**FULL TITLE**
ASP Conference Series, Vol. **VOLUME**, **YEAR OF PUBLICATION**
**NAMES OF EDITORS**
A first three-dimensional model for the carbon monoxide
concentration in the solar atmosphere
S. Wedemeyer-Böhm
Kiepenheuer-Institut für Sonnenphysik, Schöneckstr. 6, 79104 Freiburg,
Germany
I. Kamp
Space Telescope Division of ESA, STScI, 3700 San Martin Drive,
Baltimore MD 21218, USA
B. Freytag
Department for Astronomy and Space Physics, Uppsala University, Box
515, SE-75120 Uppsala, Sweden
J. Bruls
Kiepenheuer-Institut für Sonnenphysik, Schöneckstr. 6, 79104 Freiburg,
Germany
M. Steffen
Astrophysikalisches Institut Potsdam, An der Sternwarte 16, D-14482
Potsdam, Germany
Abstract.
The time-dependent and self-consistent treatment of carbon monoxide (CO) has been added to the radiation chemo-hydrodynamics code
CO5BOLD. It includes the solution of a chemical reaction network and the
advection of the resulting particle densities with the hydrodynamic flow field.
Here we present a first 3D simulation of the non-magnetic solar photosphere and
low chromosphere, calculated with the upgraded code. In the resulting model,
the highest amount of CO is located in the cool regions of the reversed granulation pattern in the middle photosphere. A large fraction of carbon is bound
by CO throughout the chromosphere with exception of hot shock waves where
the CO concentration is strongly reduced. The distribution of carbon monoxide
is very inhomogeneous due to co-existing regions of hot and cool gas caused by
the hydrodynamic flow. High-resolution observations of CO could thus provide
important constraints for the thermal structure of the solar photosphere and
chromosphere.
1.
Introduction
The observations of carbon monoxide in the solar atmosphere (e.g., Noyes &
Hall 1972b; Ayres & Testerman 1981, and many more) gave rise to the long
debated so-called ’diagnostic dilemma’ because the existence of CO requires
temperatures that are much lower than implied by other “classical” models like
1
2
Figure 1. Three-dimensional visualisation for a single timestep from the
3D model: Iso-surface for a CO number density of 4 1012 cm−3 , resembling “clouds” in the middle photosphere, and iso-surface for a gas temperature of T = 7000 K below.
The box has a total extension of
4800 km × 4800 km × 2325 km.
VAL C (Vernazza et al. 1981). A possible solution of the problem is the dynamic
co-existence of hot and cool gas that can account for both, the UV emission
and the CO features. Examples of models featuring such an atmosphere are
the detailed 1D simulations by Carlsson & Stein (1995, hereafter CS) and the
more recent 3D model by Wedemeyer et al. (2004, hereafter W04). Asensio
Ramos et al. (2003) used the CS model to calculate time-dependent CO number
densities, resulting in a vertical 1D distribution, whereas Wedemeyer-Böhm et al.
(2005, hereafter W05) carried out 2D simulations similar to W04. In both cases
the average CO densities peaked in the middle photosphere between z = 100 km
and z = 200 km, being in line with the findings by Uitenbroek (2000) based on
chemical equilibrium calculations.
However, for a detailed comparison with observations concerning the horizontal distribution a 3D model is needed. Here we present the first 3D simulation
including time-dependent CO formation.
3
16
14
0.5
T [ 103 K ]
z [Mm]
12
0.0
10
8
-0.5
6
-1.0
4
1
2
3
4
y [Mm]
12
10
8
0.0
6
-0.5
4
nCO [ 1012 cm-3 ]
z [Mm]
0.5
2
-1.0
0
1
2
3
4
y [Mm]
0.5
0.8
0.0
0.6
-0.5
0.4
nCO / nC,total
z [Mm]
1.0
0.2
-1.0
0.0
1
2
3
4
y [Mm]
Figure 2. Vertical cross-section (y - z) through a single timestep from the 3D
model at x = 1220 km. Top: gas temperature, middle: CO number density,
bottom: fraction of carbon bound in CO (nCO / (nC +nCO +nCH )). The white
dotted and dashed lines are contours for gas temperatures of T = 5000 K and
T = 8000 K, respectively.
2.
Numerical simulations with CO5 BOLD
The radiation (magneto-)hydrodynamics code CO5 BOLD (Freytag et al. 2002,
W04) is used for solving the hydrodynamic equations and the radiative transfer
time-dependently on a Cartesian grid. Since for the model presented here no
magnetic fields have been included, it refers to internetwork regions of the nonmagnetic quiet Sun only. The model extends from z = − 1300 km in the
convection zone up to z ≈ 1000 km above τ5000 = 1 in the chromosphere. The
grid cells are non-equidistant in vertical direction, starting with a resolution of
50 km at the bottom and decreasing to 15 km in the photosphere and in the
chromosphere. In horizontal direction 120 grid cells are used with a constant
resolution of 40 km. Thus, the model consists of 1203 grid cells with a total
extension of 4800 km × 4800 km × 2325 km.
4
4
3
3
y [Mm]
y [Mm]
4
2
1
2
1
1
4.0
2
3
x [Mm]
4.5
T [ 103 K ]
4
5.0
1
5.5
2
3
x [Mm]
5
nCO [ 1012 cm-3 ]
10
4
15
Figure 3.
Horizontal cross-section through the same timestep as in Fig. 2
at a height of z = 210 km. Left: gas temperature, right: CO number density.
The white line is a contour for a temperature of T = 4700 K.
The chemical reaction network consists of 27 reactions that involve the
chemical species H, H2 , C, O, CO, CH, OH and a representative catalytic metal.
See W05 for more details on the method and chemical input.
Periodic boundaries are used for the sides of the model. The upper boundary is transmitting, the lower one is open with entropy and pressure adjustment.
Future models will make use of the recently implemented cooling by CO
lines (Wedemeyer-Böhm & Steffen in prep.). The radiation transport is then
solved in a continuum band with Rosseland mean opacity and an additional IR
band with CO opacity. The latter is a direct result of the time-dependent CO
number densities.
3.
Results
The highest absolute amount of CO is found in the middle photosphere where
the effective chemical timescales are short. Hence, the CO number density is
close to instantaneous chemical equilibrium there and follows changes of the
gas temperatures. Consequently, the density of carbon monoxide neatly renders
the thermal structure of the middle photosphere that resembles the observed
reversed granulation pattern. The hot areas above intergranular lanes, where
the lateral flows are deflected into the downdrafts and thus compress and heat the
gas, have a much smaller content of CO than the cooler regions above the granule
interiors. Plotting surfaces of constant CO number density thus reveals CO
clouds in the middle photosphere (Fig. 1). That can also be seen from horizontal
and vertical cross-sections through the 3D model displayed in Figs. 2 and 3,
respectively. Most results concerning structure and dynamics are very similar
to the 2D simulations by W05. That includes the finding that a large fraction of
5
1.0
[CO]
0.8
0.6
0.4
0.2
0.0
0
200
400
600
800
1000
z [km]
Figure 4. Average concentration of carbon monoxide [CO] = nCO / (nC +
nCO + nCH ) as function of geometrical height for the static equilibrium (thin
dotted) and the time-dependent calculation (thin dashed) by W04, for the
2D simulations with full reaction network (thick dot-dashed) and only two
reactions (thick dashed) by W05, and finally for the 3D model presented here
(thick solid). See text for more details.
carbon is bound by CO throughout the low and middle chromosphere (see lower
panel of Fig. 2). At some locations the fraction can even reach values of one, i.e.
all carbon is bound in CO. An exception are regions where a shock wave just
passed. There the CO concentration gradually increases again due to the finite
recombination timescale. Obviously, a time-dependent treatment is mandatory
to model the carbon monoxide concentration in the solar chromosphere.
The importance of a time-dependent modelling with a detailed chemical
reaction network is illustrated by means of the average CO concentration in
Fig. 4. The concentration is defined as [CO] = nCO / nC,total where nC,total =
nC + nCO + nCH is the total number density of all carbon atoms whether bound
or not. The concentration is reasonably similar for the 3D and the 2D model
with full chemical reaction network (thick solid and thick dot-dashed line, resp.).
In both cases [CO] is much closer to the static approach by W04 than to their
time-dependent calculation. The 2D and 3D simulations produce concentrations that are even higher than the static result up to z = 550 km but decline
above. That can be explained by the fact that W04 only used 1D columns from
their 3D model and considered a reaction pair consisting of radiative association, C + O → CO + hν, and collisional dissociation, CO + H → C + O + H,
only. But these reactions were shown to be of minor importance compared to
the more efficient formation channel via OH (W05). The thick dashed line represents the simulation with a reduced reaction network accounting only for those
two reactions used by W04. The resulting concentrations agree reasonably well.
Remaining differences can be attributed to the use of different reaction rate coefficients (see W05), and to the fact that W04 ignored CO advection. Obviously
the full reaction network comprises reactions that are much faster and thus result in a CO concentration that is much closer to equilibrium than suggested by
the simplified time-dependent treatment by W04.
6
4.
Conclusions and outlook
The presented numerical simulations clearly show the existence of carbon monoxide as part of an inhomogeneous and dynamic atmosphere of the Sun. While
the influence of CO as cooling agent is much smaller than expected so far
(Wedemeyer-Böhm & Steffen in prep.), observations of spectral features of CO
provide an important diagnostic for the thermal structure of the atmosphere. In
the middle photosphere it traces the reversed granulation pattern. Further up
it outlines propagating shocks since molecules in these high-temperature regions
are efficiently dissociated whereas they remain and form in the undisturbed areas. The next logical step would thus be a detailed comparison of these 3D
simulations with high-resolution CO observations. This undoubtedly challenging approach will provide new insight in the structure of the solar atmosphere.
Acknowledgments. This work was supported by the Deutsche Forschungsgemeinschaft (DFG), project Ste 615/5.
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