The theory of radiative transfer provides the link between the physical conditions in an astrophysical object and the observable radiation which it emits. Thus accurately modelling radiative transfer is often a necessary part of testing theoretical models by comparison with observations. We describe a new radiative transfer code which employs Monte Carlo methods for the numerical simulation of radiation transport in expanding media. We discuss the application of this code to the calculation of synthetic spectra and light curves for a Type Ia supernova explosion model and describe the sensitivity of the results to certain approximations made in the simulations.
The theory and numerical modelling of radiation processes and radiative transfer play a key role in astrophysics: they provide the link between the physical properties of an object and the radiation it emits. In the modern era of increasingly high-qu
ality observational data and sophisticated physical theories, development and exploitation of a variety of approaches to the modelling of radiative transfer is needed. In this article, we focus on one remarkably versatile approach: Monte Carlo Radiative Transfer (MCRT). We describe the principles behind this approach, and highlight the relative ease with which they can (and have) been implemented for application to a range of astrophysical problems. All MCRT methods have in common a need to consider the adverse consequences of Monte Carlo noise in simulation results. We overview a range of methods used to suppress this noise and comment on their relative merits for a variety of applications. We conclude with a brief review of specific applications for which MCRT methods are currently popular and comment on the prospects for future developments.
A crucial aspect of 3D Monte Carlo radiative transfer is the choice of the spatial grid used to partition the dusty medium. We critically investigate the use of octree grids in Monte Carlo dust radiative transfer, with two different octree constructi
on algorithms (regular and barycentric subdivision) and three different octree traversal algorithms (top-down, neighbour list, and the bookkeeping method). In general, regular octree grids need higher levels of subdivision compared to the barycentric grids for a fixed maximum cell mass threshold criterion. The total number of grid cells, however, depends on the geometry of the model. Surprisingly, regular octree grid simulations turn out to be 10 to 20% more efficient in run time than the barycentric grid simulations, even for those cases where the latter contain fewer grid cells than the former. Furthermore, we find that storing neighbour lists for each cell in an octree, ordered according to decreasing overlap area, is worth the additional memory and implementation overhead: using neighbour lists can cut down the grid traversal by 20% compared to the traditional top-down method. In conclusion, the combination of a regular node subdivision and the neighbour list method results in the most efficient octree structure for Monte Carlo radiative transfer simulations.
Context: The Monte Carlo method is the most widely used method to solve radiative transfer problems in astronomy, especially in a fully general 3D geometry. A crucial concept in any Monte Carlo radiative transfer code is the random generation of the
next interaction location. In polarised Monte Carlo radiative transfer with aligned non-spherical grains, the nature of dichroism complicates the concept of optical depth. Aims: We investigate in detail the relation between optical depth and the optical properties and density of the attenuating medium in polarised Monte Carlo radiative transfer codes that take into account dichroic extinction. Methods: Based on solutions for the radiative transfer equation, we discuss the optical depth scale in polarised radiative transfer with spheroidal grains. We compare the dichroic optical depth to the extinction and total optical depth scale. Results: In a dichroic medium, the optical depth is not equal to the usual extinction optical depth, nor to the total optical depth. For representative values of the optical properties of dust grains, the dichroic optical depth can differ from the extinction or total optical depth by several ten percent. A closed expression for the dichroic optical depth cannot be given, but it can be derived efficiently through an algorithm that is based on the analytical result corresponding to elongated grains with a uniform grain alignment. Conclusions: Optical depth is more complex in dichroic media than in systems without dichroic attenuation, and this complexity needs to be considered when generating random free path lengths in Monte Carlo radiative transfer simulations. There is no benefit in using approximations instead of the dichroic optical depth.
A three dimensional parallel Monte Carlo (MC) dust radiative transfer code is presented. To overcome the huge computing time requirements of MC treatments, the computational power of vectorized hardware is used, utilizing either multi-core computer p
ower or graphics processing units. The approach is a self-consistent way to solve the radiative transfer equation in arbitrary dust configurations. The code calculates the equilibrium temperatures of two populations of large grains and stochastic heated polycyclic aromatic hydrocarbons (PAH). Anisotropic scattering is treated applying the Heney-Greenstein phase function. The spectral energy distribution (SED) of the object is derived at low spatial resolution by a photon counting procedure and at high spatial resolution by a vectorized ray-tracer. The latter allows computation of high signal-to-noise images of the objects at any frequencies and arbitrary viewing angles. We test the robustness of our approach against other radiative transfer codes. The SED and dust temperatures of one and two dimensional benchmarks are reproduced at high precision. We utilize the Lucy-algorithm for the optical thin case where the Poisson noise is high, the iteration free Bjorkman & Wood method to reduce the calculation time, and the Fleck & Canfield diffusion approximation for extreme optical thick cells. The code is applied to model the appearance of active galactic nuclei (AGN) at optical and infrared wavelengths. The AGN torus is clumpy and includes fluffy composite grains of various sizes made-up of silicates and carbon. The dependence of the SED on the number of clumps in the torus and the viewing angle is studied. The appearance of the 10 micron silicate features in absorption or emission is discussed. The SED of the radio loud quasar 3C 249.1 is fit by the AGN model and a cirrus component to account for the far infrared emission.
We analyze the line radiative transfer in protoplanetary disks using several approximate methods and a well-tested Accelerated Monte Carlo code. A low-mass flaring disk model with uniform as well as stratified molecular abundances is adopted. Radiati
ve transfer in low and high rotational lines of CO, C18O, HCO+, DCO+, HCN, CS, and H2CO is simulated. The corresponding excitation temperatures, synthetic spectra, and channel maps are derived and compared to the results of the Monte Carlo calculations. A simple scheme that describes the conditions of the line excitation for a chosen molecular transition is elaborated. We find that the simple LTE approach can safely be applied for the low molecular transitions only, while it significantly overestimates the intensities of the upper lines. In contrast, the Full Escape Probability (FEP) approximation can safely be used for the upper transitions ($J_{rm up} ga 3$) but it is not appropriate for the lowest transitions because of the maser effect. In general, the molecular lines in protoplanetary disks are partly subthermally excited and require more sophisticated approximate line radiative transfer methods. We analyze a number of approximate methods, namely, LVG, VEP (Vertical Escape Probability) and VOR (Vertical One Ray) and discuss their algorithms in detail. In addition, two modifications to the canonical Monte Carlo algorithm that allow a significant speed up of the line radiative transfer modeling in rotating configurations by a factor of 10--50 are described.
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S. A. Sim
,M. Kromer
,F. K. Roepke
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(2009)
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"Monte Carlo Radiative Transfer Simulations: Applications to Astrophysical Outflows and Explosions"
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Stuart A. Sim
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