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Register a new userDiscrete implicit Monte-Carlo (DIMC) scheme for simulating radiative transfer problems
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We present a new algorithm for radiative transfer, based on a statistical Monte-Carlo approach, that does not suffer from teleportation effects on the one hand, and yields smooth results on the other hand. Implicit-Monte-Carlo (IMC) techniques for modeling radiative transfer exist from the 70s. However, in optically thick problems, the basic algorithm suffers from `teleportation errors, where the photons propagate faster than the exact physical behavior, due to the absorption-black body emission processes. One possible solution is to use semi-analog Monte-Carlo, in its new implicit form (ISMC), that uses two kinds of particles, photons and discrete material particles. This algorithm yields excellent teleportation-free results, however, it also results with nosier solutions (relative to classic IMC) due to its discrete nature. Here, we derive a new Monte-Carlo algorithm, Discrete implicit Monte-Carlo (DIMC) that uses the idea of the two-kind discrete particles and thus, does not suffer from teleportation errors. DIMC implements the IMC discretization and creates new radiation photons each time step, unlike ISMC. This yields smooth results as classic IMC, due to the continuous absorption technique. One of the main parts of the algorithm is the avoidance of population explosion of particles, using particle merging. We test the new algorithm in both one and two-dimensional cylindrical problems, and show that it yields smooth, teleportation-free results. We finish in demonstrating the power of the new algorithm in a classic radiative hydrodynamic problem, an opaque radiative shock wave. This demonstrates the power of the new algorithm in astrophysical scenarios.
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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-quality 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.
We study the multi-dimensional radiative transfer phenomena using the ISMC scheme, in both gray and multi-frequency problems. Implicit Monte-Carlo (IMC) schemes have been in use for five decades. The basic algorithm yields teleportation errors, where photons propagate faster than the correct heat front velocity. Recently [Poette and Valentin, J. Comp. Phys., 412, 109405 (2020)], a new implicit scheme based on the semi-analog scheme was presented and tested in several one-dimensional gray problems. In this scheme, the material energy of the cell is carried by material-particles, and the photons are produced only from existing material particles. As a result, the teleportation errors vanish, due to the infinite discrete spatial accuracy of the scheme. We examine the validity of the new scheme in two-dimensional problems, both in Cartesian and Cylindrical geometries. Additionally, we introduce an expansion of the new scheme for multi-frequency problems. We show that the ISMC scheme presents excellent results without teleportation errors in a large number of benchmarks, especially against the slow classic IMC convergence.
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 power 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.
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 construction 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.
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