Issue |
A&A
Volume 506, Number 3, November II 2009
|
|
---|---|---|
Page(s) | 1393 - 1404 | |
Section | The Sun | |
DOI | https://doi.org/10.1051/0004-6361/200912048 | |
Published online | 11 August 2009 |
Online Material
Appendix A: NLTE modeling
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Figure A.1:
a), b): departure coefficients |
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Figure A.2:
The NLTE (solid line) and LTE (open circles) heights of formation of the core of the Ba II 4554 Å line along the slice of the snapshot yi=0.6 Mm. Dash-dotted line: continuum height
of formation at 4554 Å. Dotted line: height of formation of the
line wing for the wavelength position
|
Open with DEXTER |
Figure A.1 (panels a to f) shows the population
departure coefficients, the Ba II 4554 Å line source
functions and line profiles for two spatial grid points of the
3D snapshot representing the typical granular and intergranular
models. We use these models to illustrate the difference in the
NLTE results for granules and intergranules. The population
departure coefficients are defined as
where
and
are the NLTE and
LTE atomic level populations, respectively. The Complex behaviour
of the
-coefficients shown in Fig. A.1a, b is a
result of the interaction of several NLTE mechanisms described in
detail by Bruls et al. (1992); Carlsson et al. (1992); Shchukina & Trujillo Bueno (2001). Here we just point out that for the
barium atom the most important of them are ultraviolet line
pumping, ultraviolet overionization, resonance line scattering and
photon losses.
The resonance line scattering and photon losses manifest
themselves as a divergence of the lower
and upper
,
levels
of the Ba II resonance lines. This divergence results from the
surface losses near the layer where the optical depth is equal to
unity. The losses propagate by scattering to far below that layer.
Interestingly, for the integranule the divergence of the
-coefficients arises in the innermost layers. This happens
because the photon losses occur mainly through the line wings of
the Ba II 4554 Å line. As follows from
Fig. A.2 the line wings in integranules are
formed considerably deeper than in granules. Such a difference in
the formation heights is a result of the Doppler shift of the line
opacity coefficient caused by the velocity field. As a
consequence, in the intergranular model (see
Fig. A.1a, b) the divergence starts already in the
lower photosphere while in the granular model it happens only in
upper photosphere at heights around 400 km.
Another important conclusion that follows from
Fig. A.2 concerns the height of formation of the
Ba II 4554 Å line. The lower departure coefficient is close to unity. So the scaling of the line opacity with this
coefficient cannot lead to an appreciable difference between the
NLTE and LTE heights of formation of this line.
The excess of Ba II ions at the levels with excitation
potentials above 5 eV visible in the granule model is produced
by the pumping via the ultraviolet Ba II lines starting at
,
,
levels.
For the intergranule model the overpopulation arises only in the
uppermost layers. Such behaviour of the
-coefficients
corresponds to the temperature stratification of the models. The
overpopulation of the high excitation levels of Ba II in granules
occurs because here the excitation temperature of the ultraviolet
pumping radiation field appreciably exceeds the electron
temperature. In integranules such superthermal radiation, and
hence the level overpopulation, is present only above the
temperature minimum region. In addition, in the intergranular
photospheric layers the photon losses in the ultraviolet lines are
more pronounced than in granules.
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Figure A.3:
The total source function
|
Open with DEXTER |
The
ratio of the upper and lower level
departure coefficients of the Ba II 4554 Å line sets the
departure of its line source function SL from the Planck
function B. Figure A.1 (c, d) shows that this
departure (reflecting the corresponding departure coefficient
divergence in the upper panels of this figure) is larger in the
intergranular than in the granular model.
Figure A.3 demonstrates that such behaviour is typical
also for the total source function
at the
wavelengths corresponding to the inner wings (
mÅ). On average, in intergranular regions it drops below
the Planck function while in granules the effect is less
pronounced. Moreover, in granular areas with strong upflows the
total source function can exceed the Planck function. This excess
can be understood if one takes into account that the resonance
source line function is described by the two-level approximation,
i.e. it approximately equals mean intensity J. In the regions
with small photon losses (like granules) the J > B, hence,
and
have to be greater than B as well.
Figure A.1e, f show the NLTE and LTE disc-centre line profiles for the individual granular and integranular models. The profiles displayed in Fig. A.1g result from averaging of the emergent intensities corresponding only to the granular models. Averaged intergranular profiles are shown in Fig. A.1h. These two bottom panels quantify the statistical effect produced by the deviation from the LTE in two such types of the atmospheric models. The main conclusions that may be drawn from the results presented in Figs. A.1-A.3 are the following:
- the source function deficit, as compared to the LTE assumption,
is the main mechanism that controls the formation of the Ba
II
4554 Å line. The line opacity deficit is small and, hence, unimportant;
-
the divergence between
and B changes the shape of the individual profiles, particularly the intergranular ones.
- On average, the deviations from the LTE lead to deepening (i.e.
strengthening) of the spatially averaged Ba II
4554 Å line profiles. The NLTE effects are most pronounced around the line core and are generally more important in the intergranular regions than in the granular ones. The mean difference between the NLTE and LTE line core residual intensities does not exceed 5% for granules and 10% for intergranules.
- Towards the wings, the LTE becomes a valid description for the
Ba II
4554 Å line profile;
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