Computation of derived quantities

computeClumpingFactor(density::Vector{<:Number})::Float64

Compute the clumping factor,

\[C_\rho = \frac{\langle \rho^2 \rangle}{\langle \rho \rangle^2} \, .\]

Arguments

• density::Vector{<:Number}: The density of the cells/particles.

Returns

• The clumping factor.

computeDepletionTime(
    mass::Vector{<:Unitful.Mass},
    sfr::Vector{<:Unitful.MassFlow},
)::Vector{<:Unitful.Time}

Compute the depletion time,

\[t_\mathrm{ff} = \frac{M_\mathrm{gas}}{\dot{M}_\star} \, .\]

Arguments

• mass::Vector{<:Unitful.Mass}: The gas mass of the cells/particles.
• sfr::Vector{<:Unitful.MassFlow}: The SFR associated to each cell/particle.

Returns

• The depletion time.

computeEfficiencyFF(
    density::Vector{<:Unitful.Density},
    mass::Vector{<:Unitful.Mass},
    sfr::Vector{<:Unitful.MassFlow},
)::Vector{Float64}

Compute the star formation efficiency per free-fall time, according to the definition in equation 1 of Krumholz (2012),

\[\epsilon_\mathrm{ff} = \frac{t_\mathrm{ff}}{t_\mathrm{dep}} \, .\]

where

\[t_\mathrm{ff} = \sqrt{\frac{3 \, \pi}{32 \, G \, \rho}} \, ,\]

is the free-fall time, and

\[t_\mathrm{dep} = \frac{M_\mathrm{H_2}}{\dot{M}_\star} \, ,\]

is the depletion time.

Arguments

• density::Vector{<:Unitful.Density}: The molecular hydrogen ($\\mathrm{H_2}$) density of the cells/particles.
• mass::Vector{<:Unitful.Mass}: The gas mass of the cells/particles.
• sfr::Vector{<:Unitful.MassFlow}: The SFR associated to each cell/particle.

Returns

• The star formation efficiency per free-fall time.

References

M. R. Krumholz et al. (2012). A UNIVERSAL, LOCAL STAR FORMATION LAW IN GALACTIC CLOUDS, NEARBY GALAXIES, HIGH-REDSHIFT DISKS, AND STARBURSTS. The Astrophysical Journal, 745(1), 69. doi:10.1088/0004-637X/745/1/69

computeSFR(
    data_dict::Dict;
    <keyword arguments>
)::Vector{<:Unitful.MassFlow}

Compute the star formation rate of each stellar particle.

For stellar particles younger than age_resol, the SFR is its mass divided by age_resol. It is defined as 0 for older particles.

Arguments

• data_dict::Dict: A dictionary with the following shape:

  • :sim_data -> ::Simulation (see Simulation).
  • :snap_data -> ::Snapshot (see Snapshot).
  • :gc_data -> ::GroupCatalog (see GroupCatalog).
  • cell/particle type -> (block -> data of block, block -> data of block, ...).
  • cell/particle type -> (block -> data of block, block -> data of block, ...).
  • cell/particle type -> (block -> data of block, block -> data of block, ...).
  • ...
  • groupcat type -> (block -> data of block, block -> data of block, ...).
  • groupcat type -> (block -> data of block, block -> data of block, ...).
  • groupcat type -> (block -> data of block, block -> data of block, ...).
  • ...

• age_resol::Unitful.Time=AGE_RESOLUTION: Age resolution for the SFR.

Returns

• The star formation rate of each stellar particle.

computeStellarAge(data_dict::Dict)::Vector{<:Unitful.Time}

Compute the age of the stars.

Arguments

• data_dict::Dict: A dictionary with the following shape:

  • :sim_data -> ::Simulation (see Simulation).
  • :snap_data -> ::Snapshot (see Snapshot).
  • :gc_data -> ::GroupCatalog (see GroupCatalog).
  • cell/particle type -> (block -> data of block, block -> data of block, ...).
  • cell/particle type -> (block -> data of block, block -> data of block, ...).
  • cell/particle type -> (block -> data of block, block -> data of block, ...).
  • ...
  • groupcat type -> (block -> data of block, block -> data of block, ...).
  • groupcat type -> (block -> data of block, block -> data of block, ...).
  • groupcat type -> (block -> data of block, block -> data of block, ...).
  • ...

Returns

• The stellar ages.

computeTemperature(
    internal_energy::Vector{<:SpecificEnergy},
    electron_fraction::Vector{Float32},
)::Vector{<:Unitful.Temperature}

Compute the gas temperature.

Arguments

• internal_energy::Vector{<:SpecificEnergy}: Specific internal energy of every gas cell/particle.
• electron_fraction::Vector{Float32}: Number fraction of electrons in every gas cell/particle.

Returns

• The temperature of each gas cell/particle.

computeTime(a::Real, header::SnapshotHeader; <keyword arguments>)::Unitful.Time

Compute the physical time corresponding to the scale factor a.

To get the physical time $t$ from the scale factor a, one does the integral:

\[t = \frac{1}{H_0} \int_0^a \frac{\mathrm{d}a'}{a' \, \sqrt{\mathcal{E}(a')}} \, ,\]

where

\[\mathcal{E}(a) = \Omega_\Lambda + \Omega_m \, a^{-3} + \Omega_r \, a^{-4} + \Omega_K \, a^{-2} \, .\]

Arguments

• a::Real: Scale factor.
• header::SnapshotHeader: A header of the simulation, containing the cosmological parameters.
• a0::Float64=0.0: Initial scale factor.

Returns

• The physical time.

computeTime(
    scale_factors::Vector{<:Real},
    header::SnapshotHeader;
    <keyword arguments>
)::Vector{<:Unitful.Time}

Compute the physical time corresponding to each of the scale_factors.

To get the physical time $t$ from the scale factor a, one does the integral:

\[t = \frac{1}{H_0} \int_0^a \frac{\mathrm{d}a'}{a' \, \sqrt{\mathcal{E}(a')}} \, ,\]

where

\[\mathcal{E}(a) = \Omega_\Lambda + \Omega_m \, a^{-3} + \Omega_r \, a^{-4} + \Omega_K \, a^{-2} \, .\]

Arguments

• scale_factors::Vector{<:Real}: Scale factors.
• header::SnapshotHeader: A header of the simulation, containing the cosmological parameters.
• a0::Float64=0.0: Initial scale factor.

Returns

• A vector with the physical times.

computeTimeTicks(
    paths::Vector{<:Union{Missing,String}},
)::Tuple{Vector{Float64},Vector{Float64},Vector{<:Unitful.Time},Vector{<:Unitful.Time}}

Compute the different times stamps associated with each snapshot in paths.

Arguments

• paths::Vector{<:Union{Missing,String}}: Paths to the snapshots.

Returns

• A tuple with four elements:

  • A vector with the scale factors.
  • A vector with the redshifts.
  • A vector with the physical times (physical time since the Big Bang).
  • A vector with the lookback times (physical time left to reach the last snapshot).

integrateQty(data_dict::Dict, quantity::Symbol)::Number

Compute an integrated quantity for the whole system in data_dict.

Arguments

• data_dict::Dict: A dictionary with the following shape:

  • :sim_data -> ::Simulation (see Simulation).
  • :snap_data -> ::Snapshot (see Snapshot).
  • :gc_data -> ::GroupCatalog (see GroupCatalog).
  • cell/particle type -> (block -> data of block, block -> data of block, ...).
  • cell/particle type -> (block -> data of block, block -> data of block, ...).
  • cell/particle type -> (block -> data of block, block -> data of block, ...).
  • ...
  • groupcat type -> (block -> data of block, block -> data of block, ...).
  • groupcat type -> (block -> data of block, block -> data of block, ...).
  • groupcat type -> (block -> data of block, block -> data of block, ...).
  • ...

• quantity::Symbol: The possibilities are:

  • :stellar_mass -> Stellar mass.
  • :gas_mass -> Gas mass.
  • :hydrogen_mass -> Hydrogen mass.
  • :dm_mass -> Dark matter mass.
  • :bh_mass -> Black hole mass.
  • :molecular_mass -> Molecular hydrogen ($\mathrm{H_2}$) mass.
  • :br_molecular_mass -> Molecular hydrogen ($\mathrm{H_2}$) mass, computed using the pressure relation in Blitz et al. (2006).
  • :atomic_mass -> Atomic hydrogen ($\mathrm{HI}$) mass.
  • :ionized_mass -> Ionized hydrogen ($\mathrm{HII}$) mass.
  • :neutral_mass -> Neutral hydrogen ($\mathrm{HI + H_2}$) mass.
  • :stellar_gas_mass -> Stellar gas mass (according to our SF model).
  • :ode_metal_mass -> Metal mass (according to our SF model).
  • :ode_metallicity -> Metallicity (according to our SF model).
  • :dust_mass -> Dust mass.
  • :stellar_number -> Number of stellar particles.
  • :gas_number -> Number of gas cells.
  • :dm_number -> Number of dark matter particles.
  • :bh_number -> Number of black hole particles.
  • :molecular_fraction -> Gas mass fraction of molecular hydrogen.
  • :br_molecular_fraction -> Gas mass fraction of molecular hydrogen, computed using the pressure relation in Blitz et al. (2006).
  • :atomic_fraction -> Gas mass fraction of atomic hydrogen.
  • :ionized_fraction -> Gas mass fraction of ionized hydrogen.
  • :neutral_fraction -> Gas mass fraction of neutral hydrogen.
  • :molecular_neutral_fraction-> Fraction of molecular hydrogen in the neutral gas.
  • :ionized_neutral_fraction -> Fraction of ionized gas to neutral gas.
  • :gas_mass_density -> Mean gas mass density.
  • :stellar_gas_fraction -> Stellar gas fraction (according to our SF model).
  • :metal_gas_fraction -> Metallicity (according to our SF model).
  • :dust_fraction -> Dust mass fraction.
  • :stellar_area_density -> Stellar area mass density, for a radius of DISK_R.
  • :gas_area_density -> Gas mass surface density, for a radius of DISK_R.
  • :molecular_area_density -> Molecular mass surface density, for a radius of DISK_R.
  • :br_molecular_area_density -> Molecular mass surface density, for a radius of DISK_R, computed using the pressure relation in Blitz et al. (2006).
  • :atomic_area_density -> Atomic hydrogen area mass density, for a radius of DISK_R.
  • :ionized_area_density -> Ionized hydrogen area mass density, for a radius of DISK_R.
  • :neutral_area_density -> Neutral mass surface density, for a radius of DISK_R.
  • :sfr_area_density -> Star formation rate area density, for the last AGE_RESOLUTION and a radius of DISK_R.
  • :gas_td -> Gas depletion time.
  • :molecular_td -> The molecular hydrogen ($\mathrm{H_2}$) depletion time.
  • :br_molecular_td -> The Molecular hydrogen ($\mathrm{H_2}$) depletion time, computed using the pressure relation in Blitz et al. (2006).
  • :atomic_td -> The atomic hydrogen ($\mathrm{HI}$) depletion time.
  • :ionized_td -> The ionized hydrogen ($\mathrm{HII}$) depletion time.
  • :neutral_td -> The neutral hydrogen ($\mathrm{HI + H_2}$) depletion time.
  • :gas_metallicity -> Mass fraction of all elements above He in the gas (solar units).
  • :stellar_metallicity -> Mass fraction of all elements above He in the stars (solar units).
  • :X_gas_abundance -> Gas abundance of element $\mathrm{X}$, as $12 + \log_{10}(\mathrm{X \, / \, H})$. The possibilities are the keys of ELEMENT_INDEX.
  • :X_stellar_abundance -> Stellar abundance of element $\mathrm{X}$, as $12 + \log_{10}(\mathrm{X \, / \, H})$. The possibilities are the keys of ELEMENT_INDEX.
  • :stellar_specific_am -> Norm of the stellar specific angular momentum.
  • :gas_specific_am -> Norm of the gas specific angular momentum.
  • :dm_specific_am -> Norm of the dark matter specific angular momentum.
  • :sfr -> Star formation rate.
  • :ssfr -> The specific star formation rate.
  • :observational_sfr -> Star formation rate of the last AGE_RESOLUTION.
  • :observational_ssfr -> The specific star formation rate of the last AGE_RESOLUTION.
  • :stellar_eff -> Star formation efficiency per free-fall time for the gas that has turn into stars.
  • :gas_eff -> Star formation efficiency per free-fall time for the gas.
  • :molecular_eff -> Star formation efficiency per free-fall time for the molecular hydrogen ($\mathrm{H_2}$) gas.
  • :br_molecular_eff -> Star formation efficiency per free-fall time for the molecular hydrogen ($\mathrm{H_2}$) gas, computed using the pressure relation in Blitz et al. (2006).
  • :atomic_eff -> Star formation efficiency per free-fall time for the atomic hydrogen ($\mathrm{HI}$) gas.
  • :ionized_eff -> Star formation efficiency per free-fall time for the ionized hydrogen ($\mathrm{HII}$) gas.
  • :neutral_eff -> Star formation efficiency per free-fall time for the neutral hydrogen ($\mathrm{HI + H_2}$) gas.
  • :scale_factor -> Scale factor.
  • :redshift -> Redshift.
  • :physical_time -> Physical time since the Big Bang.
  • :lookback_time -> Physical time left to reach the last snapshot.
  • :ode_gas_it -> Integration time.
  • :ode_gas_tau_s -> Star formation time scale, $\tau_\mathrm{S}$.
  • :ode_gas_eta_d -> Photodissociation efficiency, $\eta_\mathrm{diss}$.
  • :ode_gas_eta_i -> Photoionization efficiency, $\eta_\mathrm{ion}$.
  • :ode_gas_r -> Mass recycling parameter, $R$.
  • :ode_gas_cold_mf -> Cold gas mass fraction.
  • :ode_stellar_it -> Integration time, for the gas that form the stars.
  • :ode_stellar_tau_s -> Star formation time scale, $\tau_\mathrm{S}$, for the gas that form the stars.
  • :ode_stellar_eta_d -> Photodissociation efficiency, $\eta_\mathrm{diss}$, for the gas that form the stars.
  • :ode_stellar_eta_i -> Photoionization efficiency, $\eta_\mathrm{ion}$, for the gas that form the stars.
  • :ode_stellar_r -> Mass recycling parameter, $R$, for the gas that form the stars.
  • :ode_stellar_cold_mf -> Cold gas mass fraction, for the gas that form the stars.
  • :ode_stellar_gas_rho -> Gas mass density, for the gas that form the stars.
  • :ode_stellar_gas_Z -> Gas metallicity, for the gas that form the stars (solar units).
  • :ode_stellar_gas_mass -> Cell mass, for the gas that form the stars.
  • :ode_stellar_gas_sfr -> SFR associated to the gas particles/cells within the code, for the gas that form the stars.
  • :ode_stellar_gas_P -> Gas pressure, for the gas that form the stars.

Returns

• The value of quantity for the whole system in data_dict.

References

L. Blitz et al. (2006). The Role of Pressure in GMC Formation II: The H2-Pressure Relation. The Astrophysical Journal, 650(2), 933. doi:10.1086/505417

scatterQty(data_dict::Dict, quantity::Symbol)::Vector{<:Number}

Compute a quantity for each cell/particle in data_dict.

Arguments

• data_dict::Dict: A dictionary with the following shape:

  • :sim_data -> ::Simulation (see Simulation).
  • :snap_data -> ::Snapshot (see Snapshot).
  • :gc_data -> ::GroupCatalog (see GroupCatalog).
  • cell/particle type -> (block -> data of block, block -> data of block, ...).
  • cell/particle type -> (block -> data of block, block -> data of block, ...).
  • cell/particle type -> (block -> data of block, block -> data of block, ...).
  • ...
  • groupcat type -> (block -> data of block, block -> data of block, ...).
  • groupcat type -> (block -> data of block, block -> data of block, ...).
  • groupcat type -> (block -> data of block, block -> data of block, ...).
  • ...

• quantity::Symbol: The possibilities are:

  • :stellar_mass -> Stellar mass.
  • :gas_mass -> Gas mass.
  • :hydrogen_mass -> Hydrogen mass.
  • :dm_mass -> Dark matter mass.
  • :bh_mass -> Black hole mass.
  • :molecular_mass -> Molecular hydrogen ($\mathrm{H_2}$) mass.
  • :br_molecular_mass -> Molecular hydrogen ($\mathrm{H_2}$) mass, computed using the pressure relation in Blitz et al. (2006).
  • :atomic_mass -> Atomic hydrogen ($\mathrm{HI}$) mass.
  • :ionized_mass -> Ionized hydrogen ($\mathrm{HII}$) mass.
  • :neutral_mass -> Neutral hydrogen ($\mathrm{HI + H_2}$) mass.
  • :stellar_gas_mass -> Stellar gas mass (according to our SF model).
  • :ode_metal_mass -> Metal mass (according to our SF model).
  • :ode_metallicity -> Metallicity (according to our SF model).
  • :dust_mass -> Dust mass.
  • :molecular_fraction -> Gas mass fraction of molecular hydrogen.
  • :br_molecular_fraction -> Gas mass fraction of molecular hydrogen, computed using the pressure relation in Blitz et al. (2006).
  • :atomic_fraction -> Gas mass fraction of atomic hydrogen.
  • :ionized_fraction -> Gas mass fraction of ionized hydrogen.
  • :neutral_fraction -> Gas mass fraction of neutral hydrogen.
  • :molecular_neutral_fraction -> Fraction of molecular hydrogen in the neutral gas.
  • :ionized_neutral_fraction -> Fraction of ionized gas to neutral gas.
  • :stellar_gas_fraction -> Stellar gas fraction (according to our SF model).
  • :metal_gas_fraction -> Metallicity (according to our SF model).
  • :dust_fraction -> Dust mass fraction.
  • :gas_mass_density -> Gas mass density.
  • :hydrogen_mass_density -> Hydrogen mass density.
  • :gas_number_density -> Gas number density.
  • :molecular_number_density -> Molecular hydrogen number density.
  • :br_molecular_number_density -> Molecular hydrogen number density, computed using the pressure relation in Blitz et al. (2006).
  • :atomic_number_density -> Atomic hydrogen number density.
  • :ionized_number_density -> Ionized hydrogen number density.
  • :neutral_number_density -> Neutral hydrogen number density.
  • :gas_td -> Total gas depletion time.
  • :molecular_td -> Molecular hydrogen ($\mathrm{H_2}$) depletion time.
  • :br_molecular_td -> Molecular hydrogen ($\mathrm{H_2}$) depletion time, computed using the pressure relation in Blitz et al. (2006).
  • :atomic_td -> Atomic hydrogen ($\mathrm{HI}$) depletion time.
  • :ionized_td -> Ionized hydrogen ($\mathrm{HII}$) depletion time.
  • :neutral_td -> Neutral hydrogen ($\mathrm{HI + H_2}$) depletion time.
  • :gas_metallicity -> Mass fraction of all elements above He in the gas (solar units).
  • :stellar_metallicity -> Mass fraction of all elements above He in the stars (solar units).
  • :X_gas_abundance -> Gas abundance of element $\mathrm{X}$, as $12 + \log_{10}(\mathrm{X \, / \, H})$. The possibilities are the keys of ELEMENT_INDEX.
  • :X_stellar_abundance -> Stellar abundance of element $\mathrm{X}$, as $12 + \log_{10}(\mathrm{X \, / \, H})$. The possibilities are the keys of ELEMENT_INDEX.
  • :stellar_radial_distance -> Distance of every stellar particle to the origin.
  • :gas_radial_distance -> Distance of every gas cell to the origin.
  • :dm_radial_distance -> Distance of every dark matter particle to the origin.
  • :stellar_xy_distance -> Projected distance of every stellar particle to the origin.
  • :gas_xy_distance -> Projected distance of every gas cell to the origin.
  • :dm_xy_distance -> Projected distance of every dark matter particle to the origin.
  • :gas_sfr -> SFR associated to each gas particle/cell within the code.
  • :stellar_circularity -> Stellar circularity.
  • :stellar_vcirc -> Stellar circular velocity.
  • :stellar_vradial -> Stellar radial speed.
  • :stellar_vtangential -> Stellar tangential speed.
  • :stellar_vzstar -> Stellar speed in the z direction, computed as $v_z \, \mathrm{sign}(z)$.
  • :stellar_age -> Stellar age.
  • :sfr -> Star formation rate.
  • :ssfr -> The specific star formation rate.
  • :observational_sfr -> Star formation rate of the last AGE_RESOLUTION.
  • :observational_ssfr -> The specific star formation rate of the last AGE_RESOLUTION.
  • :stellar_eff -> Star formation efficiency per free-fall time for the gas that has turn into stars.
  • :gas_eff -> Star formation efficiency per free-fall time for the gas.
  • :molecular_eff -> Star formation efficiency per free-fall time for the molecular hydrogen ($\mathrm{H_2}$) gas.
  • :br_molecular_eff -> Star formation efficiency per free-fall time for the molecular hydrogen ($\mathrm{H_2}$) gas, computed using the pressure relation in Blitz et al. (2006).
  • :atomic_eff -> Star formation efficiency per free-fall time for the atomic hydrogen ($\mathrm{HI}$) gas.
  • :ionized_eff -> Star formation efficiency per free-fall time for the ionized hydrogen ($\mathrm{HII}$) gas.
  • :neutral_eff -> Star formation efficiency per free-fall time for the neutral hydrogen ($\mathrm{HI + H_2}$) gas.
  • :temperature -> Gas temperature, as $\log_{10}(T \, / \, \mathrm{K})$.
  • :pressure -> Gas pressure.
  • :ode_gas_it -> Integration time.
  • :ode_gas_tau_s -> Star formation time scale, $\tau_\mathrm{S}$.
  • :ode_gas_eta_d -> Photodissociation efficiency, $\eta_\mathrm{diss}$.
  • :ode_gas_eta_i -> Photoionization efficiency, $\eta_\mathrm{ion}$.
  • :ode_gas_r -> Mass recycling parameter, $R$.
  • :ode_gas_cold_mf -> Cold gas mass fraction.
  • :ode_stellar_it -> Integration time, for the gas that form the stars.
  • :ode_stellar_tau_s -> Star formation time scale, $\tau_\mathrm{S}$, for the gas that form the stars.
  • :ode_stellar_eta_d -> Photodissociation efficiency, $\eta_\mathrm{diss}$, for the gas that form the stars.
  • :ode_stellar_eta_i -> Photoionization efficiency, $\eta_\mathrm{ion}$, for the gas that form the stars.
  • :ode_stellar_r -> Mass recycling parameter, $R$, for the gas that form the stars.
  • :ode_stellar_cold_mf -> Cold gas mass fraction, for the gas that form the stars.
  • :ode_stellar_gas_rho -> Gas mass density, for the gas that form the stars.
  • :ode_stellar_gas_Z -> Gas metallicity, for the gas that form the stars (solar units).
  • :ode_stellar_gas_mass -> Cell mass, for the gas that form the stars.
  • :ode_stellar_gas_sfr -> SFR associated to the gas particles/cells within the code, for the gas that form the stars.
  • :ode_stellar_gas_P -> Gas pressure, for the gas that form the stars.

Returns

• The values of quantity for every cell/particle.

References

L. Blitz et al. (2006). The Role of Pressure in GMC Formation II: The H2-Pressure Relation. The Astrophysical Journal, 650(2), 933. doi:10.1086/505417