We present an updated version of SKIRT, a 3D Monte Carlo radiative transfer code developed to simulate dusty galaxies. The main novel characteristics of the SKIRT code are the use of a stellar foam to generate random positions, an efficient combination of eternal forced scattering and continuous absorption, and a new library approach that links the radiative transfer code to the DustEM dust emission library. This approach enables a fast, accurate and self-consistent calculation of the dust emission of arbitrary mixtures of transiently heated dust grains and polycyclic aromatic hydrocarbons, even for full 3D models containing millions of dust cells. We have demonstrated the accuracy of the SKIRT code through a set of simulations based on the edge-on spiral galaxy UGC 4754. The models we ran were gradually refined from a smooth, 2D, LTE model to a fully 3D model that includes NLTE dust emission and a clumpy structure of the dusty ISM. We find that clumpy models absorb UV and optical radiation less efficiently than smooth models with the same amount of dust, and that the dust in clumpy models is on average both cooler and less luminous. Our simulations demonstrate that, given the appropriate use of optimization techniques, it is possible to efficiently and accurately run Monte Carlo radiative transfer simulations of arbitrary 3D structures of several million dust cells, including a full calculation of the NLTE emission by arbitrary dust mixtures.

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Context. A crucial ingredient for numerically solving the three-dimensional radiative transfer problem is the choice of the grid that discretizes the transfer medium. Many modern radiative transfer codes, whether using Monte Carlo or ray tracing techniques, are equipped with hierarchical octree-based grids to accommodate a wide dynamic range in densities. Aims. We critically investigate two different aspects of octree grids in the framework of Monte Carlo dust radiative transfer. Inspired by their common use in computer graphics applications, we test hierarchical k-d tree grids as an alternative for octree grids. On the other hand, we investigate which node subdivision-stopping criteria are optimal for constructing of hierarchical grids. Methods. We implemented a k-d tree grid in the 3D radiative transfer code SKIRT and compared it with the previously implemented octree grid. We also considered three different node subdivision-stopping criteria (based on mass, optical depth, and density gradient thresholds). Based on a small suite of test models, we compared the efficiency and accuracy of the different grids, according to various quality metrics. Results. For a given set of requirements, the k-d tree grids only require half the number of cells of the corresponding octree. Moreover, for the same number of grid cells, the k-d tree is characterized by higher discretization accuracy. Concerning the subdivision stopping criteria, we find that an optical depth criterion is not a useful alternative to the more standard mass threshold, since the resulting grids show a poor accuracy. Both criteria can be combined; however, in the optimal combination, for which we provide a simple approximate recipe, this can lead to a 20% reduction in the number of cells needed to reach a certain grid quality. An additional density gradient threshold criterion can be added that solves the problem of poorly resolving sharp edges and strong density gradients. Conclusions. We advocate the use of k-d trees and the proposed combination of criteria to set up hierarchical grids for 3D radiative transfer. These recipes are straightforward for implementing and should help to develop faster and more accurate 3D radiative transfer codes.

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. Probing the structure of complex astrophysical objects requires effective three-dimensional (3D) numerical simulation of the relevant radiative transfer (RT) processes. As with any numerical simulation code, the choice of an appropriate discretization is crucial. Adaptive grids with cuboidal cells such as octrees have proven very popular; however, several recently introduced hydrodynamical and RT codes are based on a Voronoi tessellation of the spatial domain. An unstructured grid of this nature poses new challenges in laying down the rays (straight paths) needed in RT codes. Aims. We show that it is straightforward to implement accurate and efficient RT on 3D Voronoi grids. Methods. We present a method for computing straight paths between two arbitrary points through a 3D Voronoi grid in the context of a RT code. We implement this grid in our RT code SKIRT, using the open source library Voro++ to obtain the relevant properties of the Voronoi grid cells based solely on the generating points. We compare the results obtained through the Voronoi grid with those generated by an octree grid for two synthetic models, and we perform the well-known Pascucci RT benchmark using the Voronoi grid. Results. The presented algorithm produces correct results for our test models. Shooting photon packages through the geometrically much more complex 3D Voronoi grid is only about three times slower than the equivalent process in an octree grid with the same number of cells, while in fact the total number of Voronoi grid cells may be lower for an equally good representation of the density field. Conclusions. The benefits of using a Voronoi grid in RT simulation codes will often outweigh the somewhat slower performance.