`` are the exponent (``n+1`` elements), ``ms`` are the mass limits between each part (``n`` elements) and
-``Mmin`` (``Mmax``) is the minimal (maximal) mass of a star.
-In ``LifeTimes``, the coefficient are given in the form of a single table (``coeff_z`` with a 3x3 shape).
-In ``SNIa``, ``a`` is the exponent of the distribution of binaries, ``bb1``  and ``bb2`` are the coefficient :math:`b_i` and the other attributes follow the same names than in the SNIa formulas.
-The ``Metals`` group from the ``SNIa`` contains the name of each elements (``elts``) and the metal mass fraction ejected by each supernovae (``data``) in the same order. They must contain the same elements than in ``Data``.
-Finally for the ``SNII``, the mass limits are given by ``Mmin`` and ``Mmax``. For the yields, the datasets required are ``Ej`` (mass fraction ejected [processed]), ``Ejnp`` (mass fraction ejected [non processed]) and one dataset for each element present in ``elts``. The datasets should all have the same size, be uniformly sampled in log and contains the attributes ``min`` (mass in log for the first element) and ``step`` (difference of mass in log between two elements).
-
-.. code:: YAML
-
-  GEARFeedback:
-    supernovae_energy_erg: 0.1e51                            # Energy released by a single supernovae.
-    yields_table: chemistry-AGB+OMgSFeZnSrYBaEu-16072013.h5  # Table containing the yields.
-    discrete_yields: 0                                       # Should we use discrete yields or the IMF integrated one?
-  GEARInitialMassFunction:
-    number_function_part:  4                       # Number of different part in the IMF
-    exponents:  [0.7, -0.8, -1.7, -1.3]            # Exponents of each part of the IMF
-    mass_limits_msun:  [0.05, 0.08, 0.5, 1, 50]    # Limits in mass between each part of the IMF
-  GEARLifetime:
-   quadratic:  [-40.1107, 5.50992, 0.782432]  # Quadratic terms in the fit
-   linear:  [141.93, -15.8895, -3.25578]      # Linear terms in the fit
-   constant:  [-261.366, 17.0735, 9.86606]    # Constant terms in the fit
-  GEARSupernovaeIa:
-    exponent:  -0.35                      # Exponent for the distribution of companions
-    min_mass_white_dwarf_progenitor:  3   # Minimal mass of a progenitor of white dwarf
-    max_mass_white_dwarf_progenitor:  8   # Maximal mass of a progenitor of white dwarf
-    max_mass_red_giant:  1.5              # Maximal mass for a red giant
-    min_mass_red_giant:  0.9              # Minimal mass for a red giant
-    coef_red_giant:  0.02                 # Coefficient for the distribution of red giants companions
-    max_mass_main_sequence:  2.6          # Maximal mass for a main sequence star
-    min_mass_main_sequence:  1.8          # Minimal mass for a main sequence star
-    coef_main_sequence:  0.05             # Coefficient for the distribution of main sequence companions
-    white_dwarf_mass:  1.38               # Mass of a white dwarf
-  GEARSupernovaeII:
-  interpolation_size:  200                # Number of elements for the interpolation of the data

doc/RTD/source/SubgridModels/GEAR/output.rst

+.. Sink particles in GEAR model
+   Darwin Roduit, 14 July 2024
+
+.. sink_GEAR_model:
+
+Snapshots ouputs
+----------------
+
+Here, we provide a summary of the quantities written in the snapshots, in addition to positions, velocities, masses, smoothing lengths and particle IDs.
+
+
+Sink particles
+~~~~~~~~~~~~~~
+
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+| Name                                  | Description                                 | Units                  | Comments                                          |
++=======================================+=============================================+========================+===================================================+
+| ``NumberOfSinkSwallows``              | | Number of merger events with other sinks  | [-]                    |                                                   |
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+| ``NumberOfGasSwallows``               | | Number of gas particles accreted          | [-]                    |                                                   |
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+| ``TargetMass``                        | | Target mass required to spawn the next    | [U_M]                  | | You can use it to determine if the target mass  |
+|                                       | | star particle                             |                        | | is so huge that the sink's mass cannot spawn    |
+|                                       |                                             |                        | | such a star. Such rare behaviour may bias the   |
+|                                       |                                             |                        | | IMF towards high masses.                        |
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+| ``Nstars``                            | | Number of stars created by this sink      | [-]                    |                                                   |
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+| ``SwallowedAngularMomentum``          | | Total angular momentum of accreted        | [U_M U_L^2 U_T^{-1}]   |                                                   |
+|                                       | | material                                  |                        |                                                   |
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+| ``MetalMassFractions``                | | Mass fraction of each tracked metal       | [-]                    | | *Only in GEAR chemistry module.*                |
+|                                       | | element                                   |                        | | Array of length ``N`` (number of elements),     |
+|                                       |                                             |                        | | set at compile time via                         |
+|                                       |                                             |                        | | ``--with-chemistry=GEAR_N``.                    |
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+| ``BirthScaleFactors``                 | | Scale factor at the time of sink creation | [-]                    | | Only used in *cosmological* runs.               |
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+| ``BirthTimes``                        | | Time when the sink was created            | [U_T]                  | | Only used in *non-cosmological* runs.           |
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+
+
+
+Stars
+~~~~~
+
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+| Name                                  | Description                                 | Units                  | Comments                                          |
++=======================================+=============================================+========================+===================================================+
+| ``BirthScaleFactors``                 | | Scale-factors when the stars were born    | [-]                    | | Only used in cosmological runs.                 |
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+| ``BirthTimes``                        | | Time when the stars were born             | [U_T]                  | | Only used in non-cosmological runs.             |
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+| ``BirthMasses``                       | | Masses of the stars at birth time         | [U_M]                  | | SF and sinks modules                            |
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+| ``ProgenitorIDs``                     | | ID of the progenitor sinks or gas         | [-]                    | | SF and sinks modules                            |
+|                                       | | particles                                 |                        |                                                   |
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+| ``BirthDensities``                    | | Gas density at star formation             | [U_M U_L^{-3}]         | | *Only in SF module*                             |
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+| ``BirthTemperatures``                 | | Gas temperature at star formation         | [K]                    | | *Only in SF module*                             |
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+| ``Potentials``                        | | Gravitational potential of the star       | [U_L^2 U_T^{-2}]       |                                                   |
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+| ``StellarParticleType``               | | Type of the stellar particle:             | [-]                    | | 0: (discrete) single star                       |
+|                                       | |                                           |                        | | 1: continuous IMF part star                     |
+|                                       | |                                           |                        | | 2: single population star                       |
+|                                       | |                                           |                        | | The last type corresponds to legacy IMF stars.  |
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+| ``MetalMassFractions``                | | Mass fraction of each metal element       | [-]                    | | *Only in GEAR chemistry module*.                |
+|                                       | |                                           |                        | | Array of length ``N`` (number of elements),     |
+|                                       | |                                           |                        | | set at compile time by                          |
+|                                       | |                                           |                        | | ``--with-chemistry=GEAR_N``.                    |
++---------------------------------------+---------------------------------------------+------------------------+---------------------------------------------------+
+
+Gas particles
+~~~~~~~~~~~~~
+
+Since hydro scheme writes its own set of outputs, we only provide the outputs that ``GEAR`` writes for gas particles. 
+
++------------------------------------------+-------------------------------------------------------------+------------------------+----------------------------------------------------+
+| Name                                     | Description                                                 | Units                  | Comments                                           |
++==========================================+=============================================================+========================+====================================================+
+| ``SmoothedMetalMassFractions``           | | Mass fraction of each metal element                       | [-]                    | | *Only in GEAR chemistry module.*                 |
+|                                          | | smoothed over the SPH kernel                              |                        | | Array of length ``N``, set at compile time by    |
+|                                          |                                                             |                        | | ``--with-chemistry=GEAR_N``                      |
++------------------------------------------+-------------------------------------------------------------+------------------------+----------------------------------------------------+
+| ``MetalMassFractions``                   | | Raw (non-smoothed) mass fraction of                       | [-]                    | | *Only in GEAR chemistry module.*                 |
+|                                          | | each metal element                                        |                        | | Same layout as above.                            |
++------------------------------------------+-------------------------------------------------------------+------------------------+----------------------------------------------------+
+| ``HI``                                   | | Mass fraction of neutral H (:math:`\mathrm{H}`)           | [-]                    | | *Only if* ``GRACKLE_1 to 3``                     |
++------------------------------------------+-------------------------------------------------------------+------------------------+----------------------------------------------------+
+| ``HII``                                  | | Mass fraction of ionized H (:math:`\mathrm{H}^+`)         | [-]                    | | *Only if* ``GRACKLE_1 to 3``                     |
++------------------------------------------+-------------------------------------------------------------+------------------------+----------------------------------------------------+
+| ``HeI``                                  | | Mass fraction of neutral He (:math:`\mathrm{He}`)         | [-]                    | | *Only if* ``GRACKLE_1 to 3``                     |
++------------------------------------------+-------------------------------------------------------------+------------------------+----------------------------------------------------+
+| ``HeII``                                 | | Mass fraction of singly ionized He (:math:`\mathrm{He}^+`)| [-]                    | | *Only if* ``GRACKLE_1 to 3``                     |
++------------------------------------------+-------------------------------------------------------------+------------------------+----------------------------------------------------+
+| ``HeIII``                                | | Mass fraction of doubly ionized He                        | [-]                    | | *Only if* ``GRACKLE_1 to 3``                     |
+|                                          | | (:math:`\mathrm{He}^{++}`)                                |                        |                                                    |
++------------------------------------------+-------------------------------------------------------------+------------------------+----------------------------------------------------+
+| ``e``                                    | | Free electron mass fraction (:math:`\mathrm{e}^-`)        | [-]                    | | *Only if* ``GRACKLE_1 to 3``                     |
++------------------------------------------+-------------------------------------------------------------+------------------------+----------------------------------------------------+
+| ``HM``                                   | | Mass fraction of :math:`\mathrm{H}^-`                     | [-]                    | | *Only if* ``GRACKLE_2 or 3``                     |
++------------------------------------------+-------------------------------------------------------------+------------------------+----------------------------------------------------+
+| ``H2I``                                  | | Mass fraction of neutral :math:`\mathrm{H}_2`             | [-]                    | | *Only if* ``GRACKLE_2 or 3``                     |
++------------------------------------------+-------------------------------------------------------------+------------------------+----------------------------------------------------+
+| ``H2II``                                 | | Mass fraction of ionized :math:`\mathrm{H}_2^+`           | [-]                    | | *Only if* ``GRACKLE_2 or 3``                     |
++------------------------------------------+-------------------------------------------------------------+------------------------+----------------------------------------------------+
+| ``DI``                                   | | Mass fraction of neutral D (:math:`\mathrm{D}`)           | [-]                    | | *Only if* ``GRACKLE_3``                          |
++------------------------------------------+-------------------------------------------------------------+------------------------+----------------------------------------------------+
+| ``DII``                                  | | Mass fraction of ionized D (:math:`\mathrm{D}^+`)         | [-]                    | | *Only if* ``GRACKLE_3``                          |
++------------------------------------------+-------------------------------------------------------------+------------------------+----------------------------------------------------+
+| ``HDI``                                  | | Mass fraction of :math:`\mathrm{HD}`                      | [-]                    | | *Only if* ``GRACKLE_3``                          |
++------------------------------------------+-------------------------------------------------------------+------------------------+----------------------------------------------------+

doc/RTD/source/SubgridModels/GEAR/sinks/index.rst

+.. Sink particles in GEAR model
+   Darwin Roduit, 17 April 2024
+
+.. sink_GEAR_model:
+
+.. _sink_GEAR_model:
+
+Sink particles and star formation in GEAR model
+===============================================
+
+.. toctree::
+   :caption: Table of Contents
+
+   introduction
+   theory
+   sink_timesteps
+   params

doc/RTD/source/SubgridModels/GEAR/sinks/introduction.rst

+.. Sink particles in GEAR model
+   Darwin Roduit, 15 March 2024
+
+.. sink_GEAR_model:
+
+Introduction
+------------
+
+GEAR sink particles provide an alternative model to star formation. Instead of stochastically transforming gas particles into stars as is done in GEAR star formation scheme under some conditions, we transform a gas into a sink particle. The main property of the sink particle is its accretion radius. When gas particles within this accretion radius are eligible to be swallowed by the sink, we remove them and transfer their mass, momentum, angular momentum, chemistry properties, etc to the sink particle.
+
+With the sink particles, the IMF splits into two parts: the continuous part and the discrete part. Those parts will correspond to two kinds of stars. Particles in the discrete part of the IMF represent individual stars. It means that discrete IMF-sampled stars have different masses. Particles in the continuous part represent a population of stars, all with the same mass.
+
+The sink particle will randomly choose a target mass, accrete gas until it reaches this target mass and finally spawn a star. Then, the sink chooses a new target mass and repeats the same procedure. When stars are spawned, they are given a new position and velocity as well as chemical properties.
+
+In ``theory.rst`` we outline all of the theory which is implemented as part of the model. This includes how sink particles are formed, how the gas is accreted, how sinks are merged and how stars are spawned. In ``params.rst`` we list and discuss all parameters used by the model. Below we outline how to configure and run the model.
+
+Compiling and running the model
+-------------------------------
+
+You can configure the model with ``--with-sink=GEAR`` in combination with other configure options of the GEAR model. The model will then be used when the ``--sinks`` flag is among the runtime options. In particular, the sink particles require ``--feedback`` runtime option.
+
+Notice that you also need to compile with ``--with-star-formation=GEAR``. The star formation module is required to collect and write star formation data. However, you do not need to run Swift with the option ``--star-formation``.
+
+Then, you do not need to do anything special. Sink particles will be created during your runs. If you want, you can have sink particles in your ICs. At the moment, sink particles do not have any special fields to be set.
+
+A full list of all relevant parameters of the model is in :ref:`sink_GEAR_parameters`. We also briefly describe the most important parameters which need to be set to run the model, as well as how to run it in different configurations.
+
+.. warning::
+   Currently, MPI is not implemented for the sink particles. If you try to run with MPI, you will encounter an error. We thus recommend configuring Swift with ``--disable-mpi`` to avoid any surprises.

doc/RTD/source/SubgridModels/GEAR/sinks/params.rst

+.. Sink particles in GEAR model
+   Darwin Roduit, 15 March 2024
+
+.. sink_GEAR_model:
+
+.. _sink_GEAR_parameters:
+
+Model parameters
+----------------
+
+The parameters of the GEAR sink model are grouped into the ``GEARSink`` section of the parameter file. 
+
+The first three parameters are:
+
+* Whether we are using a fixed cut-off radius for gas and sink accretion: ``use_fixed_cut_off_radius``,
+* The sink cut-off radius: ``cut_off_radius``,
+* The sink inner accretion radius fraction in terms of the cut-off radius: ``f_acc``.
+
+The ``use_fixed_cut_off_radius`` is mandatory and should be set to 0 or 1. If set to 1, the GEAR model will use a fixed cutoff radius equal to the value of ``cut_off_radius``. If not, the cutoff radius is allowed to vary according to the local gas density. In the code, the cutoff radius is always equal to the sink's smoothing length multiplied by a constant factor ``kernel_gamma`` - setting a fixed cutoff will fix the smoothing length at the appropriate value for all sinks.
+
+The ``cut_off_radius`` parameter is optional, and is ignored if ``use_fixed_cut_off_radius`` is 0. If a fixed cut-off is used, every sink's smoothing length will be permanently set to this number divided by ``kernel_gamma`` on formation.
+
+The ``f_acc`` parameter is also optional. Its default value is :math:`0.1`. Its value must respect :math:`0 \leq f_\text{acc} \leq 1` . It describes the inner radius :math:`f_{\text{acc}} \cdot r_{\text{cut-off}}` in which gas particles are swallowed without any further checks, as explained below.
+
+The next three mandatory parameters are:
+
+* the gas temperature threshold to form a sink when :math:`\rho_\text{threshold} < \rho_\text{gas} < \rho_\text{maximal}` :``temperature_threshold_K``,
+* the minimal gas threshold density required to form a sink:``density_threshold_Hpcm3``,
+* the maximal density at which the temperature check is not performed:``maximal_density_threshold_Hpcm3`` (Default: ``FLT_MAX``).
+
+These three parameters govern the first two criteria of the sink formation scheme. If these criteria are not passed, sink particles are not created. If they are passed, the code performs further checks to form sink particles. Some of those criteria checks can be disabled, as explained below.
+
+The next set of parameters deals with the sampling of the IMF and the representation of star particles:
+
+* minimal mass of stars represented by discrete particles: ``minimal_discrete_mass_Msun``,
+* mass of the stellar particle representing the continuous part of the IMF: ``stellar_particle_mass_Msun``,
+* minimal mass of the first stars represented by discrete particles: ``minimal_discrete_mass_first_stars_Msun``,
+* mass of the stellar particle (first stars) representing the continuous part of the IMF:: ``stellar_particle_mass_first_stars_Msun``.
+
+With sink particles, star particles can represent either a single star or a population of stars in the low mass part of the IMF (continuous IMF sampling). The stars in the continuous part of the IMF are put together in a particle of mass ``stellar_particle_mass_Msun`` or ``stellar_particle_mass_first_stars_Msun``, while individual stars in the discrete part have their mass sampled from the IMF. The limit between the continuous and discrete sampling of the IMF is controlled by  ``minimal_discrete_mass_Msun`` and ``minimal_discrete_mass_first_stars_Msun``.
+
+The next set of parameters controls the sink formation scheme. More details are provided in the GEAR documentation. Here is a brief overview:
+
+* whether or not the gas must be contracting: ``sink_formation_contracting_gas_criterion`` (default: 1), 
+* whether or not the gas smoothing length must be small enough: ``sink_formation_smoothing_length_criterion`` (default: 1),
+* whether or not the gas must be in a Jeans unstable state: ``sink_formation_jeans_instability_criterion`` (default: 1),
+* whether or not the gas must be in a bound state: ``sink_formation_bound_state_criterion`` (default: 1),
+* whether or not a new sink can be formed in a region where its ``cut_off_radius`` and the one of an existing sink overlap: ``sink_formation_overlapping_sink_criterion`` (default: 1).
+
+Those criteria are checked if the density and temperature criteria are successfully passed. They control the behaviour of the sink formation scheme. By default, they are all activated and set to ``1``.
+
+The next parameter is ``disable_sink_formation`` (default: 0). It controls whether sinks are formed or not in the simulation. The main purpose is when sinks are put in initial conditions and sinks are not wanted to be added during the run. This parameter is set to ``0`` by default, i.e. sink formation is *enabled*.
+
+The next set of parameters deals with the sink time-steps:
+
+* Courant-Friedrich-Levy constant for the CFL-like time-step constraint:``CFL_condition``,
+* age (in Myr) at which a sink is considered dead (no accretion) and without time-step limitations, except for 2-body encounters involving another young/old sink and gravity: ``timestep_age_threshold_unlimited_Myr`` (default: FLT_MAX),
+* age (in Myr) at which sinks switch from young to old for time-stepping purposes:``timestep_age_threshold``  (default: FLT_MAX),
+* maximal time-step length of young sinks (in Myr): ``max_timestep_young_Myr``  (default: FLT_MAX),
+* maximal time-step length of old sinks (in Myr): ``max_timestep_old_Myr`` (default: FLT_MAX),
+* number of times the IMF mass can be swallowed in a single time-step: ``n_IMF`` (default: FLT_MAX).
+* tolerance parameter for SF timestep constraint: ``tolerance_SF_timestep`` (default: 0.5)
+
+The last parameter is ``sink_minimal_mass_Msun``. This parameter is mainly intended for low-resolution simulations with :math:`m_\text{gas} > 100 \; M_\odot`. It prevents :math:`m_\text{sink} \ll m_\text{gas}` simulations when sinks spawn stars, which can lead to gravity run away.
+
+The full section is:
+
+.. code:: YAML
+
+   GEARSink:
+     use_fixed_cut_off_radius: 1                 # Are we using a fixed cutoff radius? If we are, in GEAR the cutoff radius is fixed at the value specified below, and the sink smoothing length is fixed at this value divided by kernel_gamma. If not, the cutoff radius varies with the sink smoothing length as r_cut = h*kernel_gamma.
+     cut_off_radius: 1e-3                        # Cut off radius of all the sinks in internal units. Ignored if use_fixed_cut_off_radius is 0. 
+     f_acc: 0.1                                  # (Optional) Fraction of the cut_off_radius that determines if a gas particle should be swallowed wihtout additional check. It has to respect 0 <= f_acc <= 1. (Default: 0.1)
+     temperature_threshold_K:        100         # Max temperature (in K) for forming a sink when density_threshold_Hpcm3 <= density <= maximal_density_threshold_Hpcm3.
+     density_threshold_Hpcm3: 1e3                # Minimum gas density (in Hydrogen atoms/cm3) required to form a sink particle.
+     maximal_density_threshold_Hpcm3: 1e5        # If the gas density exceeds this value (in Hydrogen atoms/cm3), a sink forms regardless of temperature if all other criteria are passed. (Default: FLT_MAX)
+     sink_minimal_mass_Msun:     0.              # (Optional) Sink minimal mass in Msun. This parameter prevents m_sink << m_gas in low resolution simulations. (Default: 0.0)
+     stellar_particle_mass_Msun:  20             # Mass of the stellar particle representing the low mass stars (continuous IMF sampling) (in solar mass)
+     minimal_discrete_mass_Msun: 8               # Minimal mass of stars represented by discrete particles (in solar mass)
+     stellar_particle_mass_first_stars_Msun: 20      # Mass of the stellar particle representing the low mass stars (continuous IMF sampling) (in solar mass). First stars
+     minimal_discrete_mass_first_stars_Msun: 8       # Minimal mass of stars represented by discrete particles (in solar mass). First stars
+     star_spawning_sigma_factor: 0.2                 # Factor to rescale the velocity dispersion of the stars when they are spawned. (Default: 0.2)
+     sink_formation_contracting_gas_criterion: 1     # (Optional) Activate the contracting gas check for sink formation. (Default: 1)
+     sink_formation_smoothing_length_criterion: 1    # (Optional) Activate the smoothing length check for sink formation. (Default: 1)
+     sink_formation_jeans_instability_criterion: 1   # (Optional) Activate the two Jeans instability checks for sink formation. (Default: 1)
+     sink_formation_bound_state_criterion: 1         # (Optional) Activate the bound state check for sink formation. (Default: 1)
+     sink_formation_overlapping_sink_criterion: 1    # (Optional) Activate the overlapping sink check for sink formation. (Default: 1)
+     disable_sink_formation: 0                       # (Optional) Disable sink formation. (Default: 0)
+     CFL_condition:                        0.5       # Courant-Friedrich-Levy condition for time integration.
+     timestep_age_threshold_unlimited_Myr: 100.      # (Optional) Age above which sinks no longer have time-step restrictions, except for 2-body encounters involving another young/old sink and gravity (in Mega-years). (Default: FLT_MAX)
+     timestep_age_threshold_Myr:           25.       # (Optional) Age at which sink switch from young to old for time-stepping purposes (in Mega-years). (Default: FLT_MAX)
+     max_timestep_young_Myr:               1.0       # (Optional) Maximal time-step length of young sinks (in Mega-years). (Default: FLT_MAX)
+     max_timestep_old_Myr:                 5.0       # (Optional) Maximal time-step length of old sinks (in Mega-years). (Default: FLT_MAX)
+     n_IMF:                                 2        # (Optional) Number of times the IMF mass can be swallowed in a single timestep. (Default: FLTM_MAX)
+     tolerance_SF_timestep:                 0.5      # (Optional) Tolerance parameter for SF timestep constraint. (Default: 0.5)
+
+.. warning::
+   Some parameter choices can greatly impact the outcome of your simulations. Think twice when choosing them.
+
+Sink accretion radius
+~~~~~~~~~~~~~~~~~~~~~
+
+The most critical parameter is ``cut_off_radius``. As explained in the theory, to form a sink, the gas smoothing kernel edge :math:`\gamma_k h` (:math:`\gamma_k` is a kernel dependent constant) must be smaller than ``cut_off_radius`` (if this criterion is enabled). Therefore, the cut-off radius strongly depends on the resolution of your simulations. Moreover, if you use a minimal gas smoothing length `h`, and plan to use sink particles, consider whether the cut-off radius will meet the smoothing length criterion. If `h` never meets the aforementioned criterion, you will never form sinks and thus never have stars.
+
+On the contrary, if you set a too high cut-off radius, then sinks will accrete a lot of gas particles and spawn a lot of stars in the same cell, which the code might not like and crash with the error:
+
+``runner_others.c:runner_do_star_formation_sink():274: Too many stars in the cell tree leaf! The sorting task will not be able to perform its duties. Possible solutions: (1) The code need to be run with different star formation parameters to reduce the number of star particles created. OR (2) The size of the sorting stack must be increased in runner_sort.c.``
+
+This problem can be mitigated by choosing a higher value of ``stellar_particle_mass_Msun`` and ``stellar_particle_mass_first_stars_Msun``, or higher values of ``minimal_discrete_mass_Msun`` and ``minimal_discrete_mass_first_stars_Msun``. Of course, this comes at the price of having fewer individual stars. Finally, all parameters will depend on your needs.
+
+*If you do not want to change your parameters*, you can increase the ``sort_stack_size`` variable at the beginning ``runner_sort.c``. The default value is 10 in powers of 2 (so the stack size is 1024 particles). Increase it to the desired value. Be careful to not overestimate this.
+
+Note that if a cutoff radius is not specified, and the radius is instead left to vary with the local gas density, the smoothing length criterion is always satisfied.
+
+Guide to choose the the accretion radius or the density threshold
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+We provide some advice to help you set up the sink accretion radius or the threshold density appropriately.
+
+First, you must choose either the sink accretion radius or the threshold density. Choosing the density might be easier based on your previous work or if you have an expected star formation density. Once you fix the density or the accretion radius, you can use the following formula to estimate the remaining parameter. In the code, the gas smoothing length is determined with:
+
+.. math::
+   h = \eta \left( \frac{X_{\text{H}} m_B}{m_{\text{H}} n_{\text{H}}} \right)^{1/3} \, ,
+
+where :math:`\eta` is a constant related to the number of neighbours in the kernel, :math:`X_{\text{H}}` is the hydrogen mass fraction, :math:`m_B` the gas particle's mass, :math:`m_{\text{H}}` the hydrogen particle mass and :math:`n_{\text{H}}` the hydrogen number density.
+
+Let us provide an example. In GEAR, we do not model physical processes below the parsec scale. Hence, let us take :math:`h \sim 1` pc. In zoom-in simulations we have :math:`m_B \simeq 95 \; M_{\odot}`. The remaining parameters are :math:`\eta = 1.2348` and :math:`X_{\text{H}} = 0.76`. So, after inverting the formula, we find :math:`n_H \simeq 5500 \text{ hydrogen atoms/cm}^3`. In practice, we use :math:`n_H = 1000 \text{ hydrogen atoms/cm}^3`, close to the estimation, and an accretion radius :math:`r_{\text{acc}} = 10` pc. These values are slightly different for safety reasons, but they are consistent.
+
+Remember that this was a way, among others, to determine good accretion radius and threshold density. It can help you with your first runs with sink particles.
+
+Comment on star formation efficiency
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Notice that this model does not have parameters to control the star formation rate of the sink. The SFR is self-regulated by the gas/sink accretion and other feedback mechanisms. Supernovae tend to create bubbles of lower density at the site of star formation, removing the gas and preventing further gas accretion. However, the sink might run into this stack size problem by the time the first supernovae explode. Other pre-stellar feedback mechanisms could do the job earlier, though they are not implemented in GEAR.
+
+.. note:: 
+   We provide a piece of general advice: do some calibration on low-resolution simulations. This will help to see what works and what does not work. Keep in mind that you might want to put a higher ``stellar_particle_mass_X_Msun`` at the beginning to avoid spawning too many stars. For the high-resolution simulations, you then can lower the particle's mass.