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Benchmark for Disk Configurations
We tested the behaviour of 5 different RT codes in a defined
2D configuration in order to provide benchmark solutions for the verification
of continuum RT codes. Three of the codes, namely
MC3D, MCTRANSF and
RADMC, uses the Monte Carlo (MC) method while the other two, namely
RADICAL and
STEINRAY, are grid-based codes. Both approaches have advantages and
drawbacks. MC methods allow to track in detail the propagation of photons
and thus treat complicated spatial distributions and arbitrary scattering
functions and polarizations. However, the error control is limited to integrated
quantities like flux conservation.Grid-based solvers provide error control
for each calculated intensity but stiff grids need to be applied to solve
complex three-dimensional structures.
Model Definition
To test the RT codes in 2D, we model a star embedded
in a circumstellar disk with an inner cavity free of dust. The
star is assumed to be point-like, at the center of the configuration
and emits like a black body at the temperature of the Sun. The
disk extends from 1 AU to 1000 AU and is made of spherical astronomical
silicates having a radius of 0.12 micron and a density of 3.6
g/cm3. The dust optical data
are taken from
Draine & Lee (1984) and are provided
here for the 61 wavelengths we use to solve the RT problem.
The disk is slightly flared with a
density structure is similar to that derived by
Chiang & Goldreich (1997). Symbols and values of the model
parameters are summarized in the following
Table. We perform calculations for four values of visual optical
depth going from 0.1 to 100. The optical depth is calculated along
the disk midplane from the inner to the outer disk radius. This
means that the optical depth we refer to is always the maximum
optical depth for each computation.
Results
We compare both Temperatures and Spectral Energy Distributions (SEDs) emerging
from the chosen models. We find that all the codes correctly reproduce
the shape of the temperature distribution and of the SEDs. Going from
optically thin to optically thick configurations makes the solution
of the RT problem more difficult. Thus, deviations of the codes are
slightly higher. However, differences in the temperature remain below
15% for all the proposed models and at all computed wavelengths. In
Fig. 1 we show a plot of the radial temperature near to the disk
midplane and percentage of difference among the codes for the most
optically thick model. We compare the SEDs for three disk inclinations:
near to face-on (12.5 o), at
42.5o and almost edge-on (77.5o).
The SEDs agree better than 7% in the most optically thin case. Differences
are smaller than 20% for all the other cases but for the most optically
thick model near to 10 micron both for MCTRANSF and for STEINRAY.
In
Fig. 2 we show the percentage of difference in the emerging SEDs.
Resulting temperatures and SEDs from all the codes are available here.
This page is maintained
by I. Pascucci
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