Table 2
Physical ingredients and approximations used in each code for the test models in this paper.
Code | RT method | Homologous expansion | γ-ray deposition | Non-thermal deposition | Excitation | Ionisation | Radiation field Jv | Line Opacity κv | Thermalisation parameter є |
---|---|---|---|---|---|---|---|---|---|
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
ARTIS | MC | Yes | MC | LTE(Tr) | approx. dn/dt = 0 | Scaled LTE(TR) | Sobolev | … | |
ARTIS nebular | MC | Yes | MC | Spencer-Fano | dn/dt = 0 | dn/dt = 0 | dJ/dt | Sobolev | … |
CMFGEN | RTE-CMF | Yes | MC | Spencer-Fano | dn/dt | dn/dt | dJ/dt | κv | … |
CRAB | RH-1G | No | Grey | Kozma/Fransson | LTE(Tr) | LTE(Tr) | dJ/dt | Expansion | 0.9 |
KEPLER | FLD | No | Grey | … | … | LTE(Te) | LTE(Te) | κ = const. | … |
SEDONA | MC | Yes | MC | … | LTE(Te) | LTE(Te) | dJ/dt | Expansion | 0.8 or 1.0 |
SUMO | MC | Yes | Grey | Spencer-Fano | dn/dt = 0 | dn/dt = 0 | dJ/dt = 0 | Sobolev | … |
STELLA | RH-MG | No | Grey | … | LTE(Te) | LTE(Te) | dJ/dt | Expansion | 0.9 |
SuperNu | MC | Yes | MC grey | … | LTE(Te) | LTE(Te) | dJ/dt | κv | 1.0 |
TARDIS | MC | Yes | … | … | scaled LTE(TR) | scaled LTE(TR) | Scaled LTE(TR) | Sobolev | … |
URΓLIGHT | MC | Yes | MC | … | LTE(Te) | LTE(Te) | dJ/dt | Expansion | 0.8 |
Notes. Column headings: (1) Code name. (2) Numerical method used to solve the radiative-transfer equation: FLD = Flux Limited Diffusion, MC=Monte Carlo, RH-1G = one-group (grey) radiation hydrodynamics, RH-MG = multi-group radiation hydrodynamics, RTE-CMF = Radiation Transfer Equation Co-Moving Frame. (3) The ejecta are assumed to be in homologous expansion (v = rt) in radiative-transfer codes. This is not the case for radiation-hydrodynamics codes (CRAB, KEPLER, STELLA). (4) Treatment of γ-ray energy deposition. (5) Non-thermal heating, excitation, and ionisation rates are calculated through a solution of the Spencer-Fano equation (Spencer & Fano 1954) or read in from tabulated values (Kozma & Fransson 1992). (6) Solution method for the atomic level populations. LTE(TX) refers to a solution of the Boltzmann excitation formula setting the temperature to that of the electrons (Te) or the radiation field (TR). An approximate non-LTE treatment of excitation scales the Boltzmann occupation numbers by the dilution factor W (cf. dilute-LTE treatment in TARDIS; Sect. 3.9). A non-LTE treatment requires the solution of the rate equations, either including time dependence (dn/dt) or assuming steady-state (statistical equilibrium, dn/dt = 0). (7) Treatment of ionisation. Here LTE(TX) refers to a solution of the Saha–Boltzmann equation, which can be scaled for an approximate non-LTE treatment (cf. nebular approximation in TARDIS; Sect. 3.9). The non-LTE solution results from the solution of the rate equations, either including time dependence (dn/dt) or assuming steady-state (dn/dt = 0). (8) The radiation field can be computed via a solution of the radiative-transfer equation (possibly assuming steady-state, dJ/dt = 0) or by following the propagation of photon packets in Monte Carlo codes. Alternatively, LTE treatments assume a Planckian radiation field (black body Bv) at a reference temperature TX, possibly scaled by the dilution factor W. (9) Treatment of line opacity. This can be explicitly line by line, taking into account overlap in the co-moving frame (κv), or with use of the Sobolev approximation. Other treatments involve the use of an approximate frequency-dependent ‘expansion’ opacity, or assuming a constant value (e.g. KEPLER; Sect. 3.4). (10) Global value of the thermalisation parameter є, which sets the probability that a photon absorbed in a given transition is re-emitted in a different transition (see e.g. URILIGHT; Sect. 3.10).
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