322 research outputs found
The Failure of Monte Carlo Radiative Transfer at Medium to High Optical Depths
Computer simulations of photon transport through an absorbing and/or
scattering medium form an important research tool in astrophysics. Nearly all
software codes performing such simulations for three-dimensional geometries
employ the Monte Carlo radiative transfer method, including various forms of
biasing to accelerate the calculations. Because of the probabilistic nature of
the Monte Carlo technique, the outputs are inherently noisy, but it is often
assumed that the average values provide the physically correct result. We show
that this assumption is not always justified. Specifically, we study the
intensity of radiation penetrating an infinite, uniform slab of material that
absorbs and scatters the radiation with equal probability. The basic Monte
Carlo radiative transfer method, without any biasing mechanisms, starts to
break down for transverse optical depths above ~20 because so few of the
simulated photon packets reach the other side of the slab. When including
biasing techniques such as absorption/scattering splitting and path length
stretching, the simulated photon packets do reach the other side of the slab
but the biased weights do not necessarily add up to the correct solution. While
the noise levels seem to be acceptable, the average values sometimes severely
underestimate the correct solution. Detecting these anomalies requires the
judicious application of statistical tests, similar to those used in the field
of nuclear particle transport, possibly in combination with convergence tests
employing consecutively larger numbers of photon packets. In any case, for
transverse optical depths above ~75 the Monte Carlo methods used in our study
fail to solve the one-dimensional slab problem, implying the need for
approximations such as a modified random walk.Comment: Accepted for publication in the ApJ; 13 pages, 6 figure
SKIRT: the design of a suite of input models for Monte Carlo radiative transfer simulations
The Monte Carlo method is the most popular technique to perform radiative
transfer simulations in a general 3D geometry. The algorithms behind and
acceleration techniques for Monte Carlo radiative transfer are discussed
extensively in the literature, and many different Monte Carlo codes are
publicly available. On the contrary, the design of a suite of components that
can be used for the distribution of sources and sinks in radiative transfer
codes has received very little attention. The availability of such models, with
different degrees of complexity, has many benefits. For example, they can serve
as toy models to test new physical ingredients, or as parameterised models for
inverse radiative transfer fitting. For 3D Monte Carlo codes, this requires
algorithms to efficiently generate random positions from 3D density
distributions. We describe the design of a flexible suite of components for the
Monte Carlo radiative transfer code SKIRT. The design is based on a combination
of basic building blocks (which can be either analytical toy models or
numerical models defined on grids or a set of particles) and the extensive use
of decorators that combine and alter these building blocks to more complex
structures. For a number of decorators, e.g. those that add spiral structure or
clumpiness, we provide a detailed description of the algorithms that can be
used to generate random positions. Advantages of this decorator-based design
include code transparency, the avoidance of code duplication, and an increase
in code maintainability. Moreover, since decorators can be chained without
problems, very complex models can easily be constructed out of simple building
blocks. Finally, based on a number of test simulations, we demonstrate that our
design using customised random position generators is superior to a simpler
design based on a generic black-box random position generator.Comment: 15 pages, 4 figures, accepted for publication in Astronomy and
Computin
Using 3D Voronoi grids in radiative transfer simulations
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. Such an unstructured grid poses new challenges in laying down the rays
(straight paths) needed in RT codes. We show that it is straightforward to
implement accurate and efficient RT on 3D Voronoi grids. 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 such a 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. 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. We conclude that the benefits of using a
Voronoi grid in RT simulation codes will often outweigh the somewhat slower
performance.Comment: 9 pages, 7 figures, accepted by A
Optical depth in polarised Monte Carlo radiative transfer
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 dichroic extinction into account.
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 tens of 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
Analytical expressions and numerical evaluation of the luminosity distance in a flat cosmology
Accurate and efficient methods to evaluate cosmological distances are an
important tool in modern precision cosmology. In a flat CDM cosmology,
the luminosity distance can be expressed in terms of elliptic integrals. We
derive an alternative and simple expression for the luminosity distance in a
flat CDM based on hypergeometric functions. Using a timing experiment
we compare the computation time for the numerical evaluation of the various
exact formulae, as well as for two approximate fitting formulae available in
the literature. We find that our novel expression is the most efficient exact
expression in the redshift range . Ideally, it can be combined with
the expression based on Carlson's elliptic integrals in the range
for high precision cosmology distance calculations over the entire redshift
range. On the other hand, for practical work where relative errors of about
0.1% are acceptable, the analytical approximation proposed by Adachi & Kasai
(2012) is a suitable alternative.Comment: 4 pages, 1 figure, accepted for publication in MNRA
FitSKIRT: genetic algorithms to automatically fit dusty galaxies with a Monte Carlo radiative transfer code
We present FitSKIRT, a method to efficiently fit radiative transfer models to
UV/optical images of dusty galaxies. These images have the advantage that they
have better spatial resolution compared to FIR/submm data. FitSKIRT uses the
GAlib genetic algorithm library to optimize the output of the SKIRT Monte Carlo
radiative transfer code. Genetic algorithms prove to be a valuable tool in
handling the multi- dimensional search space as well as the noise induced by
the random nature of the Monte Carlo radiative transfer code. FitSKIRT is
tested on artificial images of a simulated edge-on spiral galaxy, where we
gradually increase the number of fitted parameters. We find that we can recover
all model parameters, even if all 11 model parameters are left unconstrained.
Finally, we apply the FitSKIRT code to a V-band image of the edge-on spiral
galaxy NGC4013. This galaxy has been modeled previously by other authors using
different combinations of radiative transfer codes and optimization methods.
Given the different models and techniques and the complexity and degeneracies
in the parameter space, we find reasonable agreement between the different
models. We conclude that the FitSKIRT method allows comparison between
different models and geometries in a quantitative manner and minimizes the need
of human intervention and biasing. The high level of automation makes it an
ideal tool to use on larger sets of observed data.Comment: 14 pages, 10 figures; accepted for publication in Astronomy and
Astrophysic
Polarization in Monte Carlo radiative transfer and dust scattering polarization signatures of spiral galaxies
Polarization is an important tool to further the understanding of interstellar dust and the sources behind it. In this paper we describe our implementation of polarization that is due to scattering of light by spherical grains and electrons in the dust Monte Carlo radiative transfer code SKIRT. In contrast to the implementations of other Monte Carlo radiative transfer codes, ours uses co-moving reference frames that rely solely on the scattering processes. It fully supports the peel-off mechanism that is crucial for the efficient calculation of images in 3D Monte Carlo codes. We develop reproducible test cases that push the limits of our code. The results of our program are validated by comparison with analytically calculated solutions. Additionally, we compare results of our code to previously published results. We apply our method to models of dusty spiral galaxies at near-infrared and optical wavelengths. We calculate polarization degree maps and show them to contain signatures that trace characteristics of the dust arms independent of the inclination or rotation of the galaxy
SKIRT: hybrid parallelization of radiative transfer simulations
We describe the design, implementation and performance of the new hybrid
parallelization scheme in our Monte Carlo radiative transfer code SKIRT, which
has been used extensively for modeling the continuum radiation of dusty
astrophysical systems including late-type galaxies and dusty tori. The hybrid
scheme combines distributed memory parallelization, using the standard Message
Passing Interface (MPI) to communicate between processes, and shared memory
parallelization, providing multiple execution threads within each process to
avoid duplication of data structures. The synchronization between multiple
threads is accomplished through atomic operations without high-level locking
(also called lock-free programming). This improves the scaling behavior of the
code and substantially simplifies the implementation of the hybrid scheme. The
result is an extremely flexible solution that adjusts to the number of
available nodes, processors and memory, and consequently performs well on a
wide variety of computing architectures.Comment: 21 pages, 20 figure
The dynamical structure of broken power-law and double power-law models for dark matter haloes
Galaxy kinematics and gravitational lensing are two complementary ways to
constrain the distribution of dark matter on galaxy scales. The typical dark
matter density profiles adopted in dynamical studies cannot easily be adopted
in lensing studies. Ideally, a mass model should be used that has the global
characteristics of realistic dark matter distributions, and that allows for an
analytical calculation of the magnifications and deflection angles. A simple
model with these properties, the broken-power-law (BPL) model, has very
recently been introduced. We examine the dynamical structure of the family of
BPL models. We derive simple closed expressions for basic dynamical properties,
and study the distribution function under the assumption of velocity isotropy.
We find that none of the BPL models with realistic parameters has an isotropic
distribution function that is positive over the entire phase space, implying
that the BPL models cannot be supported by an isotropic velocity distribution,
or models with a more radially anisotropic orbital structure. This result
limits the attractiveness of the BPL family as a tool for lensing studies to
some degree. More generally, we find that not all members of the general family
of double power-law or Zhao models, often used to model dark matter haloes, can
be supported by an isotropic or radially anisotropic distribution function. In
other words, the distribution function may become negative even for spherically
symmetric models with a well-behaved density profile.Comment: 12 pages, 5 figures, accepted for publication in MNRA
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