An iterative technique for solving equations of statistical equilibrium

Superlevel partitioning is combined with a simple relaxation procedure to construct an iterative technique for solving equations of statistical equilibrium. In treating an N -level model atom, the technique avoids the N ³ scaling in computer time for direct solutions with standard linear equation routines and also does not fail at large N due to the accumulation of round-off errors. As a consequence, the technique allows detailed model atoms with N ≳10³ , such as those required for iron peak elements, to be incorporated into diagnostic codes for analysing astronomical spectra. Tests are reported for a 394-level Fe  ii ion and a 1266-level Ni  i – iv atom.     

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.     

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.     

Large-scale variability in the profiles of Hα and Hβ in the spectrum of the Herbig B8e star MWC 419 and a model interpretation of it

Spectroscopic data taken with a moderate resolution spectrograph in the region of the Hα and Hβ lines are presented for the Herbig B8e star MWC 419. The spectroscopic observations were accompanied by broad band BVR photometric measurements. The observations reveal a variability in the line profiles that is typical of Herbig Ae/Be stars with signs of a strong stellar wind. The greatest changes are observed in the region of the absorption components of the line profiles, which convert the profile from a type P CygII to P CygIII, as well as in the intensities of the central emission components. A model technique is used for quantitative interpretation of this variability and it shows that the P Cyg profile conversion of the absorption component can be explained in terms of a stellar wind model in which its distribution over latitude varies on a time scale of a few days. __________ Translated from Astrofizika, Vol. 50, No. 2, pp. 259–280 (May 2007).     

Recombination lines and free‐free continua formed in asymptotic ionized winds: Analytic solution for the radiative transfer

In dense hot star winds, the infrared and radio continua are dominated by free‐free opacity and recombination emission line spectra. In the case of a spherically symmetric outflow that is isothermal and expanding at constant radial speed, the radiative transfer for the continuum emission from a dense wind is analytic. Even the emission profile shape for a recombination line can be derived. Key to these derivations is that the opacity scales with only the square of the density. These results are well‐known. Here an extension of the derivation is developed that also allows for line blends and the inclusion of an additional power‐law dependence beyond just the density dependence. The additional power‐law is promoted as a representation of a radius dependent clumping factor. It is shown that differences in the line widths and equivalent widths of the emission lines depend on the steepness of the clumping power‐law. Assuming relative level populations in LTE in the upper levels of He II, an illustrative application of the model to Spitzer/IRS spectral data of the carbon‐rich star WR 90 is given (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Radiative transfer in disc galaxies – II. The influence of scattering and geometry on the attenuation curve

We investigate the influence of scattering and geometry on the attenuation curve in disc galaxies. We investigate both qualitatively and quantitatively which errors are made by either neglecting or approximating scattering, and which uncertainties are introduced as a result of a simplification of the star–dust geometry. We find that the magnitude of these errors depends on the inclination of the galaxy and, in particular, that, for face-on galaxies, the errors due to improper treatment of scattering dominate those due to imprecise star–dust geometry. Therefore we argue that, in all methods aimed at determining the opacity of disc galaxies, scattering should be taken into account in a proper way.