From 1cdf9d8ad2c13cbd84d012f37236e6c8dc326f0e Mon Sep 17 00:00:00 2001 From: Matthieu Schaller <schaller@strw.leidenuniv.nl> Date: Thu, 23 May 2019 23:28:52 +0200 Subject: [PATCH] Added RTD documentation for the EAGLE star formation model. --- doc/RTD/source/SubgridModels/EAGLE/index.rst | 68 ++++++++++++++++++-- 1 file changed, 62 insertions(+), 6 deletions(-) diff --git a/doc/RTD/source/SubgridModels/EAGLE/index.rst b/doc/RTD/source/SubgridModels/EAGLE/index.rst index 35f579b9b2..8ce5f09de4 100644 --- a/doc/RTD/source/SubgridModels/EAGLE/index.rst +++ b/doc/RTD/source/SubgridModels/EAGLE/index.rst @@ -70,7 +70,8 @@ temperatures, the slopes are expressed using a power-law in terms of entropy and *not* in terms of temperature. For a slope of :math:`\gamma` in the parameter file, the temperature as a function of density will be limited to be above a power-law with slope :math:`\gamma - 1` (as shown on -the figure above). +the figure above). To simplify things, all constants are converted +to the internal system of units upon reading the parameter file. For a normal EAGLE run, that section of the parameter file reads: @@ -410,6 +411,34 @@ the snapshots for each gas and star particle: Star formation: Schaye+2008 modified for EAGLE ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +The star formation is based on the pressure implementation of `Schaye & Dalla +Vecchia (2008) <http://adsabs.harvard.edu/abs/2008MNRAS.383.1210S>`_ with a +metal-dependent star-formation density threshold following the relation derived +by `Schaye (2004) <http://adsabs.harvard.edu/abs/2004ApJ...609..667S>`_. Above a +density threshold :math:`n^*_{\rm H}`, expressed in number of Hydrogen atoms per +(physical) cubic centimeters, the star formation rate is expressed as a +pressure-law :math:`\dot{m}_* = m_g \times A \times \left( 1 {\rm +M_\odot}~{\rm pc^2} \right)^{-n} \times \left(\frac{\gamma}{G_{\rm +N}}f_gP\right)^{(n-1)/2}`, where :math:`n` is the exponent of the +Kennicutt-Schmidt relation (typically :math:`n=1.4`) and :math:`A` is the +normalisation of the law (typically :math:`A=1.515\times10^{-4} {\rm +M_\odot}~{\rm yr^{-1}}~{\rm kpc^{-2}}`). :math:`m_g` is the gas particle mass, +:math:`\gamma` is the adiabatic index, :math:`f_g` the gas fraction of the disk +and :math:`P` the total pressure of the gas including any subgrid turbulent terms. + +Once a gas particle has computed its star formation rate, we compute the +probability that this particle turns into a star using :math:`Prob= +\min\left(\frac{\dot{m}_*\Delta t}{m_g},1\right)`. We then draw a random number +and convert the gas particle into a star or not depending on our luck. + +The density threshold itself has a metallicity dependence. We use the *smoothed* +metallicty (metal mass fraction) of the gas (See :ref:`EAGLE_chemical_tracers`) +and apply the relation :math:`n^*_{\rm H} = n_{\rm H,norm}\left(\frac{Z_{\rm +smooth}}{Z_0}\right)^{n_{\rm Z}}`, alongside a maximal value. The model is +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 :width: 400px :align: center @@ -427,6 +456,15 @@ Star formation: Schaye+2008 modified for EAGLE does *not* enter the model at all). The values used to produce this figure are the ones assumed in the reference EAGLE model. +In the EAGLE model, the pressure entering the star formation includes pressure +from the unresolved turbulence. This is modeled in the form of a polytropic +equation of state for the gas :math:`P = P_{\rm +norm}\left(\frac{\rho}{\rho_0}\right)^{\gamma_{\rm eff}}`. For practical reasons, +this relation is expressed in term of 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 :width: 400px :align: center @@ -442,7 +480,25 @@ Star formation: Schaye+2008 modified for EAGLE point will also be put on this equation of state when computing its star formation rate. The values used to produce this figure are the ones assumed in the reference EAGLE model. - + +To prevent star formation in non-collapsed objects (for instance at high +redshift when the whole Universe has a density above the threshold), we apply an +over-density criterion. Only gas with a density larger than a multiple of the +critical density for closure can form stars. + +Additionally to the pressure-law corresponding to the Kennicutt-Schmidt relation +described, above, we implement a second density threshold above which the slope +of the relationship varies (typically steepens). This is governed by two +additional parameters: the density at which the relation changes and the second +slope. Finally, we optionally use a maximal density above which any gas particle +automatically gets a probability to form a star of 100%. + +The code applying this star formation law is located in the directory +``src/star_formation/EAGLE/``. To simplify things, all constants are converted +to the internal system of units upon reading the parameter file. + +For a normal EAGLE run, that section of the parameter file reads: + .. code:: YAML # EAGLE star formation parameters @@ -455,13 +511,13 @@ Star formation: Schaye+2008 modified for EAGLE KS_min_over_density: 57.7 # The over-density above which star-formation is allowed. KS_high_density_threshold_H_p_cm3: 1e3 # Hydrogen number density above which the Kennicut-Schmidt law changes slope in Hydrogen atoms per cm^3. KS_high_density_exponent: 2.0 # Slope of the Kennicut-Schmidt law above the high-density threshold. - KS_temperature_margin_dex: 0.5 # Logarithm base 10 of the maximal temperature difference above the EOS allowed to form stars. - KS_max_density_threshold_H_p_cm3: 1e5 # Hydrogen number density above which a particle gets automatically turned into a star in Hydrogen atoms per cm^3. + KS_temperature_margin_dex: 0.5 # (Optional) Logarithm base 10 of the maximal temperature difference above the EOS allowed to form stars. + KS_max_density_threshold_H_p_cm3: 1e5 # (Optional) Hydrogen number density above which a particle gets automatically turned into a star in Hydrogen atoms per cm^3. threshold_norm_H_p_cm3: 0.1 # Normalisation of the metal-dependant density threshold for star formation in Hydrogen atoms per cm^3. threshold_Z0: 0.002 # Reference metallicity (metal mass fraction) for the metal-dependant threshold for star formation. threshold_slope: -0.64 # Slope of the metal-dependant star formation threshold 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. - gas_fraction: 0.1 # The gas fraction used internally by the model. + gas_fraction: 1.0 # (Optional) The gas fraction used internally by the model. .. _EAGLE_enrichment: @@ -471,7 +527,7 @@ Stellar enrichment: Wiersma+2009b .. _EAGLE_feedback: Supernova feedback: Dalla Vecchia+2012 & Schaye+2015 -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code:: YAML -- GitLab