Abstract

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.

Highlights

  • 1.1 The role of radiative transfer in astrophysicsMuch of astrophysics is at a disadvantage compared to other fields of physics

  • Adopting the parameters suggested by Abdikamalov et al (2012) and listed in Appendix A.1, we perform a simple time-independent Monte Carlo radiative transfer (MCRT) simulation in spherical symmetry, injecting packets according to the local emissivity and following them until they either escape from the computational domain or are absorbed

  • We provide an overview of some of the MCRT techniques used in astrophysics

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Summary

The role of radiative transfer in astrophysics

Much of astrophysics is at a disadvantage compared to other fields of physics. While normally theories can be tested and phenomena studied by performing repeatable experiments in the controlled environment of a lab, astrophysics generally lacks this luxury. Instead of discretizing the RT equations, the underlying RT process is “simulated” by introducing a large number of “test particles” (later referred to as “packets” in this article) These test particles behave in a manner similar to their physical counterparts, namely real photons. The most severe disadvantage is a direct consequence of the probabilistic nature of MC techniques: inevitably, any physical quantity extracted from MC calculations will be subject to stochastic fluctuations This MC noise can be decreased by increasing the number of particles, which naturally requires more computational resources.

Scope of this review
Structure of this review
Radiative transfer background
Historical sketch of the Monte Carlo method
Monte Carlo basics
Random number generation
Random sampling
Sampling from an inverse transformation
Alternative sampling techniques
Monte Carlo quanta
Discretization into photon packets
Energy packets and indivisibility of packets
Initialisation of packets
Propagation of quanta
Basic propagation principle
Absorption as continuous weight degradation
Material properties and numerical discretization
Absorption and scattering
Propagation example
MCRT: time-dependent applications
Thermal and line emission in MCRT
Known emissivity
Radiative equilibrium in MCRT by iteration
Example: effective resonant scattering in a two-level atom
Fluorescence and thermal emissivity via redistribution parameters
Fluorescence and redistribution: macro atom method
Example and discussion: macro atom scheme for a three-level atom
The thermal energy pool
Indivisible energy packets beyond radiative equilibrium
MCRT: application in outflows and explosions
The mixed-frame approach
Line interactions in outflows
MCRT and expansion work
Extracting information from MCRT simulations
MC noise
Direct counting of packets
Volume-based estimators
Constructing volume-based estimators: radiation field quantities
Constructing volume-based estimators: extracting physical rates
Example: photoionization rate estimators
Volume-based estimators for energy and momentum flow
Biasing
Biased emission
Forced scattering
Peel-off
Further biasing techniques
Limitations—Russian Roulette and composite biasing
10 Implicit and diffusion Monte Carlo techniques
10.1 Implicit Monte Carlo
10.2 Efficient Monte Carlo techniques in optically thick media
10.2.1 Modified random walk
10.2.2 Discrete diffusion Monte Carlo
11 MCRT and dynamics
11.1 Reconstructing energy and momentum transfer terms
ΔV cΔt
11.2 Coupling to fluid dynamics
11.3 Example application
11.4 Challenges and limitations
12 Example astrophysical application
12.1 Type Ia supernovae
12.2 Model type Ia supernova
12.3 Spectral synthesis with MCRT
Findings
13 Summary and conclusions
Full Text
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