Three-dimensional numerical cosmological radiative transfer in an inhomogeneous medium

A numerical scheme is proposed for the solution of the three-dimensional (3D) radiative transfer equation with variable optical depth. We show that time-dependent ray tracing is an attractive choice for simulations of astrophysical ionization fronts, particularly when one is interested in covering a wide range of optical depths within a three-dimensional clumpy medium. Our approach combines the explicit advection of radiation variables with the implicit solution of local rate equations given the radiation field at each point. Our scheme is well suited to the solution of problems for which line transfer is not important, and could, in principle, be extended to those situations also. This scheme allows us to calculate the propagation of supersonic ionization fronts into an inhomogeneous medium. The approach can be easily implemented on a single workstation and should also be fully parallelizable.     

A new moment method for continuum radiative transfer in cosmological re-ionization

We introduce a new code for computing time-dependent continuum radiative transfer and non-equilibrium ionization states in static density fields with periodic boundaries. Our code solves the moments of the radiative transfer equation, closed by an Eddington tensor computed using a long characteristics (LC) method. We show that traditional short characteristics and the optically thin approximation are inappropriate for computing Eddington factors for the problem of cosmological re-ionization. We evolve the non-equilibrium ionization field via an efficient and accurate (errors <1 per cent) technique that switches between fully implicit or explicit finite differencing depending on whether the local time-scales are long or short compared to the time-step. We tailor our code for the problem of cosmological re-ionization. In tests, the code conserves photons, accurately treats cosmological effects and reproduces analytic Strömgren sphere solutions. Its chief weakness is that the computation time for the LC calculation scales relatively poorly compared to other techniques  ( t _LC∝ N ^∼1.5_cells)  ; however, we mitigate this by only recomputing the Eddington tensor when the radiation field changes substantially. Our technique makes almost no physical approximations, so it provides a way to benchmark faster but more approximate techniques. It can readily be extended to evolve multiple frequencies, though we do not do so here. Finally, we note that our method is generally applicable to any problem involving the transfer of continuum radiation through a periodic volume.     

Hyperbolic character of the angular moment equations of radiative transfer and numerical methods

We study the mathematical character of the angular moment equations of radiative transfer in spherical symmetry and conclude that the system is hyperbolic for general forms of the closure relation found in the literature. Hyperbolicity and causality preservation lead to mathematical conditions allowing us to establish a useful characterization of the closure relations. We apply numerical methods specifically designed to solve hyperbolic systems of conservation laws (the so-called Godunov-type methods) to calculate numerical solutions of the radiation transport equations in a static background. The feasibility of the method in all regimes, from diffusion to free-streaming, is demonstrated by a number of numerical tests, and the effect of the choice of the closure relation on the results is discussed.     

Multidimensional simulations of radiative transfer in Type Ia supernovae

A three-dimensional Monte Carlo code for modelling radiation transport in Type Ia supernovae is described. In addition to tracking Monte Carlo quanta to follow the emission, scattering and deposition of radiative energy, a scheme involving volume-based Monte Carlo estimators is used to allow properties of the emergent radiation field to be extracted for specific viewing angles in a multidimensional structure. This eliminates the need to compute spectra or light curves by angular binning of emergent quanta. The code is applied to two test problems to illustrate consequences of multidimensional structure on the modelling of light curves. First, elliptical models are used to quantify how large-scale asphericity can introduce angular dependence to light curves. Secondly, a model which incorporates complex structural inhomogeneity, as predicted by modern explosion models, is used to investigate how such structure may affect light-curve properties.     

An MHD gadget for cosmological simulations

Various radio observations have shown that the hot atmospheres of galaxy clusters are magnetized. However, our understanding of the origin of these magnetic fields, their implications on structure formation and their interplay with the dynamics of the cluster atmosphere, especially in the centres of galaxy clusters, is still very limited. In preparation for the upcoming new generation of radio telescopes (like Expanded Very Large Array, Low Wavelength Array, Low Frequency Array and Square Kilometer Array), a huge effort is being made to learn more about cosmological magnetic fields from the observational perspective. Here we present the implementation of magnetohydrodynamics (MHD) in the cosmological smoothed particle hydrodynamics (SPH) code gadget . We discuss the details of the implementation and various schemes to suppress numerical instabilities as well as regularization schemes, in the context of cosmological simulations. The performance of the SPH–MHD code is demonstrated in various one- and two-dimensional test problems, which we performed with a fully, three-dimensional set-up to test the code under realistic circumstances. Comparing solutions obtained using athena , we find excellent agreement with our SPH–MHD implementation. Finally, we apply our SPH–MHD implementation to galaxy cluster formation within a large, cosmological box. Performing a resolution study we demonstrate the robustness of the predicted shape of the magnetic field profiles in galaxy clusters, which is in good agreement with previous studies.     

Lyman α radiative transfer in a multiphase medium

Hydrogen Lyman α (Lyα) is our primary emission-line window into high-redshift galaxies. Despite an extensive literature, Lyα radiative transfer in the most realistic case of a dusty, multiphase medium has received surprisingly little detailed theoretical attention. We investigate Lyα resonant scattering through an ensemble of dusty, moving, optically thick gas clumps. We treat each clump as a scattering particle and use Monte Carlo simulations of surface scattering to quantify continuum and Lyα surface scattering angles, absorption probabilities, and frequency redistribution, as a function of the gas dust content. This atomistic approach speeds up the simulations by many orders of magnitude, making possible calculations which are otherwise intractable. Our fitting formulae can be readily adapted for fast radiative transfer in numerical simulations. With these surface scattering results, we develop an analytic framework for estimating escape fractions and line widths as a function of gas geometry, motion, and dust content. Our simple analytic model shows good agreement with full Monte Carlo simulations. We show that the key geometric parameter is the average number of surface scatters for escape in the absence of absorption,     , and we provide fitting formulae for several geometries of astrophysical interest. We consider the following two interesting applications. (i) Equivalent widths ( EWs ). Lyα can preferentially escape from a dusty multiphase interstellar medium if most of the dust lies in cold neutral clouds, which Lyα photons cannot penetrate. This might explain the anomalously high EWs sometimes seen in high-redshift/submillimetre sources. (ii) Multiphase galactic outflows . We show the characteristic profile is asymmetric with a broad red tail, and relate the profile features to the outflow speed and gas geometry. Many future applications are envisaged.     

A new exact method for line radiative transfer

We present a new method, the coupled escape probability (CEP), for exact calculation of line emission from multi-level systems, solving only algebraic equations for the level populations. The CEP formulation of the classical two-level problem is a set of linear equations , and we uncover an exact analytic expression for the emission from two-level optically thick sources that holds as long as they are in the 'effectively thin' regime. In a comparative study of a number of standard problems, the CEP method outperformed the leading line transfer methods by substantial margins.
The algebraic equations employed by our new method are already incorporated in numerous codes based on the escape probability approximation. All that is required for an exact solution with these existing codes is to augment the expression for the escape probability with simple zone-coupling terms. As an application, we find that standard escape probability calculations generally produce the correct cooling emission by the C  ii 158-μm line but not by the ³P lines of O  i .     

Introducing a hybrid radiative transfer method for smoothed particle hydrodynamics

A new means of incorporating radiative transfer into smoothed particle hydrodynamics (SPH) is introduced, which builds on the success of two previous methods – the polytropic cooling approximation as devised by Stamatellos et al. and flux-limited diffusion. This hybrid method preserves the strengths of its individual components, while removing the need for atmosphere matching or other boundary conditions to marry optically thick and optically thin regions. The code uses a non-trivial equation of state to calculate temperatures and opacities of SPH particles, which captures the effects of H₂ dissociation, H⁰ ionization, He⁰ and He⁺ ionization, ice evaporation, dust sublimation, molecular absorption, bound-free and free–free transitions and electron scattering. The method is tested in several scenarios, including (i) the evolution of a  0.07 M_⊙  protoplanetary disc surrounding a  0.5 M_⊙  star; (ii) the collapse of a  1 M_⊙  protostellar cloud and (iii) the thermal relaxation of temperature fluctuations in a static homogeneous sphere.     

Radiative transfer in disc galaxies – I. A comparison of four methods to solve the transfer equation in plane-parallel geometry

Accurate photometric and kinematic modelling of disc galaxies requires the inclusion of radiative transfer models. Because of the complexity of the radiative transfer equation (RTE), sophisticated techniques are required. Various techniques have been employed for the attenuation in disc galaxies, but a quantitative comparison of them is difficult, because of the differing assumptions, approximations and accuracy requirements that are adopted in the literature. In this paper, we present an unbiased comparison of four methods to solve the RTE, in terms of accuracy, efficiency and flexibility. We apply them all to one problem that can serve as a first approximation of large portions of disc galaxies: a one-dimensional plane-parallel geometry, with both absorption and multiple scattering taken into account, with arbitrary vertical distributions of stars and dust and an arbitrary angular redistribution of the scattering. We find that the spherical harmonics method is by far the most efficient way to solve the RTE, whereas both Monte Carlo simulations and the iteration method, which are straightforward to extend to more complex geometries, have a cost that is about 170 times larger.