Issue |
A&A
Volume 509, January 2010
|
|
---|---|---|
Article Number | A36 | |
Number of page(s) | 15 | |
Section | Numerical methods and codes | |
DOI | https://doi.org/10.1051/0004-6361/200913064 | |
Published online | 14 January 2010 |
A 3D radiative transfer framework
VI. PHOENIX/3D example applications
P. H. Hauschildt1 - E. Baron1,2,3
1 - Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany
2 - Homer L. Dodge Dept. of Physics and Astronomy,
University of
Oklahoma, 440 W. Brooks, Rm 100, Norman, OK 73019, USA
3 - Computational Research Division, Lawrence Berkeley National
Laboratory, MS 50F-1650, 1 Cyclotron Rd, Berkeley, CA 94720-8139, USA
Received 5 August 2009 / Accepted 10 November 2009
Abstract
Aims. We demonstrate the application of our 3D
radiative transfer framework in the model atmosphere code PHOENIX
for a number of spectrum synthesis calculations for very different
conditions.
Methods. The 3DRT framework discussed in the
previous papers of this series was added to our general-purpose model
atmosphere code PHOENIX/1D and an extended 3D
version PHOENIX/3D was created. The PHOENIX/3D
code is parallelized via the MPI library using a hierarchical domain
decomposition and displays very good strong scaling.
Results. We present the results of several test
cases for widely different atmosphere conditions and compare the 3D
calculations with equivalent 1D models to assess the internal accuracy
of the 3D modeling. In addition, we show the results for a number of
parameterized 3D structures.
Conclusions. With presently available computational
resources it is possible to solve the full 3D radiative transfer
(including scattering) problem with the same micro-physics as included
in 1D modeling.
Key words: radiative transfer - methods: numerical - stars: atmospheres
1 Introduction
In a series of papers (Hauschildt & Baron 2009; Baron et al. 2009; Baron & Hauschildt 2007; Hauschildt & Baron 2006,2008, hereafter: Papers I-V), we have described a framework for the solution of the radiative transfer equation in 3D systems (3DRT), including a detailed treatment of scattering in continua and lines with a non-local operator splitting method. These papers deal solely with the radiation transport problem and its numerical solution for test cases designed to stress-test the algorithms and codes. It is important, however, to apply the radiative transfer codes to ``real'' problems, e.g., model atmosphere simulations and to compare the results to 1D equivalents. We have extended our general purpose model atmosphere code PHOENIX to use the 3DRT framework so that the new version of PHOENIX can calculate both 1D (PHOENIX/1D) and 3D (PHOENIX/3D) models and spectra. In this paper we will describe the implementation and the results of PHOENIX calculations comparing the results of 1D and 3D spectrum syntheses for different model parameters.
2 Method
In the following discussion we use notation of Papers I-V. The basic framework and the methods used for the formal solution and the solution of the scattering problem via non-local operator splitting are discussed in detail in these papers and will not be repeated here.
3 PHOENIX/3D implementation and micro-physics
We have implemented PHOENIX/3D to use as much as possible of the micro-physics of PHOENIX/1D. This applies to the ACES equation of state (Barman, in preparation), to the b-f and f-f opacities, to dust opacities, and to the line opacities (PHOENIX/3D is presently restricted to LTE population densities). This includes individual line profiles (Gauss profiles for weak lines and Voigt profiles for strong lines depending on user-selectable selection criteria) for atomic and molecular lines with the same physics that is implemented in PHOENIX/1D, so that the results of the opacity calculations are equal for the same physical conditions for the two modes of PHOENIX.
The important considerations of PHOENIX/3D
implementation are memory and CPU time
consumption. The memory requirements of PHOENIX/3D
compared to PHOENIX/1D are mostly due
the the much larger number of voxels in the 3D case (typically
106 voxels)
compared to the 1D case (usually 64-128 layers). As the memory
required to
store (and to compute) physical data such as the partial pressures of
close to
900 species or the opacities scales linearly with the number
of cells (or
layers in 1D), it is obvious that only very small tests can be run
without
using domain decomposition methods on large scale parallel
supercomputers. The
domain decomposition implementation of PHOENIX/3D
distributes the task of solving
(and storing) the equation of state data and the wavelength dependent
opacities
to sets of processes each with its private memory. This linearly (with
number
of processes used) reduces the amount of memory and time required for
these
tasks. For 1024 processes, this reduces the memory
requirements to just a few
MB per process to store the full equation of state results. The 3DRT
requires, in comparison, a total of about 450 MB for the same
problem (due to the storage
requirements of the non-local star-operator).
Including the storage required
for the computation of the line opacities, this is still just about
0.5GB/process, which is small compared to the typically available
4-16 GB/core
(CPU) on modern parallel supercomputers. In order to fully utilize the
available memory per core and to increase flexibility we have
implemented a
hierarchical scheme similar to the parallel PHOENIX/1D
implementation discussed in Hauschildt
et al. (1997) and in Baron
& Hauschildt (1998) and to the 3DRT parallelization
in Paper II: We use a number of ``clusters'' of processes where every
cluster works on a different wavelength. Each cluster internally uses
(on its subset of processes) the domain decomposition discussed above
and the 3DRT parallelizations discussed in Paper I. This
scheme can be adjusted to (a) fit the problem in the memory available
for each core and (b) to optimize overall performances (e.g., depending
on the number of solid angle points for the 3DRT solution or the
coordinate system
used). In the calculations presented here, we typically use clusters
with
256-1024 processes, the number of clusters is limited only by
the number
of available CPUs.
4 Results
We have calculated a number of test models to compare the results of PHOENIX/1D calculations with PHOENIX/3D results. This comparison can be used to adjust the parameters of the 3D calculations (number of voxels or solid angle points) to give an accuracy that is acceptable for a given investment in computer time. The models that we show here were taken from the latest PHOENIX/1D grid (in preparation) of model atmospheres. In all stellar models (1D and 3D) we have used the set of solar abundances given in Asplund et al. (2005).
![]() |
Figure 1:
Comparison between the PHOENIX/1D optical
spectrum and the flux vectors across the outermost voxels for the
PHOENIX/3D spectra computed for the M dwarf test
model (
|
Open with DEXTER |
![]() |
Figure 2:
Comparison between the PHOENIX/1D near infrared
spectrum and the flux vectors across the outermost voxels for the
PHOENIX/3D spectra computed for the M dwarf test
model (
|
Open with DEXTER |
![]() |
Figure 3:
Comparison between the PHOENIX/1D infrared
spectrum and the flux vectors across the outermost voxels for the
PHOENIX/3D spectra computed for the M dwarf test
model (
|
Open with DEXTER |
![]() |
Figure 4:
Comparison between the PHOENIX/1D near UV
spectrum and the flux vectors across the outermost voxels for the
PHOENIX/3D spectra computed for the G2V dwarf test model (
|
Open with DEXTER |
![]() |
Figure 5:
Comparison between the PHOENIX/1D optical
spectrum and the flux vectors across the outermost voxels for the
PHOENIX/3D spectra computed for the G2V dwarf test model (
|
Open with DEXTER |
![]() |
Figure 6:
Comparison between the PHOENIX/1D optical
spectrum and the flux vectors across the outermost voxels for the
PHOENIX/3D spectra computed for the A dwarf test
model (
|
Open with DEXTER |
![]() |
Figure 7:
Comparison between the PHOENIX/1D UV spectrum
and the flux vectors across the outermost voxels for the
PHOENIX/3D spectra computed for the A dwarf test model (
|
Open with DEXTER |
![]() |
Figure 8:
Comparison between the PHOENIX/1D optical
spectrum and the flux vectors across the outermost voxels for the
higher resolution PHOENIX/3D spectra computed
for the M dwarf test model (
|
Open with DEXTER |
![]() |
Figure 9:
Comparison between the PHOENIX/1D UV spectrum
and the flux vectors across the outermost voxels for the higher
resolution PHOENIX/3D spectra computed for the
G2V dwarf test model (
|
Open with DEXTER |
![]() |
Figure 10:
Comparison between the optical PHOENIX/1D
spectrum and the flux vectors across the outermost voxels for the
higher resolution PHOENIX/3D spectra computed
for the A dwarf test model (
|
Open with DEXTER |
Table 1: Strong scaling behavior of a M dwarf model test case for different configurations and total number of processors used. (See text for details).
4.1 Stellar models
We have computed synthetic spectra for stellar model atmospheres
with the parameters
(M dwarf),
(solar type star) and
(A star). The PHOENIX/1D models were computed
with the latest setup in the input physics,
including the ACES equation of state and the latest version of the
atomic and molecular line databases.
The model structures were then used as inputs to PHOENIX/3D
to calculate synthetic spectra with the same
sampling rates as the spectra from the PHOENIX/1D
calculations. In the PHOENIX/3D calculations we
have used a 3D spherical
coordinate system with
,
and
points
for a total of about 1M voxels. The calculations used
(if not specified otherwise) 642 solid angle
points. For each object we calculated synthetic spectra with PHOENIX/1D
and PHOENIX/3D and compare the fluxes of the
1D spectra to the flux vectors of the 3D results. As in
paper IV we can use the
components of the 3D flux vector in 3D spherical coordinates to
estimate the internal accuracy of
the solution (as the
and
components
are zero for spherically symmetric configurations). Figures 1 to 7 show selected
results for the different models. In these cases, the error due to the
number of solid angle points is about 3% and in all tests run
the differences
between the PHOENIX/1D fluxes and the
component of
the PHOENIX/3D calculation is of the same order.
The differences
between the 1D and 3D calculations are within the accuracy
set by the number of solid angles in the 3D model. In order to verify
that the errors get smaller with larger number of
solid angles (as shown in Paper IV for simple test
cases), we have run test models with 2562
angles. Three example plots are shown in Figs. 8 to 10 The results
show clearly that the higher solid angle resolution reduces the errors
in
and
considerably
and also improves the comparison for
to the 1D result,
as the higher internal accuracy due to more solid angle points
also increases the internal accuracy of
.
This also shows
that in 3D radiative transfer calculations the spatial resolution
is not the only factor governing the quality of the solution, the solid
angle resolution may in fact be more important, depending
on the coordinate system used and the details of the problem
that isve calculated a number of test models to compare the
results of PHOENIX/1D calculations with PHOENIX/3D
results. This comparison
can be used to adjust the parameters of the 3D calculations
(number
of voxels or solid angle points) to give an accuracy that is
acceptable for a given investment in computer time. The models
that we show here were taken from the latest PHOENIX/1D
grid (in preparation)
of model atmospheres. In all stellar models (1D and 3D) we have used
the set of solar abundances given in Asplund
et al. (2005).
We have calculated a number of test models to compare the
results of PHOENIX/1D calculations with PHOENIX/3D
results. This comparison
can be used to adjust the parameters of the 3D calculations (number
of voxels or solid angle points) to give an accuracy that is
acceptable for a given investment in computer time. The models
that we show here were taken from the latest PHOENIX/1D
grid (in preparation)
of model atmospheres. In all stellar models (1D and 3D) we have used
the set of solar abundances given in Asplund
et al. (2005).
4.2 Scaling
In order to investigate the strong scaling properties of PHOENIX/3D
we have constructed a small test case for a M dwarf model with
1000 wavelength points in a 3D spherical coordinate system
with ,
and
points for a total of about 1M voxels and 642
solid angle
points and ran the
calculations with different configurations of the domain decomposition
and
different total numbers of processes. The total workload remains
constant in these calculations, so this is a strong scaling test where
the workload
per CPU drops as the number of processes increase (in contrast
to a weak scaling test where the workload per process remains
constant). The results are given in Table 1. In this table, ``n(MPI)''
is the total number of MPI processes
used, ``cluster size'' is the number of processes that collaboratively
work on a single wavelength (spatial domain decomposition) and ``n(cluster)''
is the number of such clusters, each working on a different wavelength
(energy domain decomposition). The product ``cluster size''
``n(cluster)'' is always equal to ``n(MPI)''.
The column ``Comm'' gives the time spent in MPI communication to
collect the opacities from the different processes before the 3DRT
calculation starts. The communication requirements of the 3DRT
calculations are included in the 3DRT column. The columns ``line
opacity'' give the time in seconds and scaling efficiency for all line
opacity calculations, respectively, The columns ``total'' give the
total time and scaling efficiency, respectively, of the overall time
spent in the computation of the 3D spectrum, this time does
not include (small) contributions from the
EOS solution and the line selection procedures. In the largest cluster
size of 512 processes each process only works on 8 solid
angles, whereas in the
smallest cluster size (128) each process works on 32 solid
angles. The work
per solid angle is not perfectly constant and the amount of
communication
increases linearly as more processes collaborate, therefore, the
scaling
efficiency drops if more than about 512 processes are used for
this problem
size (i.e., number of solid angles). The scaling efficiency for the
overall
problem is quite good, the optimal value is about 98%. The drop-off for
cluster sizes of 512 (and more) is due to (a) the relatively small
number of solid angles
leading to very little work for each 3DRT process and relatively
more internal communication time in the 3DRT and (b) the small effect
of the communication related to the spatial domain decomposition.
We could not test setups with more than (the maximum available)
2048 processes; however, the test case should scale to
256 k processes (number of wavelength points times cluster
size), although for such a setup the overheads for, e.g., the solution
of the equation of state and the line selection would be very
noticeable.
![]() |
Figure 11:
Comparison between the flux vectors across the outermost voxels for the
PHOENIX/3D UV spectra computed for the 3D
hydro structure and the PHOENIX/1D spectrum for
the G2V dwarf test model (
|
Open with DEXTER |
![]() |
Figure 12:
Comparison between the flux vectors across the outermost voxels for the
PHOENIX/3D near UV spectra computed for the
3D hydro structure and the PHOENIX/1D spectrum
for the G2V
dwarf test model (
|
Open with DEXTER |
![]() |
Figure 13:
Comparison between the flux vectors across the outermost voxels for the
PHOENIX/3D UV spectra computed for the 3D
hydro structure and the PHOENIX/1D spectrum for
the G2V dwarf test model (
|
Open with DEXTER |
![]() |
Figure 14:
Comparison between the flux vectors across the outermost voxels for the
PHOENIX/3D optical spectra computed for the
3D hydro structure and the PHOENIX/1D spectrum
for the G2V
dwarf test model (
|
Open with DEXTER |
![]() |
Figure 15:
Illustration of horizontal energy flow for the outermost voxels of the
the 3D hydro structure for the red spectral range. The graphics shows
the flowlines of the x and y
components of the flux vector |
Open with DEXTER |
![]() |
Figure 16:
Illustration of horizontal energy flow for the outermost voxels of the
the 3D hydro structure for the red spectral range. The graphics shows
the flowlines of the x and y
components of the flux vector |
Open with DEXTER |
![]() |
Figure 17:
Illustration of horizontal energy flow for the outermost voxels of the
the 3D hydro structure for the red spectral range. The graphics shows
the flowlines of the x and y
components of the flux vector |
Open with DEXTER |
![]() |
Figure 18:
Illustration of horizontal energy flow for the outermost voxels of the
the 3D hydro structure for the red spectral range. The graphics shows
the flowlines of the x and y
components of the flux vector |
Open with DEXTER |
![]() |
Figure 19:
Illustration of horizontal energy flow for the outermost voxels of the
the 3D hydro structure for the red spectral range. The graphics shows
the flowlines of the x and y
components of the flux vector |
Open with DEXTER |
![]() |
Figure 20:
Illustration of horizontal energy flow for the outermost voxels of the
the 3D hydro structure for the red spectral range. The graphics shows
the flowlines of the x and y
components of the flux vector |
Open with DEXTER |
![]() |
Figure 21:
Illustration of horizontal energy flow for the outermost voxels of the
the 3D hydro structure for the red spectral range. The graphics shows
the flowlines of the x and y
components of the flux vector |
Open with DEXTER |
![]() |
Figure 22:
Illustration of horizontal energy flow for the outermost voxels of the
the 3D hydro structure for the red spectral range. The graphics shows
the flowlines of the x and y
components of the flux vector |
Open with DEXTER |
4.3 3D hydro model of solar convection
For a test with a computed 3D structure, we use the same example
snapshot
structure from Ludwig (Caffau et al. 2007;
Wedemeyer
et al. 2004) of a radiation-hydrodynamical
simulation of convection in the solar atmosphere as in
Paper III. The radiation transport calculations were performed
with a total of Cartesian
grid points in x, y, and z,
respectively, for a total of
3 002 031 voxels, the periodic boundary
conditions are set in the (horizontal) x,y
plane. The 3D radiative transport equation is solved for
and
solid angle points, so that a total of about
intensities are calculated for each 3DRT iteration and wavelength
point. For the tests described here, we are only using the
temperature-pressure structure of the hydro model and ignore the
velocity field.
![]() |
Figure 23:
Comparison between the PHOENIX/1D co-moving
frame UV spectrum (computed with 256 layers, * symbols) and
the co-moving frame flux vectors across the outermost voxels for the
PHOENIX/3D spectra computed for the Supernova test model. In
the PHOENIX/3D calculations we have used a
3D spherical coordinate system with |
Open with DEXTER |
We show example results in Figs. 11 to 14 in terms of
the x, y, and z
components of the flux vectors of each outer boundary voxel. The Fz
components are, in addition, compared to the 1D model for the G2V star
with the parameters
(*symbols in the figures). The general shape of the 3D spectra compare
well to
the 1D solar type model, of course there are large variations across
the horizontal
plane. In the UV the differences are largest, a number of voxel flux
vectors show
strong line emission, whereas the radiative+convective equilibrium 1D
model only
shows absorption features. This is to be expected as the 3D simulation
of
convection gives significant temperature variations across the volume
considered, in particular in the horizontal plane. These variations
have
considerable effect on the radiative transfer solution: The horizontal
components of the flux vectors of each voxel compared to the length of
the flux vector
,
Fx/F
and Fy/F,
show quite substantial variations for different wavelengths. The
variations are much larger for smaller wavelengths
(e.g., in the UV), due to the larger temperature dependence of the
source
functions for smaller wavelengths which translates to larger horizontal
flux components for small wavelengths compared to longer wavelengths.
The components of the flux vectors in the x-y plane can be larger than the z component, strongly dependent on the wavelength and on the location of the voxel. This is illustrated in Figs. 15-22, which show the flowlines of the x-y components of the flux vector at the surface. The flow distances are much larger at optical wavelengths than in the UV due to the larger UV opacities. The ``pattern'' of the horizontal energy flow depends strongly on the wavelength, it is also significantly different in the cores of strong lines compared to the surrounding continuum. The horizontal heat exchange could have in turn noticeable effects on the gas flow pattern.
4.4 Supernovae
The modeling of supernova spectra is a very important
application of PHOENIX/3D modeling as it is
expected, and explosion
models show, that supernova explosions are intrinsically 3D driven.
For the calculations shown here we use the Lagrangian frame 3DRT in
spherical 3D coordinates as discussed in paper V. The test
model is a simplified model for a type II supernova atmosphere
with a maximum expansion speed of about 0.13c. The
model is a simple uniform composition model with the
density parameterized as ,
and a ``photospheric
velocity'' of v0
= 7600 km s-1, and a model
temperature of
K.
These conditions correspond roughly to
those of SN 1999em seven days after explosion.
In Fig. 23
we show the CMF spectrum of the PHOENIX/3D run
compared to the corresponding PHOENIX/1D
synthetic spectrum. Due to computer
time limitations we could only run a relatively small 3D model
with
,
and
points
and 1282 solid angle points. The small angular
resolution
causes the scatter in the
plots and the errors in the
and
components. In general the agreement is acceptable for this test run,
for a full scale
3D SN spectrum the resolution in
should
be increased to (65,129) at least and the angular resolution
should be at least 5122 (which reduces the
bandwidth dramatically,
see Paper V).
5 Summary and conclusions
We have described first results we have obtained by incorporating the 3D radiative transfer framework we have discussed in Papers I-V into our general purpose model atmosphere package PHOENIX, thus allowing both 1D models (PHOENIX/1D) and 3D models (PHOENIX/3D) with the same micro-physics. We have verified and tested PHOENIX/3D by computing a number of test spectra for 1D conditions and comparing the results to the corresponding PHOENIX/1D calculations. The conditions range from M dwarfs, solar type stars to A stars and type II supernovae with relativistic expansions speeds. In addition, we have calculated spectra for a 3D hydrodynamical simulation of solar atmosphere convection. These tests demonstrate the it is now possible to calculate realistic spectra for 3D configurations including complex micro-physics. PHOENIX/3D can be used to calculate synthetic spectra for a number of complex 3D atmosphere model, including irradiated stars or planets, novae, and supernovae. We are currently working on extensions of the 3D radiative transfer framework to arbitrary velocity fields in the Euler (for low velocities, e.g., in convection simulations or planetary winds) and the Lagrangian (for Supernovae, accretion disks and matter flow in the vicinity of black holes) frames, which will extend the applications of PHOENIX/3D significantly.
AcknowledgementsThis work was supported in part by DFG GrK 1351 and SFB 676, as well as NSF grant AST-0707704, and US DOE GrantDE-FG02-07ER41517. The calculations presented here were performed at the Höchstleistungs Rechenzentrum Nord (HLRN); at the Hamburger Sternwarte IBM Regatta Systems, Apple G5, and Delta Opteron clusters financially supported by the DFG and the State of Hamburg; and at the National Energy Research Supercomputer Center (NERSC), which is supported by the Office of Science of the US Department of Energy under Contract No. DE-AC03-76SF00098. We thank all these institutions for a generous allocation of computer time.
References
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All Tables
Table 1: Strong scaling behavior of a M dwarf model test case for different configurations and total number of processors used. (See text for details).
All Figures
![]() |
Figure 1:
Comparison between the PHOENIX/1D optical
spectrum and the flux vectors across the outermost voxels for the
PHOENIX/3D spectra computed for the M dwarf test
model (
|
Open with DEXTER | |
In the text |
![]() |
Figure 2:
Comparison between the PHOENIX/1D near infrared
spectrum and the flux vectors across the outermost voxels for the
PHOENIX/3D spectra computed for the M dwarf test
model (
|
Open with DEXTER | |
In the text |
![]() |
Figure 3:
Comparison between the PHOENIX/1D infrared
spectrum and the flux vectors across the outermost voxels for the
PHOENIX/3D spectra computed for the M dwarf test
model (
|
Open with DEXTER | |
In the text |
![]() |
Figure 4:
Comparison between the PHOENIX/1D near UV
spectrum and the flux vectors across the outermost voxels for the
PHOENIX/3D spectra computed for the G2V dwarf test model (
|
Open with DEXTER | |
In the text |
![]() |
Figure 5:
Comparison between the PHOENIX/1D optical
spectrum and the flux vectors across the outermost voxels for the
PHOENIX/3D spectra computed for the G2V dwarf test model (
|
Open with DEXTER | |
In the text |
![]() |
Figure 6:
Comparison between the PHOENIX/1D optical
spectrum and the flux vectors across the outermost voxels for the
PHOENIX/3D spectra computed for the A dwarf test
model (
|
Open with DEXTER | |
In the text |
![]() |
Figure 7:
Comparison between the PHOENIX/1D UV spectrum
and the flux vectors across the outermost voxels for the
PHOENIX/3D spectra computed for the A dwarf test model (
|
Open with DEXTER | |
In the text |
![]() |
Figure 8:
Comparison between the PHOENIX/1D optical
spectrum and the flux vectors across the outermost voxels for the
higher resolution PHOENIX/3D spectra computed
for the M dwarf test model (
|
Open with DEXTER | |
In the text |
![]() |
Figure 9:
Comparison between the PHOENIX/1D UV spectrum
and the flux vectors across the outermost voxels for the higher
resolution PHOENIX/3D spectra computed for the
G2V dwarf test model (
|
Open with DEXTER | |
In the text |
![]() |
Figure 10:
Comparison between the optical PHOENIX/1D
spectrum and the flux vectors across the outermost voxels for the
higher resolution PHOENIX/3D spectra computed
for the A dwarf test model (
|
Open with DEXTER | |
In the text |
![]() |
Figure 11:
Comparison between the flux vectors across the outermost voxels for the
PHOENIX/3D UV spectra computed for the 3D
hydro structure and the PHOENIX/1D spectrum for
the G2V dwarf test model (
|
Open with DEXTER | |
In the text |
![]() |
Figure 12:
Comparison between the flux vectors across the outermost voxels for the
PHOENIX/3D near UV spectra computed for the
3D hydro structure and the PHOENIX/1D spectrum
for the G2V
dwarf test model (
|
Open with DEXTER | |
In the text |
![]() |
Figure 13:
Comparison between the flux vectors across the outermost voxels for the
PHOENIX/3D UV spectra computed for the 3D
hydro structure and the PHOENIX/1D spectrum for
the G2V dwarf test model (
|
Open with DEXTER | |
In the text |
![]() |
Figure 14:
Comparison between the flux vectors across the outermost voxels for the
PHOENIX/3D optical spectra computed for the
3D hydro structure and the PHOENIX/1D spectrum
for the G2V
dwarf test model (
|
Open with DEXTER | |
In the text |
![]() |
Figure 15:
Illustration of horizontal energy flow for the outermost voxels of the
the 3D hydro structure for the red spectral range. The graphics shows
the flowlines of the x and y
components of the flux vector |
Open with DEXTER | |
In the text |
![]() |
Figure 16:
Illustration of horizontal energy flow for the outermost voxels of the
the 3D hydro structure for the red spectral range. The graphics shows
the flowlines of the x and y
components of the flux vector |
Open with DEXTER | |
In the text |
![]() |
Figure 17:
Illustration of horizontal energy flow for the outermost voxels of the
the 3D hydro structure for the red spectral range. The graphics shows
the flowlines of the x and y
components of the flux vector |
Open with DEXTER | |
In the text |
![]() |
Figure 18:
Illustration of horizontal energy flow for the outermost voxels of the
the 3D hydro structure for the red spectral range. The graphics shows
the flowlines of the x and y
components of the flux vector |
Open with DEXTER | |
In the text |
![]() |
Figure 19:
Illustration of horizontal energy flow for the outermost voxels of the
the 3D hydro structure for the red spectral range. The graphics shows
the flowlines of the x and y
components of the flux vector |
Open with DEXTER | |
In the text |
![]() |
Figure 20:
Illustration of horizontal energy flow for the outermost voxels of the
the 3D hydro structure for the red spectral range. The graphics shows
the flowlines of the x and y
components of the flux vector |
Open with DEXTER | |
In the text |
![]() |
Figure 21:
Illustration of horizontal energy flow for the outermost voxels of the
the 3D hydro structure for the red spectral range. The graphics shows
the flowlines of the x and y
components of the flux vector |
Open with DEXTER | |
In the text |
![]() |
Figure 22:
Illustration of horizontal energy flow for the outermost voxels of the
the 3D hydro structure for the red spectral range. The graphics shows
the flowlines of the x and y
components of the flux vector |
Open with DEXTER | |
In the text |
![]() |
Figure 23:
Comparison between the PHOENIX/1D co-moving
frame UV spectrum (computed with 256 layers, * symbols) and
the co-moving frame flux vectors across the outermost voxels for the
PHOENIX/3D spectra computed for the Supernova test model. In
the PHOENIX/3D calculations we have used a
3D spherical coordinate system with |
Open with DEXTER | |
In the text |
Copyright ESO 2010
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