MAGRITTE: a new multidimensional accelerated general-purpose radiative transfer code

Magritte is a new deterministic radiative transfer code. It is a ray-tracing code that computes the radiation field by solving the radiative transfer equation along a fixed set of rays for each grid cell. Its ray-tracing algorithm is independent of the type of input grid and thus can handle smoothed-particle hydrodynamics (SPH) particles, structured as well as unstructured grids. The radiative transfer solver is highly parallelized and optimized to have well scaling performance on several computer architectures. Magritte also contains separate dedicated modules for chemistry and thermal balance. These enable it to self-consistently model the interdependence between the radiation field and the local thermal and chemical states. The source code for Magritte will be made publically available at github.com/Magritte-code

Radiative transfer as a Bayesian linear regression problem

Electromagnetic radiation plays a crucial role in various physical and chemical processes. Hence, almost all astrophysical simulations require some form of radiative transfer model. Despite many innovations in radiative transfer algorithms and their implementation, realistic radiative transfer models remain very computationally expensive, such that one often has to resort to approximate descriptions. The complexity of these models makes it difficult to assess the validity of any approximation and to quantify uncertainties on the model results. This impedes scientific rigour, in particular, when comparing models to observations, or when using their results as input for other models. We present a probabilistic numerical approach to address these issues by treating radiative transfer as a Bayesian linear regression problem. This allows us to model uncertainties on the input and output of the model with the variances of the associated probability distributions. Furthermore, this approach naturally allows us to create reduced-order radiative transfer models with a quantifiable accuracy. These are approximate solutions to exact radiative transfer models, in contrast to the exact solutions to approximate models that are often used. As a first demonstration, we derive a probabilistic version of the method of characteristics, a commonly-used technique to solve radiative transfer problems

MAGRITTE, a modern software library for 3D radiative transfer: I. Non-LTE atomic and molecular line modelling

Radiative transfer is a key component in almost all astrophysical and cosmological simulations. We present MAGRITTE: a modern open-source software library for 3D radiative transfer. It uses a deterministic ray-tracer and formal solver, i.e. it computes the radiation field by tracing rays through the model and solving the radiative transfer equation in its second-order form along a fixed set of rays originating from each point. MAGRITTE can handle structured and unstructured input meshes, as well as smoothed-particle hydrodynamics (SPH) particle data. In this first paper, we describe the numerical implementation, semi-analytic tests and cross-code benchmarks for the non-LTE line radiative transfer module of MAGRITTE. This module uses the radiative transfer solver to self-consistently determine the populations of the quantized energy levels of atoms and molecules using an accelerated Lambda iteration (ALI) scheme. We compare MAGRITTE with the established radiative transfer solvers RATRAN (1D) and LIME (3D) on the van Zadelhoff benchmark and present a first application to a simple Keplerian disc model. Comparing with LIME, we conclude that MAGRITTE produces more accurate and more precise results, especially at high optical depth, and that it is faster

SPH modelling of companion-perturbed AGB outflows including a new morphology classification scheme

CONTEXT: Asymptotic giant branch (AGB) stars are known to lose a significant amount of mass by a stellar wind, which controls the remainder of their stellar lifetime. High angular-resolution observations show that the winds of these cool stars typically exhibit mid- to small-scale density perturbations such as spirals and arcs, believed to be caused by the gravitational interaction with a (sub-)stellar companion. AIMS: We aim to explore the effects of the wind-companion interaction on the 3D density and velocity distribution of the wind, as a function of three key parameters: wind velocity, binary separation and companion mass. For the first time, we compare the impact on the outflow of a planetary companion to that of a stellar companion. We intend to devise a morphology classification scheme based on a singular parameter. METHODS: We ran a small grid of high-resolution polytropic models with the smoothed particle hydrodynamics (SPH) numerical code PHANTOM to examine the 3D density structure of the AGB outflow in the orbital and meridional plane and around the poles. By constructing a basic toy model of the gravitational acceleration due to the companion, we analysed the terminal velocity reached by the outflow in the simulations. RESULTS: We find that models with a stellar companion, large binary separation and high wind speed obtain a wind morphology in the orbital plane consisting of a single spiral structure, of which the two edges diverge due to a velocity dispersion caused by the gravitational slingshot mechanism. In the meridional plane the spiral manifests itself as concentric arcs, reaching all latitudes. When lowering the wind velocity and/or the binary separation, the morphology becomes more complex: in the orbital plane a double spiral arises, which is irregular for the closest systems, and the wind material gets focussed towards the orbital plane, with the formation of an equatorial density enhancement (EDE) as a consequence. Lowering the companion mass from a stellar to a planetary mass, reduces the formation of density perturbations significantly. CONCLUSIONS: With this grid of models we cover the prominent morphology changes in a companion-perturbed AGB outflow: slow winds with a close, massive binary companion show a more complex morphology. Additionally, we prove that massive planets are able to significantly impact the density structure of an AGB wind. We find that the interaction with a companion affects the terminal velocity of the wind, which can be explained by the gravitational slingshot mechanism. We distinguish between two types of wind focussing to the orbital plane resulting from distinct mechanisms: global flattening of the outflow as a result of the AGB star’s orbital motion and the formation of an EDE as a consequence of the companion’s gravitational pull. We investigate different morphology classification schemes and uncover that the ratio of the gravitational potential energy density of the companion to the kinetic energy density of the AGB outflow yields a robust classification parameter for the models presented in this paper

SPH modelling of wind-companion interactions in eccentric AGB binary systems

The late evolutionary stages of low- and intermediate-mass stars are characterised by mass loss through a dust-driven stellar wind. Recent observations reveal complex structures within these winds, that are believed to be formed primarily via interaction with a companion. How these complexities arise, and which structures are formed in which type of systems, is still poorly understood. Particularly, there is a lack of studies investigating the structure formation in eccentric systems. We aim to improve our understanding of the wind morphology of eccentric AGB binary systems by investigating the mechanism responsible for the different small-scale structures and global morphologies that arise in a polytropic wind with different velocities. Using the smoothed particle hydrodynamics (SPH) code Phantom, we generate nine different high-resolution, 3D simulations of an AGB star with a solar-mass companion with various wind velocity and eccentricity combinations. The models assume a polytropic gas, with no additional cooling. We conclude that for models with a high wind velocity, the short interaction with the companion results in a regular spiral morphology, that is flattened. In the case of a lower wind velocity, the stronger interaction results in the formation of a high-energy region and bow-shock structure that can shape the wind into an irregular morphology if instabilities arise. High-eccentricity models show a complex, phase-dependent interaction leading to wind structures that are irregular in three dimensions. However, the significant interaction with the companion compresses matter into an equatorial density enhancement, irrespective of eccentricity.Comment: 23 pages, 22 figure

MAGRITTE, a modern software library for 3D radiative transfer - II. Adaptive ray-tracing, mesh construction, and reduction

Radiative transfer is a notoriously difficult and computationally demanding problem. Yet, it is an indispensable ingredient in nearly all astrophysical and cosmological simulations. Choosing an appropriate discretization scheme is a crucial part of the simulation, since it not only determines the direct memory cost of the model but also largely determines the computational cost and the achievable accuracy. In this paper, we show how an appropriate choice of directional discretization scheme as well as spatial model mesh can help alleviate the computational cost, while largely retaining the accuracy. First, we discuss the adaptive ray-tracing scheme implemented in our 3D radiative transfer library MAGRITTE, that adapts the rays to the spatial mesh and uses a hierarchical directional discretization based on HEALPIX. Second, we demonstrate how the free and open-source software library GMSH can be used to generate high-quality meshes that can be easily tailored for MAGRITTE. In particular, we show how the local element size distribution of the mesh can be used to optimize the sampling of both analytically and numerically defined models. Furthermore, we show that when using the output of hydrodynamics simulations as input for a radiative transfer simulation, the number of elements in the input model can often be reduced by an order of magnitude, without significant loss of accuracy in the radiation field. We demonstrate this for two models based on a hierarchical octree mesh resulting from adaptive mesh refinement, as well as two models based on smoothed particle hydrodynamics data

Determining the effects of clumping and porosity on the chemistry in a non-uniform AGB outflow

(abridged) In the inner regions of AGB outflows, several molecules have been detected with abundances much higher than those predicted from thermodynamic equilibrium (TE) chemical models. The presence of the majority of these species can be explained by shock-induced non-TE chemical models, where shocks caused by the pulsating star take the chemistry out of TE in the inner region. Moreover, a non-uniform density structure has been detected in several AGB outflows. A detailed parameter study on the quantitative effects of a non-homogeneous outflow has so far not been performed. We implement a porosity formalism for treating the increased leakage of light associated with radiation transport through a clumpy, porous medium. The effects from the altered UV radiation field penetration on the chemistry, accounting also for the increased reaction rates of two-body processes in the overdense clumps, are examined. We present a parameter study of the effect of clumping and porosity on the chemistry throughout the outflow. Both the higher density within the clumps and the increased UV radiation field penetration have an important impact on the chemistry, as they both alter the chemical pathways. The increased amount of UV radiation in the inner region leads to photodissociation of parent species, releasing the otherwise deficient elements. We find an increased abundance in the inner region of all species not expected to be present assuming TE chemistry, such as HCN in O-rich outflows, H$_2$O in C-rich outflows, and NH$_3$ in both. Outflows whose clumps have a large overdensity and that are very porous to the interstellar UV radiation field yield abundances comparable to those observed in O- and C-rich outflows for most of the unexpected species investigated. The inner wind abundances of H$_2$O in C-rich outflows and of NH$_3$ in O- and C-rich outflows are however underpredicted.Comment: 33 pages, 20 figures, 15 tables, accepted for publication in Astronomy & Astrophysic