Astron. Nachr./AN 324, No. 4, 410–411 (2003) / DOI 10.1002/asna.200310150
3-D hydrodynamic simulations of the solar chromosphere
S. W EDEMEYER1 , B. F REYTAG2 , M. S TEFFEN3 , H.-G. L UDWIG4 and H. H OLWEGER1
1
2
3
4
Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität, D-24098 Kiel, Germany
Department for Astronomy and Space Physics, Uppsala University, Box 515, SE-75120 Uppsala, Sweden
Astrophysikalisches Institut Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany
Lund Observatory, Box 43, SE-22100 Lund, Sweden
Received 29 October 2002; accepted 23 December 2002; published online 20 May 2003
Abstract. We present first results of three-dimensional numerical simulations of the non-magnetic solar chromosphere,
computed with the radiation hydrodynamics code CO5 BOLD. Acoustic waves which are excited at the top of the convection
zone propagate upwards into the chromosphere where the waves steepen into shocks. The interaction of the waves leads to
the formation of complex structures which evolve on short time scales. Consequently, the model chromosphere is highly
dynamical, inhomogeneous, and thermally bifurcated.
Key words: stars: chromospheres – Sun
1. Introduction
Despite the progress which has been made in the recent
years, still a major question about the nature of the nonmagnetic chromosphere of the Sun remains under debate (e.g.
Kalkofen 2001): Is it persistent, homogeneous, and stratified like in the semi-empirical models by Vernazza, Avrett
& Loeser (1981)? Or is the chromosphere of the quiet Sun
spatially and temporally intermittent with large fluctuations
like suggested by the numerical simulations by Carlsson &
Stein (1995)?
We contribute to this debate with first results from
a 3-D model which has been computed with CO5 BOLD
(”COnservative COde for the COmputation of COmpressible
COnvection in a BOx of L Dimensions, l = 2, 3”), a radiation
hydrodynamics code developed by B. Freytag and M. Steffen
(see Freytag, Steffen & Dorch 2002).
2. Modelling with CO5BOLD
The 3-D model presented here has an extension of
5600 km (∼ 7. 7) horizontally and ∼ 3100 km vertically. The
lower boundary is located in the convection zone at z ∼
−1380 km, the upper one at z ∼ 1700 km. The origin of
the height scale is defined by the average height for optical
depth unity. The numerical resolution is 40 km in the horizontal directions and changes in vertical direction from 12 km
Correspondence to: wedemeyer@astrophysik.uni-kiel.de
in the chromosphere and in the photosphere to 46 km in the
convection zone. On this grid the hydrodynamic equations
and the radiative transfer are solved time-dependently. For
the radiation transport we used a Rosseland mean opacity table based on data of OPAL (Iglesias, Rogers & Wilson 1992)
and PHOENIX (Hauschildt, Baron & Allard 1997) which has
been compiled by H.-G. Ludwig.
Since the model extends from the top of the convection
zone to the middle chromosphere, the generation, propagation, and dissipation of acoustic waves can be simulated in
a self-consistent way. Note that our model refers to the nonmagnetic internetwork regions only.
3. A dynamic, inhomogeneous chromosphere
In the numerical simulations acoustic waves are excited by
the motions at the top of the convection zone from where they
propagate upwards into the thinner layers. In the low chromosphere these waves have turned into shocks. The waves
collide and interact with each other because the waves also
expand horizontally and often run in an oblique direction. As
a result complex structures are formed which can be seen as
a network of hot matter in a horizontal slice of the 3-D model
(Fig. 1). Enclosed are cool regions where the temperature is
much lower than in the hot network.
Figure 2 shows the temporal variation of the gas temperature at a particular grid cell in the model chromosphere. Between the temperature peaks which are caused by the passage
of a hot shock wave the gas cools down to temperatures as
c
2003
WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 0004-6337/03/0406-0410 $ 17.50+.50/0
S. Wedemeyer et al.: Hydrodynamic simulations of the solar chromosphere
411
z = 1000 km
7000
5000
6000
4000
T [K]
y [km]
5000
3000
4000
2000
3000
1000
2000
1000
3000
2000
3000
x [km]
4000
5000
Temperature [K]
4000
5000
0
6000
500
1000
time [s]
1500
2000
7000
Fig. 1. Temperature in a horizontal slice from a snapshot of our 3-D
model at a height of ∼ 1000 km (middle chromosphere).
Fig. 2. Temporal variation of the temperature for a single grid cell at
a height of ∼ 1000 km.
4. Conclusions
low as ∼ 2000 K. On average it takes only roughly a minute
until the next wave front arrives and the temperature rises
again.
Thus, the model chromosphere is highly time-dependent,
and inhomogeneous, with large temperature fluctuations –
in contrast to the layers below which exhibit only relatively
small deviations from an average temperature stratification.
Due to these temporal and spatial inhomogeneities the chromospheric temperature distribution cannot be represented adequately by an average static 1-D stratification as done in
the semi-empirical models by Vernazza et al. (1981) and related models. These models feature a temperature minimum
and a chromospheric temperature rise whereas the mean gas
temperature in our simulation does not show a significant increase at all. This is a result which is already known from the
dynamic 1-D model by Carlsson & Stein (1995). However,
Carlsson & Stein (1995) showed that the temperature rise in
the semi-empirical models can be explained by the enhanced
radiative emission in shock waves due to the non-linear behaviour of the UV Planck function and a consequently misleading temporal averaging which has been done for the construction of the semi-empirical models. Instead of an average high persistent emission from all parts of the chromosphere, the chromospheric emission can be sustained mainly
by shock waves. Carlsson & Stein (1995) conclude that the
chromospheric temperature rise in the semi-empirical models
is an artifact due to the neglect of the temporal fluctuations.
Our simulations support this result and even imply that also
the horizontal fluctuations should be taken into account for a
proper description of the solar chromosphere.
Our first numerical simulations of the non-magnetic solar
chromosphere produce a highly dynamic and inhomogeneous
model chromosphere with a complicated network-like temperature distribution due to propagating and interacting shock
waves. Such a chromosphere can hardly be described with
static 1-D models but demands a time-dependent, multidimensional modelling. The dynamic and inhomogeneous
picture will have many consequences for the properties of the
chromosphere, like e.g. the temperature distribution, which
have to be worked out further.
Moreover, the thermal bifurcation of the non-magnetic
model chromosphere offers a possibility to combine temperatures high enough to produce chromospheric emission lines
and regions cold enough for molecular features (e.g. carbon
monoxide) at the same time and thus might be very important
for the interpretation of observations.
Acknowledgements. The main-author (S.W.) wishes to thank the organizers of the GREGOR workshop, held on July 24th-26th,2002 in
Göttingen, for financial support.
References
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