4,477 research outputs found
Benchmark problems for continuum radiative transfer. High optical depths, anisotropic scattering, and polarisation
Solving the continuum radiative transfer equation in high opacity media
requires sophisticated numerical tools. In order to test the reliability of
such tools, we present a benchmark of radiative transfer codes in a 2D disc
configuration. We test the accuracy of seven independently developed radiative
transfer codes by comparing the temperature structures, spectral energy
distributions, scattered light images, and linear polarisation maps that each
model predicts for a variety of disc opacities and viewing angles. The test
cases have been chosen to be numerically challenging, with midplane optical
depths up 10^6, a sharp density transition at the inner edge and complex
scattering matrices. We also review recent progress in the implementation of
the Monte Carlo method that allow an efficient solution to these kinds of
problems and discuss the advantages and limitations of Monte Carlo codes
compared to those of discrete ordinate codes. For each of the test cases, the
predicted results from the radiative transfer codes are within good agreement.
The results indicate that these codes can be confidently used to interpret
present and future observations of protoplanetary discs.Comment: 15 pages, 10 figures, accepted for publication in A&
Time Dependent Radiative Transfer Calculations for Supernovae
In previous papers we discussed results from fully time-dependent radiative
transfer models for core-collapse supernova (SN) ejecta, including the Type
II-peculiar SN 1987A, the more "generic" SN II-Plateau, and more recently Type
IIb/Ib/Ic SNe. Here we describe the modifications to our radiative modeling
code, CMFGEN, which allowed those studies to be undertaken. The changes allow
for time-dependent radiative transfer of SN ejecta in homologous expansion. In
the modeling we treat the entire SN ejecta, from the innermost layer that does
not fall back on the compact remnant out to the progenitor surface layers. From
our non-LTE time-dependent line-blanketed synthetic spectra, we compute the
bolometric and multi-band light curves: light curves and spectra are thus
calculated simultaneously using the same physical processes and numerics. These
upgrades, in conjunction with our previous modifications which allow the
solution of the time dependent rate equations, will improve the modeling of SN
spectra and light curves, and hence facilitate new insights into SN ejecta
properties, the SN progenitors and the explosion mechanism(s). CMFGEN can now
be applied to the modeling of all SN typesComment: 20 pages, 10 figures, to appear in MNRA
Molecular line radiative transfer in protoplanetary disks: Monte Carlo simulations versus approximate methods
We analyze the line radiative transfer in protoplanetary disks using several
approximate methods and a well-tested Accelerated Monte Carlo code. A low-mass
flaring disk model with uniform as well as stratified molecular abundances is
adopted. Radiative transfer in low and high rotational lines of CO, C18O, HCO+,
DCO+, HCN, CS, and H2CO is simulated. The corresponding excitation
temperatures, synthetic spectra, and channel maps are derived and compared to
the results of the Monte Carlo calculations. A simple scheme that describes the
conditions of the line excitation for a chosen molecular transition is
elaborated. We find that the simple LTE approach can safely be applied for the
low molecular transitions only, while it significantly overestimates the
intensities of the upper lines. In contrast, the Full Escape Probability (FEP)
approximation can safely be used for the upper transitions (J_{\rm up} \ga 3)
but it is not appropriate for the lowest transitions because of the maser
effect. In general, the molecular lines in protoplanetary disks are partly
subthermally excited and require more sophisticated approximate line radiative
transfer methods. We analyze a number of approximate methods, namely, LVG, VEP
(Vertical Escape Probability) and VOR (Vertical One Ray) and discuss their
algorithms in detail. In addition, two modifications to the canonical Monte
Carlo algorithm that allow a significant speed up of the line radiative
transfer modeling in rotating configurations by a factor of 10--50 are
described.Comment: 47 pages, 12 figures, accepted for publication in Ap
A High-Order Low-Order Algorithm with Exponentially-Convergent Monte Carlo for Thermal Radiative Transfer Problems
We have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer (TRT) problems. Within each discrete time step, fixed-point iterations are performed between a high-order (HO) exponentially-convergent Monte Carlo (ECMC) solver and a low-order (LO) system of equations. The LO system is based on spatial and angular moments of the transport equation and a linear-discontinuous finite-element (LDFE) spatial representation, producing equations similar to the standard S2 equations. The LO solver is fully implicit in time and efficiently converges the non-linear temperature dependence with Newton's method. The HO solver provides a globally accurate solution for the angular intensity to a fixed-source, pure absorber transport problem. This global solution is used to compute consistency terms in the LO equations that require the HO and LO solutions to converge towards the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the solution.
We investigated several extensions of this algorithm. A parametric closure of the LO system was used for the spatial variable, based on local relations computed with the HO solver. The spatial closure improves consistency between the two solvers compared to a standard LDFE spatial discretization of the LO system. The ECMC algorithm has been extended to integrate the angular intensity in time, with a consistent time closure of the LO radiation equations. The time closure increases accuracy in optically-thin problems compared to a backward Euler discretization. Finally, we have applied standard source iteration and Krylov procedures to iteratively solve the LO equations, with linear diffusion synthetic acceleration.
Herein, we present results for one-dimensional, gray test problems. Results demonstrate several desirable properties of this algorithm: the HOLO method preserves the equilibrium diffusion limit, prevents violation of the maximum principle, and can provide high-fidelity MC solutions to the TRT equations with minimal statistical noise. We have compared results with an implicit Monte Carlo (IMC) code and compared the efficiency of ECMC to standard Monte Carlo in this HOLO algorithm. Our HOLO algorithm is more accurate and more efficient than standard IMC. The extent to which this is so is problem-dependent
An efficient algorithm for two-dimensional radiative transfer in axisymmetric circumstellar envelopes and disks
We present an algorithm for two-dimensional radiative transfer in
axisymmetric, circumstellar media. The formal integration of the transfer
equation is performed by a generalization of the short characteristics (SC)
method to spherical coordinates. Accelerated Lambda Iteration (ALI) and Ng's
algorithm are used to converge towards a solution. By taking a logarithmically
spaced radial coordinate grid, the method has the natural capability of
treating problems that span several decades in radius, in the most extreme case
from the stellar radius up to parsec scale. Flux conservation is guaranteed in
spherical coordinates by a particular choice of discrete photon directions and
a special treatment of nearly-radially outward propagating radiation. The
algorithm works well from zero up to very high optical depth, and can be used
for a wide variety of transfer problems, including non-LTE line formation, dust
continuum transfer and high temperature processes such as compton scattering.
In this paper we focus on multiple scattering off dust grains and on non-LTE
transfer in molecular and atomic lines. Line transfer is treated according to
an ALI scheme for multi-level atoms/molecules, and includes both random and
systematic velocity fields. The algorithms are implemented in a multi-purpose
user-friendly radiative transfer program named RADICAL. We present two example
computations: one of dust scattering in the Egg Nebula, and one of non-LTE line
formation in rotational transitions of HCO in a flattened protostellar
collapsing cloud.Comment: 18 pages, 32 figure
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