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.     

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.     

An implementation of radiative transfer in the cosmological simulation code gadget

We present a novel numerical implementation of radiative transfer in the cosmological smoothed particle hydrodynamics (SPH) simulation code gadget . It is based on a fast, robust and photon-conserving integration scheme where the radiation transport problem is approximated in terms of moments of the transfer equation and by using a variable Eddington tensor as a closure relation, following the Optically Thin Variable Eddington Tensor suggestion of Gnedin & Abel. We derive a suitable anisotropic diffusion operator for use in the SPH discretization of the local photon transport, and we combine this with an implicit solver that guarantees robustness and photon conservation. This entails a matrix inversion problem of a huge, sparsely populated matrix that is distributed in memory in our parallel code. We solve this task iteratively with a conjugate gradient scheme. Finally, to model photon sink processes we consider ionization and recombination processes of hydrogen, which is represented with a chemical network that is evolved with an implicit time integration scheme. We present several tests of our implementation, including single and multiple sources in static uniform density fields with and without temperature evolution, shadowing by a dense clump and multiple sources in a static cosmological density field. All tests agree quite well with analytical computations or with predictions from other radiative transfer codes, except for shadowing. However, unlike most other radiative transfer codes presently in use for studying re-ionization, our new method can be used on-the-fly during dynamical cosmological simulation, allowing simultaneous treatments of galaxy formation and the re-ionization process of the Universe.     

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.     

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.     

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.     

An ISO survey of possible water and hydroxyl IRASER transitions towards the star-forming regions W49, W3(OH) and Sgr B2M

We report ISO LWS observations towards the star-forming regions W49N, W3(OH) and Sgr B2M in LWS04 mode (high-resolution Fabry–Perot scans). Possible far-infrared laser emission was detected in a water line at 133.55 μm towards W49N, but the spectral resolution was inadequate to establish firmly the nature of the emission. An additional water line was marginally detected in absorption at the 3 σ level, also towards W49N, at 169.74 μm. No OH lines were detected towards Sgr B2M or W3(OH) at either 134.83 or 135.95 μm, either in emission or in absorption.     

Modelling line profiles in infalling cores

Results are presented from a model of molecular line formation in collapsing star-forming cores. The study includes, for the first time, a self-consistent chemical and dynamical model which is then directly coupled to an appropriate radiative transfer model. The assumptions of chemical uniformity or simple monotonic variations within such cores are shown to be unacceptable. The results show that the abundance variations and the line profiles are highly sensitive to the assumed values of the free parameters in the chemical model. Extreme caution is therefore advised in the quantitative analysis of emission-line profiles from infall sources. The implied degeneracy can be overcome by multiple line-of-sight observations of many species and transitions.     

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.