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The SKIRT project
advanced radiative transfer for astrophysics
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The SKIRT project
advanced radiative transfer for astrophysics
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This page provides an overview of SKIRT's capabilities for the self-consistent iterative calculation of the medium state and radiation field. It introduces the relevant concepts and provides some examples.
The medium state (MediumState) in a SKIRT simulation consists of a list of variables stored for each cell in the spatial grid. The list includes variables common to all medium components, such as the cell volume or the bulk velocity of the material in the cell. Other variables are specific to each medium component, such as the density (present for all components) or the gas temperature (optional). Depending on its needs, a MaterialMix subclass can also request additional, custom variables to be stored in the medium state for the component(s) it is associated with.
In a first simulation phase, SKIRT determines the radiation field (RF) based on just the primary emission. In a second phase, it performs secondary emission from the media using spectra calculated based on this RF.
Some SKIRT media allow the density or other properties stored in the medium state to depend on the local RF. These changes to the medium properties may sufficiently affect the RF to again cause a significant change in the medium properties, so that the RF must be calculated self-consistently by iterating over primary and/or secondary emission. We call this a dynamic medium state (DMS).
If the changes to the medium state significantly affect the medium opacity in the wavelength range of primary sources, iteration over primary emission is required. We call this a primary-dynamic medium state (PDMS). Radiative dust destruction is an example of a PDMS process.
Alternatively, the media properties depending on the RF may be significant only for determining the secondary emission spectrum without a noticable effect during primary emission. As a result, there is no need for iteration over primary emission. We call this a secondary-dynamic medium state (SDMS). The hydrogen spin-flip transition is an example of an SDMS process because the opacity change at 21 cm does not affect primary emission which occurs at much shorter wavelengths. In this specific example, there is actually no need for iteration over the secondary emission either, but this might be different for other processes.
Similarly, secondary emission may sufficiently affect the RF to cause a significant change in the secondary emission spectrum (which is calculated from that RF). If this is the case, the RF must be calculated self-consistently by iterating over the secondary emission. We call this dynamic secondary emission (DSE). Dust emission in high-optical depth regions is an example of a DSE process. The dust population may absorb a non-neglible portion of its own thermal emission, affecting its internal energy state, which in turn affects the thermal emission spectrum.
SKIRT allows the algorithms or prescriptions for updating the medium state to reside in three regions of the code, depending on the characteristics of each specific process.
A soon as a panchromatic simulation includes a medium (other than Lyman-alpha), the configuration allows to enable self-consistent iterations over primary emission. Similarly, as soon as a simulation includes secondary emission, the configuration allows to enable self-consistent iterations over secondary emission. In that case, one can opt to also iterate over primary emission in various combinations. See the MonteCarloSimulation class documentation for more details.
We consider three examples that correspond to the three styles of DMS update algorithms discussed in the previous section.
Some astrophysical systems contain a body of dust with a high optical depth even at longer wavelengths. Examples include circumnuclear disks of active galactic nuclei, planetary disks, and compact galaxies at higher redshifts. In those systems, the dust population may absorb a non-neglible portion of its own thermal emission, affecting its internal energy state, in turn affecting the thermal emission spectrum. Modelling this process requires iterations to self-consistently calculate these interdependent quantities.
This iterative approach can be easily enabled for any SKIRT model that includes a dust medium and thermal dust emission in addition to primary sources. After the iterateSecondaryEmission property of the MonteCarloSimulation class has been set to true, the properties offered by the DustEmissionOptions and IterationOptions classes (both part of the MediumSystem) further control the iteration process. Most importantly, the DustEmissionOptions set the convergence criteria that determine when the result is sufficiently accurate and the iteration cycle can be terminated. The first criterion specifies that convergence is reached when the total absorbed dust luminosity is less than a given fraction of the total absorbed primary luminosity. This is to avoid time-consuming iterations in case the global thermal emission is too small to have a significant effect on the dust temperature, compared to the effect of primary emission. The second criterion specifies that convergence is reached when the total absorbed dust luminosity has changed by less than a given fraction compared to the previous iteration. This is the actual iterative convergence criterion. Furthermore, the IterationOptions set the minimum and maximum number of iterations as a safety net.
As mentioned earlier, the calculation of the dust grain temperature probability distribution and resulting emission spectrum is performed on the fly while launching photon packets in the DustSecondarySource class. This class indirectly calls on the EquilibriumDustEmissionCalculator or the StochasticDustEmissionCalculator depending on the value of the dustEmissionType property in the DustEmissionOptions.
Electronic and rovibrational transitions in atoms and molecules often cause both radiative emission and absorption with a similar line profile. Calculating energy level population densities that are self-consistent with the radiation field across a spatial domain requires an iterative approach.
The NonLTELineGasMix class allows performing such calculations with SKIRT for certain transitions in selected molecules and atoms. Specifically, it causes the medium state to store values representing the energy level population densities for each spatial cell, and it includes a procedure to update these values based on the currently established radiation field. Based on this information, the material mix calculates aborption cross sections and emission luminosities upon request.
Simulations that include the NonLTELineGasMix must also include one or more primary sources that trigger the molecular/atomic lines directly (e.g. the cosmic microwave background) or indirectly (e.g. by heating the dust and thus causing thermal dust emission). Because the secondary emission and the radiation field are calculated self-consistently, iterateSecondaryEmission in MonteCarloSimulation should be enabled. If the opacity of the medium at the line wavelengths significantly affects the radiation field caused by primary emission (as would be the case for the cosmic microwave background), then includePrimaryEmission in IterationOptions must be enabled as well. This causes so-called merged iterations, where each iteration step includes both primary and secondary emission. In any case, iteratePrimaryEmission can be left disabled unless such iteration is required for other reasons (for example, to self-consistently calculate radiative dust destruction, see below).
During each iteration, after the radiation field has been (re-)established, the NonLTELineGasMix is requested to update the medium state for each cell, and iteration continues until convergence is reached. The convergence criteria are configured through three properties of the NonLTELineGasMix class. The first two properties (maxChangeInLevelPopulations and maxFractionNotConvergedCells) configure a criterion based on statistics per spatial cell. The third property (maxChangeInGlobalLevelPopulations) configures a global criterion. For more information, see the NonLTELineGasMix documentation. Finally, the IterationOptions allow specifying the minimum and maximum number of iterations as a safety net.
Energetic radiation sources such as active galactic nuclei destroy dust grains in their immediate environment. The effect depends on the radiation spectrum and on grain properties such as size and chemical composition, and the source often is anisotropic. Rather than attempting to include all of these factors in an input model, a SKIRT simulation can self-consistently determine the resulting the density distribution for the various grain populations through an iterative process.
As an example, we consider an anisotropic point source embedded in a body of dust. We limit the simulation to primary emission in the UV and optical wavelength range, and use the DraineLiDustMix class to represent the dust grain mixture. As a first step towards self-consistent calculation of grain destruction near the source, we need to allow different grain types and sizes in the dust mixture to be handled separately. To this end, we insert a FragmentDustMixDecorator around the DraineLiDustMix. We set the fragmentSizeBins property to true, so that the decorated mixture is fragmented into individual grain size bins as configured in the DraineLiDustMix for each material type. We also set the hasDynamicDensities property to true, causing the medium state to store a seperate density fraction for each of these dust population fragments relative to the density distribution determined by the input model.
We set the iteratePrimaryEmission property of the MonteCarloSimulation class to true, and we use the properties offered by the DynamicStateOptions and IterationOptions classes to further control the iteration process. Most importantly, we include an instance of the LinearDustDestructionRecipe in the list of DynamicStateRecipe's managed by the DynamicStateOptions. The LinearDustDestructionRecipe class implements a basic dust destruction recipe that depends on the equilibrium temperature of the grain and on two cutoff temperatures specified by the user in the parameter file for each type of grain material (silicate or graphite). After each primary emission iteration, this recipe is applied for each spatial cell to each dust population fragment separately, calculating the equilibrium temperature based on the radiation field and the grain properties of each fragment. As a result, the dust destruction fractions and the radiation field across the spatial grid are updated iteratively until convergence is reached.
The convergence criterion is configured by a combination of the maximum change on the dynamic density fraction in a spatial cell (densityFractionTolerance property of LinearDustDestructionRecipe inherited from DustDestructionRecipe) and the number of cells allowed to exceed this maximum change (maxNotConvergedCells property of LinearDustDestructionRecipe inherited from DynamicStateRecipe). Finally, the IterationOptions set the minimum and maximum number of iterations as a safety net.