Issue |
A&A
Volume 508, Number 3, December IV 2009
|
|
---|---|---|
Page(s) | 1403 - 1416 | |
Section | Stellar atmospheres | |
DOI | https://doi.org/10.1051/0004-6361/200912840 | |
Published online | 08 October 2009 |
A&A 508, 1403-1416 (2009)
Oxygen lines in solar granulation
II. Centre-to-limb variation, NLTE line
formation, blends, and the solar oxygen abundance![[*]](/icons/foot_motif.png)
T. M. D. Pereira1,2 - M. Asplund3 - D. Kiselman2
1 - Research School of Astronomy and Astrophysics, Australian National
University, Cotter Rd., Weston, ACT 2611, Australia
2 - The Institute for Solar Physics of the Royal Swedish Academy of
Sciences, AlbaNova University Center, 106 91 Stockholm, Sweden
3 - Max-Planck-Institut für Astrophysik, Postfach 1317, 85741 Garching
b. München, Germany
Received 7 July 2009 / Accepted 9 September 2009
Abstract
Context. There is a lively debate about the solar
oxygen abundance and the role of 3D models in its recent
downward revision. These models have been tested using high-resolution
solar atlases of flux and disk-centre intensity. Further testing can be
done using centre-to-limb variations.
Aims. Using high-resolution and high S/N
observations of neutral oxygen lines across the solar surface, we seek
to test that the 3D and 1D models reproduce their observed
centre-to-limb variation. In particular we seek to assess whether the
latest generation of 3D hydrodynamical solar model atmospheres
and NLTE line formation calculations are appropriate to derive the
solar oxygen abundance.
Methods. We use our recent observations of
O I 777 nm, O I
615.81 nm, [O I] 630.03 nm,
and nine lines of other elements for five viewing angles
of the quiet solar disk. We compared them with the predicted line
profiles from the 3D and 1D models computed with the
most up-to-date line formation codes and line data and allowing for
departures of LTE. The centre-to-limb variation of the O I 777 nm
lines is also used to obtain an empirical correction for the poorly
known efficiency of the inelastic collisions with H I.
Results. The 3D model generally reproduces the
centre-to-limb observations of the lines very well, particularly the
oxygen lines. From the O I
777 nm lines we find that the classical Drawin recipe slightly
overestimates H I collisions
(
agrees best with the observations). The limb observations of the
O I 615.82 nm
line allow us to identify a previously unknown contribution of
molecules for this line, prevalent at the solar limb. A detailed
treatment of the [O I] 630.03 nm
line that includes the recent nickel abundance shows that the
3D modelling closely agrees with the observations. The derived
oxygen abundances with the 3D model are 8.68 (777 nm
lines), 8.66 (630.03 nm line), and 8.62 (615.82 nm
line).
Conclusions. These additional tests have reinforced
the trustworthiness of the 3D model and line formation for abundance
analyses.
Key words: line: formation - Sun: photosphere - Sun: granulation - Sun: abundances - convection
1 Introduction
Oxygen is arguably one of the most important elements in the Universe. After hydrogen and helium it is the most common element, projecting its importance to many fields in astrophysics: from stellar abundances to the interstellar medium and galactic evolution. The solar oxygen abundance is often used as a reference in many studies. As a volatile element, its meteoritic abundance is not representative, so the most reliable probe for the reference oxygen abundance is the solar photosphere.
With high-quality data readily available, a longstanding
expertise in solar observations and much improved knowledge of stellar
atmospheres in the past decades would lead one to expect that a
measurement as fundamental as the solar photospheric abundance of
oxygen would be firmly established; on the contrary, the solar oxygen
abundance has been hotly debated in recent times. From the high (and
widely used) value of
(Anders & Grevesse
1989), the proposed oxygen abundance has been revised
downward to the low value of
(Asplund et al. 2004).
The pivotal causes for this change have been proper treatment of the
statistical inhomogeneities caused by the solar granulation (making use
of a 3D photosphere model), the proper treatment of departures
from local thermodynamical equilibrium (LTE), and improved line data
(including better blend identification). A low oxygen abundance has
caused significant grievances among the solar/stellar interior
modelling community by undoing the almost perfect agreement between the
solar interior models and helioseismology, which has sparked much
debate. In past years the downward revision of the solar oxygen has
been supported by some studies (e.g. Socas-Navarro &
Norton 2007; Meléndez & Asplund 2008)
but contested by others (e.g. Ayres 2008; Centeno
& Socas-Navarro 2008). Some recent studies find
intermediate oxygen abundances (e.g. Caffau
et al. 2008). Centeno
& Socas-Navarro (2008) claim a model-independent
determination of the oxygen abundance, which is dismissed by Scott et al. (2009).
A measure of the photospheric oxygen abundance is made difficult for several reasons. Of the few atomic oxygen lines available in the solar spectrum, some are very weak, others significantly blended. An example is the popular [O I] 630.03 nm line, which is weak and has a non-negligible blend with a nickel line. On the other hand, departures from LTE are also important for some O I lines - the O I 777 nm triplet lines being the typical example. These lines are known to show significant departures from LTE, requiring the use of detailed NLTE line formation that requires detailed atomic input data that may not exist.
For the NLTE modelling the collisions with neutral hydrogen
are particularly relevant. There is disagreement in the literature
regarding the importance of inelastic collisions with H I.
At this point, the lack of experimental data or quantum mechanical
calculations makes its estimation complicated. A customary approach is
to adopt a generalization of the classical Drawin formula (Drawin 1968), using the recipe
of Steenbock & Holweger
(1984), often scaled by an empirical factor ,
and Lambert (1993)
corrected a mistake in these original formulæ. However, there are
different views regarding which scaling factor to use for oxygen. Nissen et al. (2002)
and Asplund et al. (2004)
chose
,
based on evidence that the Drawin formula overestimates the H I collision
efficiency with some atoms for which experimental or detailed quantum
mechanical data exists (e.g. Barklem
et al. 2003). Caffau
et al. (2008), on the other hand, have adopted a
seemingly ad-hoc value of
.
For the solar O I
777 nm lines, the adopted recipe for H I collisions
has a significant effect on the line shape and strength and
consequently, on the derived oxygen abundance. Using the same
3D model of Asplund
et al. (2004), Allende
Prieto et al. (2004) empirically found that
agree somewhat better than
,
while the LTE case can be ruled out.
In addition to the line formation physics, the centre-to-limb variation of the lines provides a robust test of the model atmospheres by probing the depth variation of the source functions, as seen from the Eddington-Barbier approximation. In this work we study atomic oxygen lines using observations of their centre-to-limb variation. We study the effects of using different atmospheric models, allow departures from LTE in the line formation, and properly account for blends. Our aim is to provide additional observational tests of some of the models used to infer the oxygen abundance, using new solar observations.
We obtained high spatial and spectral resolution observations
of oxygen and other lines across the solar surface. Similar
observations of oxygen lines have been obtained in the past (notably Allende Prieto
et al. 2004; Müller et al. 1968; Altrock 1968).
However, available data from early works is limited to equivalent
widths, and the more recent work of Allende
Prieto et al. (2004) covers only the O I 777 nm
triplet lines. Furthermore, the long slit used by Allende
Prieto et al. (2004) increases the uncertainty of
the
value for their limb data. The observations outlined in the present
work include five neutral oxygen lines: the O I
615.81 nm, [O I]
630.03 nm, and the three O I
777 nm over five positions in the solar disk. In addition,
lines from other elements are also included in the observed spectral
regions.
Our observations are briefly outlined in the next section. In Sect. 3 we outline the model atmospheres and the line formation codes used, which are compared with the observations in Sect. 4. Conclusions are made in Sect. 5.
2 Observations
2.1 Overview
We make use of the observations of Pereira et al. (2009, hereafter Paper I), which we refer to for a detailed description of the programme, instruments, and reduction. Paper I focused on high spatial resolution, and here we study the centre-to-limb variations of the spatial and temporaly mean spectra. Thus, in terms of the observations, the main difference is that we average the spectrograms in space and time to obtain a mean spectrum for each position in the solar disk.
Using 25 spectrograms for each
position and 50 spectrograms for
means that our mean spectra comprise an average of more than
20 000 spectra (>40 000 for disk-centre). The
S/N for the spectrum of one spatially averaged spectrogram is
about 700. The total S/N would be
times that value, if the images were all independent, which is not the
case because the time separation does not always guarantee that they
sample a different granulation pattern. In any case, a conservative
estimate of the S/N should be at least 1500 - more than enough for the
present analysis. Unlike Paper I, no Fourier filtering is
applied, since most of the photon noise is eliminated by the averaging
of many spectra.
It is worth noting that, for the
set, some facular features were visible on the slit-jaw images, though
the slit did not cross them. Because we want to study quiet regions and
to avoid any possible interference due to magnetic fields, we have
removed the middle third of the spectral images for the
set, so that the final spectrum was averaged only from quiet regions.
This procedure reduces the S/N for this set by about 20%.
![]() |
Figure 1: Observed profiles at disk-centre and limb. For the weak 615.81 and 630.03 nm lines the location is indicated. In this figure the wavelengths for the limb spectra have been adjusted to compensate for solar rotation and other systematics. |
Open with DEXTER |
After obtaining the spatial and temporally averaged spectra for each ,
the continuum levels are found manually. In some cases such as the
O I 615.81 nm line,
a local continuum is used to compensate for blends not included in the
line synthesis. The wavelength calibration, explained in
Paper I, is linked to the Fourier transform spectrograph (FTS)
disk-centre intensity atlas of Brault
& Neckel (1987). It consists in identifying the same
spectral lines in the FTS atlas and our observations, and then
obtaining the dispersion relation by a polynomial fit to the line
cores. It lacks precision, and a more precise wavelength calibration is
necessary for analysing some lines. In the analysis section we outline
a correction to the wavelength calibration using the atmosphere models
and Fe I lines. The
reduced spectra for disk-centre and the limb can be found in
Fig. 1.
2.2 Comparison with previous studies
The oxygen lines we observed have been the object of several studies in
the past. Most notably, the centre-to-limb variation of these lines has
been studied in Müller
et al. (1968), Altrock
(1968), and Allende Prieto
et al. (2004). The last work only covers the
777 nm triplet lines. These works use different
instrumentation and techniques, which makes them fairly independent of
our observations. We compare the equivalent widths of the present work
with the ones from these studies in Fig. 2. Equivalent
width measurements have a somewhat subjective component due to
different normalizations and different wavelength ranges where it is
computed. However, it is the only comparison that can be made at least
with Müller et al. (1968)
and Altrock (1968). With
Allende Prieto et al. (2004),
we used the available online spectra and computed the equivalent widths
in the same way as for our data (direct integration, same wavelength
range). It should be noted that their normalization around
the 777.41 and 777.53 nm lines is slightly different
from ours, leading to a higher continuum level. This in turn makes the
lines stronger when computing the equivalent widths by direct
integration. The equivalent widths as a function of
for all the lines included in this work are listed in Table 1. The
uncertainties arise mostly from the continuum placement. For the lines
in the 777 nm region, the errors are larger because a larger
integration region was used. The smooth variation of the equivalent
widths with
in our data indicates a low statistical error and highlights its high
quality.
![]() |
Figure 2:
Equivalent width vs. |
Open with DEXTER |
Table 1:
Equivalent widths for the lines included in this analysis, as a
function of .
3 Theoretical line profiles
We employ the 3D time-dependent hydrodynamical simulation of the solar photosphere used in Paper I (Trampedach et al., in preparation; Asplund et al., in preparation). This model was computed using a more recent version of the Stein & Nordlund codes. When compared with the 3D model of Asplund et al. (2000), it includes more detailed radiative transfer: 12 opacity bins, additional sources of continuum opacities such as photo-ionization cross-sections from the Opacity and Iron Projects (Cunto et al. 1993; Hummer et al. 1993), etc. In Fig. 3 we show the differences in the mean temperature structure (averaged over surfaces of constant optical depth) between both 3D models. A comparison is also made with one-dimensional, hydrostatic, time-independent solar model atmospheres, including the semi-empirical model of Holweger & Müller (1974) and the MARCS model (Gustafsson et al. 2008).
We computed the synthetic LTE and NLTE (oxygen only) line
profiles, making use of our LTE line formation code and the MULTI3D
code (Botnen
1997; Asplund
et al. 2003). For a more detailed description of the
3D model, line formation, and atomic data used, we refer to
Paper I; however, a few things are done differently from
Paper I. We made use of 90 snapshots of the
3D simulation (in Paper I we used
20 snapshots). These cover min
of solar time and have
.
To save computational time, 3D NLTE line formation
was only carried out on four snapshots (chosen to have a representative
range of effective temperature and time coverage). Using MULTI3D,
we computed NLTE and LTE line profiles, which were used to obtain the
wavelength-dependent NLTE/LTE ratio for each
value. In contrast with Paper I, the NLTE/LTE ratio was
averaged over all the spatial points and the four snapshots. For
each
value, we then multiplied the NLTE/LTE ratio by the spatially and
temporally averaged LTE line profiles (computed with our LTE code for
all the 90 snapshots). The NLTE line profiles were computed
for eight different values of
:
0.01, 0.1, 0.3, 0.5, 1, 1.5, 3, 10.
With the 1D MARCS and
Holweger-Müller model atmospheres, line profiles were computed using
the same procedures, opacities, and radiative transfer. The exception
is that a microturbulence of
was used when computing these line profiles. In addition, 1D line
profiles were convolved with a Gaussian to account for macroturbulence.
The adopted macroturbulences vary from line to line (see Sect. 4). For
consistency, 1D NLTE line formation was computed in a similar manner to
the 3D model, obtaining the NLTE to LTE ratio from MULTI3D
and multiplying it by the profiles obtained with the LTE code (even
though there is only one snapshot for the 1D models).
Our main focus are oxygen lines. However, a few lines from other elements are also present in our observations. These lines and their properties, along with the oxygen lines, are listed in Table 2. In Sect. 4.4 we briefly discuss the results for the centre-to-limb variation of these lines. For the oxygen lines and, when available, for lines of other elements the collisional (van der Waals) broadening was computed using the quantum mechanical theory of Barklem & O'Mara (1997); Barklem et al. (1998); Anstee & O'Mara (1995), avoiding the need for conventional Unsöld (1955) enhancement factors.
Table 2: Lines studied in the present work and their parameters.
![]() |
Figure 3: Comparison of the mean temperature structure of the new 3D model used in this work and the former 3D model of Asplund et al. (2000), plotted against the optical depth at 500 nm. |
Open with DEXTER |
4 Results
The synthetic line profiles are compared with the observations by means
of fitting and equivalent width. Before a comparison was made with our
observations, the synthetic line profiles were convolved with a
Gaussian (equivalent to 000)
to account for the instrumental profile of the spectrograph. When
comparing line profiles with the FTS intensity atlas, no convolution
took place, because of the very high resolution of the atlas. The
line-profile fitting was performed using the L-BFGS-B optimization
algorithm (Byrd et al. 1995).
![]() |
Figure 4:
Top panels: equivalent width vs. |
Open with DEXTER |
4.1 O I infrared triplet
4.1.1 Context
The three O I lines around 777 nm are strong and lie in a part of the solar spectrum that is relatively free of blends and telluric lines. These two characteristics alone make them a good abundance indicator. However, these lines show significant departures from LTE in the Sun (Altrock 1968), because of a radiation field weaker than Planckian in the line formation region (e.g. Kiselman 1993; Eriksson & Toft 1979).
Aside from the increased computational expense of computing
the 3D NLTE radiative transfer for these lines, departures
from LTE introduce additional uncertainties stemming from the input
physics, in particular photo-ionization rates and collisional
cross-sections with electrons and H I.
The latter, as noted in Sect. 1, are often
taken from the classical estimates and scaled by an
factor. For the O I 777 nm lines,
a scaling factor for the H I collisions
was tried by Kiselman (1993)
to reconcile different 1D models with observed centre-to-limb
variation of the equivalent widths. Further investigation of
the 3D and NLTE effects on these lines is provided by Kiselman & Nordlund (1995),
using an early 3D model and showing the feasibility of the
line centre-to-limb variations to probe for the atomic parameters
(i.e.,
).
This suggestion was followed by Allende
Prieto et al. (2004, hereafter AAF04), who used the
centre-to-limb variation of the O I 777 nm
lines and a 3D model to empirically deduce that
was preferable to
.
Our work differs from AAF04 in that we use a different set of
observations and 3D model, a greater range of values,
a more up-to-date atom, and more detailed radiative transfer for the
NLTE calculations (more simulation snapshots included in the full
3D NLTE, more angles used in MULTI3D).
4.1.2 Comparison with observations
Our goal is to find the
that best describes the centre-to-limb variation of the line strength.
For this purpose we have two diagnostics: equivalent widths and
line-profile fitting. Measuring the variation of line strengths by
profile fitting has the advantage of being less sensitive to
systematics (e.g. blends, noise) than the equivalent widths. But when
the shape of the line profiles does not match the observations, the
line profiles adjusted in abundance will have a slightly different
equivalent width than the observations. We present the results using
both diagnostics, and they both suggest a very similar result.
To fit the line profiles, we vary two parameters: oxygen abundance and wavelength shift (of the observations). The latter is necessary because of the uncertainty in the wavelength calibration. For the 1D models, another free parameter was allowed in the fit: macroturbulence. Ideally it should not be allowed to vary freely, but instead extracted from nearby lines. The scarcity of lines in our observed window around 777 nm makes this task difficult; in our observed window, there is only one other line, a strong Fe I line. Deriving the macroturbulence from only one line would probably introduce a similar or larger error as allowing it to be a free parameter in the fit for the O I 777 nm lines.
The results for profile fitting and equivalent width for the
3D model are given in Fig. 4. For
the equivalent widths, the oxygen abundance was adjusted for each line
so that it matched the observations at disk-centre. The same abundance
was then used for all the other values of .
Both diagnostics indicate that
agrees most closely with the observations, with a small variation from
line to line. It is shown with a high confidence level that LTE line
formation is not a valid approximation for these lines. In
Table 3
we list the derived abundances from fitting the disk-centre line
profiles, using 3D NLTE radiative transfer for different values
of
both for our observations and the FTS atlas of Brault & Neckel (1987).
Line profiles were fitted in the following wavelength ranges:
777.175-777.24 nm, 777.36-777.46 nm and
777.50-777.565 nm.
Corresponding results for the 1D models are given in
Fig. 5,
but only for the O I 777.41 nm
line; the other lines behave similarly. They indicate a mixed scenario.
On one hand, the Holweger-Müller model gives a similar result to the
3D model: the best agreement is with .
But for the MARCS model, no value of
can agree reasonably with the observations, both in equivalent width
and line profile fitting.
![]() |
Figure 5: Same as Fig. 4 but for the 1D models and only for the O I 777.41 nm line. |
Open with DEXTER |
In Fig. 6
the 3D model predicted line profiles for disk-centre (adjusted in
abundance) and the limb (using the disk-centre abundance) are shown for
LTE and ,
0.3, and 1. It can be seen that LTE performs very poorly at
the limb (too weak), so that
does not fare much better (too strong) and that
agrees better.
One can also see that the LTE profiles seem to fit the
observations better at disk-centre. The disk-centre profiles for
are narrower and deeper than the observed. At the limb, in terms of
shape alone,
profiles have a much better fit. The
that best describes the centre-to-limb variation of the line strengths
does not seem to be the best at describing the shapes of line profiles
at disk-centre. This same effect is more obvious when looking at the
granulation variation of the FWHM at disk-centre (Paper I). It
may very well be connected with the finding of Paper I that no
single
agrees well with the observed equivalent widths for both granular and
intergranular regions. The reason for these discrepancies is not clear
yet.
To better quantify the agreement with the observations of
different ,
a
minimization was made with the equivalent widths, simultaneously for
the three lines and for the five
values. For each value of
,
we varied the oxygen abundance and found the value that minimizes the
squared difference between observed and predicted equivalent widths,
weigthed by the observational error bars. The reduced
is defined as
,
where N is the number of degrees of freedom
(in this case, N=15-1). The
values, as a function of
are shown in Fig. 7.
Comparing for all the
,
we identify the value that agrees better, using a parabolic fit to the
lower
values.
For the 3D model, we find the
minimum to be at
.
We used this value to derive the oxygen abundance from these lines.
Averaging over the three lines we obtain an oxygen abundance of
for the 3D model. By repeating the procedure for the
1D Holweger-Müller model we also obtain
,
deriving an abundance of 8.66. Although with the 1D MARCS
model no
reproduces the observations, for comparison we derive an abundance
of 8.61 using
.
4.1.3 Comparison with previous work
At first glance our findings are consistent with the
estimated by AAF04. But these two findings cannot be directly compared,
as we use a different 3D model. To compare our methods and observations
with AAF04, we repeated our analysis for the same 3D model they use.
The best-fitting value is then
,
which is close to the observations as
with the new 3D model. Between
and
(the two values tested by AAF04) we find that the latter agrees better
with the observations, consistent with the findings of AAF04. But the
best fit of
indicates a model dependence in this derivation, also seen for the
1D models. Interestingly, although the best-fitting
varies for the two 3D models, the abundances derived from
profile fits with the best choice
are almost unchanged between the two models (
).
Table 3:
Derived disk-centre oxygen abundances (
)
from from the 3D model.
![]() |
Figure 6:
Our observations (dots) and 3D synthetic line profiles (solid line).
Each panel shows the 777 nm triplet lines at disk-centre and |
Open with DEXTER |
4.1.4
Effect of blends and electron collisions on the inferred
and abundances
There are a few weak CN and C lines in the
777 nm region. The VALD database also lists some weak atomic
lines. Most of these lines are very weak and their effect on the
O I lines negligible. At
disk-centre the known blends
of the O I lines are very
faint, and their effect on the abundance obtained by profile fitting is
negligible. But as molecular lines get stronger at the higher layers
probed by the limb spectra, it is important to determine whether they
have any effect on the inferred
.
To investigate for such effects, we computed the spectra of O I 777 nm
over a larger spectral region including additional molecular and atomic
lines, with data from Sauval (2008, private communication). Our testing
showed that the blends have very little influence on the
derived
value. Because the atomic and molecular data for these weak blending
lines is not known accurately, they have not been included in our main
analysis.
We also investigated the effect of computing the O I lines
simultaneously. Their wings are very extended and overlap, especially
in LTE and for 777.41 and 777.53 nm. For LTE at
disk-centre, computing the three O I lines
simultaneously caused a reduction of 0.002 dex in the fitted
oxygen abundance of 777.41 nm line. At the limb there
is virtually no difference between computing the lines separately or
together, because the lines are much weaker. For the same line
strength, the LTE profiles have the most extended wings when
compared with NLTE (the extent of the wings gets smaller with
smaller ),
so the issue of overlapping wings gets more important for the LTE
profiles.
Our single-line approximation is thus fully justified.
We used the revised electron collision data of Barklem (2007). Although this
data is believed to be the most accurate currently available, it is
important to check to what extent our empirically estimated
depends on the adopted electron collision rates. To assess this effect,
we performed several tests by artificially changing the electron
collisions. Due to time constraints, these tests were performed in
1D models, although they were confirmed with a few
3D runs. An interesting find is that, if the electron
collision rates are artificially decreased, the best-fitting
value
is still the same (even if we neglect electron collisions altogether).
Obviously the fitted abundance values will differ (especially for
), but the
best fitting value remains the same. This result indicates that
H I collisions are more
important than electron collisions in the centre-to-limb variation of
the lines, because the electron pressure decreases more quickly with
height. On the other hand, if the electron collision rates are
increased by one order of magnitude, it will change the best-fitting
value.
This makes sense, as an increase in the collisions from electrons will
shift the result more towards LTE, regardless of the
used.
![]() |
Figure 7:
Reduced |
Open with DEXTER |
4.2 [O I] 630.03 nm and Ni I blend
4.2.1 Context
Although the forbidden O I line at
630.03 nm is the strongest of the [O I] lines,
it is still very weak in the Sun. Unlike the permitted lines, LTE is a
very good approximation in the formation of the [O I] line
(see Asplund et al. 2004).
Accordingly, we only use the synthetic LTE profiles in the
following analysis. As a weak line it is highly susceptible even to
faint blends. In particular, it is blended with an Ni I
feature at 630.0335 nm (Johansson et al. 2003;
Allende Prieto
et al. 2001; Lambert 1978). For the Sun,
the contribution of the Ni I
component to the blend is about 30%, depending on the
Ni abundance used. With such a significant blend, it is
paramount to properly account for the Ni contribution. This
work is similar to the work of Allende
Prieto et al. (2001, hereafter ALA01), which
included an analysis of [O I] 630.03 nm
with a 3D model (albeit an earlier version), but for the flux
profile instead of intensity at different
values; also Caffau et al.
(2008) and Ayres (2008)
has performed similar studies using a different 3D model.
4.2.2 Ni I blend
Properly accounting for the Ni I
blend means one needs to know its properties with high precision. Johansson et al. (2003)
measured the
for this Ni I transition to
be -2.11. Because of the presence of several Ni isotopes and
their isotopic splitting, the Ni contribution at 630.03 nm is
given as a series of blends. In our treatment we included the five most
abundant Ni isotopes, scaling the
by their isotopic abundance (see Table 4). We used a
fixed Ni abundance of
,
as inferred from other Ni lines using the present
3D model (Asplund
et al. 2009).
Table 4:
Ni I isotopes used and scaled
values.
An important difference between the present work and ALA01 was
the treatment of the Ni I blend. We
used a fixed Ni abundance of 6.22 and adopted the
measured
of -2.11, whereas at the time of ALA01 there was no
experimental
,
and Ni was treated as a free parameter. Their best-fitting
is equivalent to an Ni abundance of 6.05 with the present
value of
,
less than the Ni abundance we used. In ALA01, the blend of the
O I and Ni I
was done by co-adding the individual flux profiles for the different
species. Because these are very weak lines, that was a reasonable
approximation. However, the approximation of co-adding the profiles
starts to break down as one looks at profiles of lower
values, where the difference between co-adding and a proper treatment
of the blend (summing the opacities for each component) can amount to a
few percent of the equivalent width. In this work we opted to treat the
blend properly, instead of co-adding the profiles.
4.2.3 Wavelength calibration
Another important point in the treatment of this line is the wavelength calibration. As Ayres (2008) notes, the balance between the components of the blend is sensitive to velocity errors of a few hundred m s-1, or a few mÅ. If the wavelength calibration translates the line to be blueshifted from its ``true'' location, the fitting will favour a higher oxygen abundance. There is a degeneracy between the wavelength shift and the Ni abundance, which makes it difficult to determine the best-fitting values when both are allowed to vary.
Unfortunately, the absolute wavelength calibration of neither
our observations nor the FTS atlas is precise enough for the analysis
of this blend, so we adopt a correction to the laboratory wavelength
similar to that of Ayres (2008):
using strong Fe I lines in
the neighbourhood to find the wavelength difference between the 3D
model and the observations. By measuring the wavelength difference
between the synthetic profiles and the observations for a set of
reference Fe I lines, one
can effectively put the profiles on the same ``laboratory'' wavelength
scale. This approach has the advantange of removing the systematics
associated with the observations (e.g. solar rotation) and any
shortcomings in the 3D model (e.g. overshooting of convective
blueshifts). We chose the three Fe I lines
at 629.77, 630.15, and 630.24 nm - because they were
available in the limited wavelength window of our observations - to
calibrate the wavelength scale. To measure the wavelength difference we
fit the theoretical 1D and 3D line profiles of these
Fe I lines and allow a
wavelength shift of the observations as a free parameter. The mean
wavelength shift from the three lines was extracted for line profiles
at all the solar disk positions of our observations. The standard
deviation between the shifts from the three Fe I lines
were 19, 27, 33, 51, 140 m s-1
for ,
respectively. Except for the
measurement, the numbers are an encouraging sign of how precise the
wavelength calibration is. For the observations at
,
we adopted the wavelength shift as given by the Fe I 629.77 nm
line because of the scatter between Fe I line
indicators.
If the wavelength shift of the synthetic line profile was
allowed to be a free parameter in the fit, then the best-fitting shift
to the FTS intensity atlas is very close (<
)
to the fixed shift obtained by the Fe I line
procedure. Its effect on the derived abundance is thus small
(<0.01 dex). Even if one accounts for some uncertainty
around the wavelength shift, the effects on the oxygen abundance are
weak. A relatively large variarion of (
)
around the used waveshift for the FTS intensity atlas has an effect on
the oxygen abundance of
dex,
although the agreement with the observed profile deteriorates
significantly. These variations in the oxygen abundance are much
smaller than the ones found by ALA01 when trying different shifts. The
difference stems likely from our keeping the nickel abundance fixed,
while ALA01 allowed it to be a free parameter in the fit. With nickel
fixed, the fitting procedure cannot compensate with more or less
nickel, which means that the line shifting has less effect on the
oxygen abundance.
Besides the absolute wavelength calibration of the
observations, there is also the problem of the uncertainties in the
laboratory wavelengths for the oxygen and nickel transitions. The total
uncertainty in the wavelength difference between the lines is approx. 0.236 pm,
being
0.2 pm
for [O I] (Eriksson 1965) and
0.125 pm
for Ni I (Johansson et al. 2003),
weighted by the isotopes. We tested the line-profile fitting for the
lines using the two extreme cases of wavelength differences allowed by
the errors and found that its effect on the derived oxygen abundance is
negligible (<0.01 dex). Once again, this value is less
than the 0.05 dex found by ALA01, because we do not have the
nickel abundance as a free parameter.
4.2.4 Continuum level and fitting range
The local continuum of the [O I] +
Ni I line wings is slightly
depressed by the nearby Fe I and
Si I lines, and also by 70 weak
CN lines between 630.00-630.06 nm, as noted by ALA01.
To account for this effect, we multiplied each set of observations by a
factor C. For the FTS intensity, atlas C=1.0054
was used. It is important to note that the determination of this local
continuum is a major source of the total uncertainty. If, for example,
one took just the FTS intensity atlas's continuum and computed the
equivalent width for this line, the equivalent width would be
30% higher.
Care was taken in determining the local continuum for our observations,
but one should keep the uncertainty attached to it in mind.
Another important but seldom discussed point in the profile fitting is the wavelength range for fitting the profile. ALA01 did the profile fitting in the range 630.015-630.04 nm, others are not as explicit. Ideally one would like to perform the profile fitting in as broad as possible a range to include the maximum amount of information about the line. The presence of blends, especially unknown features, forces one to narrow the fitting range to avoid the influence on the fit of features not included in the line synthesis. We adopted the same wavelength range as ALA01, as it avoids several weak blends but includes most of the [O I] line.
4.2.5 Comparison with observations
![]() |
Figure 8:
Synthetic line profiles (solid lines) for the O I+Ni I
630.03 nm blend vs. observations (circles). Shaded regions
indicate the range over which the profiles were fitted. Left
panels: fit for FTS Intensity atlas, done over the wavelength
range of Allende-Prieto et al. (2001). Middle panels:
fit for our observations, disk-centre. Right panels:
our observations at |
Open with DEXTER |
The line profiles for the [O I] +
Ni I blend were computed for a
fixed
and assuming LTE. In the fit for this line profile we only
allowed one free parameter: the oxygen abundance. The waveshift for
each position was obtained by the Fe I lines
method, and the local continuum multiplication factor C
obtained empirically, as noted above.
We present the results for the equivalent width analysis over
the observed positions in the solar disk, the profile fitting of our
observations at ,
and the FTS intensity atlas for comparison with other studies. Some
results from line fitting are in Fig. 8, and the
equivalent width results are in Fig. 9. Fitting the
line profile to the FTS intensity atlas we obtain an oxygen abundance
of
,
while we obtain 8.64for our observations at
.
In the variation of equivalent width with
in Fig. 9,
one can see that the 3D model predicts a slightly stronger line
as
decreases. In terms of fitting the line profiles for different
,
the variation in fitted abundance for the 3D model is never
more than 0.02 dex for the disk-centre abundance. In the
rightmost column of Fig. 8, we plot
the observations at
with a synthetic profile using the oxygen abundances derived from the
disk-centre fits (our observations), the continuum level adjusted
independently. The 3D model at
is slightly stronger than the observations, and the line profile is
slightly wider and not as deep as the observations. Still, in terms of
best-fitting abundance, the difference is minimal.
![]() |
Figure 9:
Equivalent width vs. |
Open with DEXTER |
For the 1D models we applied the same wavelength correction with
Fe I lines, repeating the procedure
for line profiles synthesized with the 1D Holweger-Müller and MARCS
models. The best-fitting macroturbulence was also extracted from these
Fe I lines and then used
for [O I] + Ni I.
The Holweger-Müller (HM) model does a good job describing the line
strengths, as shown by the equivalent widths in Fig. 9. However, a
closer inspection of the line profiles shows a red wing that is too
strong. This may possibly indicate an excess of nickel:
was used for this model, as derived with the same model using other Ni
lines. Looking at Fig. 8, in
particular at the residuals, it is clear that the agreement is not as
good as for the 3D model. This is expected, because the
1D models do not reproduce the convective motions in the
photosphere realistically (unlike the 3D model), even when
using micro and macroturbulences. In particular for the HM at
,
the macroturbulence derived from the Fe I lines
is probably low, as the line profile is noticeably deeper than the
observations, while the equivalent widths are very similar. For the MARCS
model, the trend in equivalent width vs.
is different. The model predicts slightly weaker line strengths than
the observations. The fitted line profiles at disk-centre also indicate
an excess of intensity in the red wing. The line profile at
low
with the disk-centre abundance shows a slightly weaker line than the
observations. The oxygen abundances from profile fitting with the FTS
disk-centre atlas for the HM and MARCS models
were, respectively, 8.69 and 8.66.
![]() |
Figure 10:
Synthetic LTE line profiles for the O I
615.81 nm lines (including blends from Fe I,
one C |
Open with DEXTER |
4.2.6 Comparison with previous work
An easy comparison to be made is with ALA01. Some things have been done differently in the present study. We computed a proper blend of the two transitions (adding line opacities), instead of computing separate line profiles for each line and co-adding them. We also performed a more precise wavelength calibration using Fe I lines. And finally, we employed a more recent 3D model and a higher Ni abundance. Fitting the flux profiles against the FTS flux atlas and using the same fitting range in ALA01, we obtained an oxygen abundance 0.07 dex lower. The reason for this difference is mainly the higher Ni abundance used (6.22 vs. 6.05), which translates to a
Fitting the line profiles with
instead of 6.05 leads to closer agreement with the observed disk-centre
profile (
), but worse
agreement for the observed flux profile (
).
4.3 O I 615.81 nm
4.3.1 Context
The O I 615.81 nm line is
a triplet, with components at 615.8149, 615.8172, and
615.8187 nm, according to the NIST database. The last is the
strongest component. The components are so close that they are
unresolved in the solar spectrum. Its position in the solar spectrum is
far from optimal. The line is close to a strong (4.8 pm)
Fe I line at
615.77 nm, and there are multiple weak blends around. The VALD
database lists several atomic lines in this region, but besides the
strong Fe I line, only the
Nd II 615.782 nm,
Ni I 615.800 nm,
and Fe I 615.803 nm
lines have any measurable effect, though they are still just barely
noticeable. Spectral synthesis using only these lines is still not
enough to explain the solar spectrum. However, there seem to be several
molecular lines in this region. These are mostly CN lines,
with a few C
lines.
The molecular lines are important for our analysis, and their effect is
discussed below. It should be noted that, even accounting for the
molecules, there are still unidentified features in this spectral
region, most notably the feature at around 615.793 nm.
The presence of these blends depresses the continuum level
around the O I lines, so that it
becomes a significant source of uncertainty. Our analysis, whether
computing the equivalent widths from the observations or fitting the
line profiles, suffers from the same problems. For example, if one
assumed this oxygen line has no blends and takes the continuum level of
the FTS disk-centre intensity atlas, then the equivalent width could be
up to
higher than our estimate for the oxygen-only contribution. This effect
is amplified as one looks at spectra closer to the limb because the
different blends vary differently in strength over the solar disk,
which makes a precise determination of the continuum level difficult.
Unlike the stronger O I 777 nm
triplet, the predicted NLTE effect is rather weak for the O I 615.8 nm lines:
Asplund et al. (2004)
predict it to be -0.03 dex when neglecting H I collisions.
4.3.2 Wavelength calibration
A similar approach to the wavelength calibration of [O I] 630.03 nm was used. Because a precise wavelength calibration for this line is not as crucial as [O I], we derived the wavelength calibration using only the nearby Fe I 615.77 nm line. It is important to make the wavelengths of the O I consistent with this Fe I line because they lie on its red wing, and a different wavelength difference between them would imply either a lower or higher blend influence.
By using the reference laboratory wavelengths from the NIST
database for the Fe I
615.77 nm and O I 615.81 nm
lines and calibrating with the waveshift of Fe I
lines, the synthetic O I profiles
are shifted from the observations. This can be seen in the left panels
of Fig. 10.
The 3D synthetic profile is blueshifted relative to the
observations, while the opposite happens for the 1D models.
None of them matches the observations perfectly. For the
3D case, the shift to the observations is about ,
or 1.8 pm. This could mean that there is a significant error
in the laboratory wavelengths, the predicted line shifts from the
3D models are inconsistent for the Fe I
and O I lines, or there
are blending features causing a shift in the profile. Including known
molecular and weak atomic lines is not the explanation. In the top
middle panel of Fig. 10
we artificially shifted the O I lines,
so that the synthetic profile matches the FTS intensity atlas.
For the rest of the analysis, we use these artificially shifted
profiles (both for 3D and 1D models), but the derived
abundance from fitting the disk-centre profiles remains essentially the
same if the profiles are not shifted (but as seen in Fig. 10, the
agreement with the observations is worse). The results for the
equivalent widths are not affected by this shift.
Table 5: Molecular lines included in the 615.8 nm region.
4.3.3 Molecular blends and comparison with observations
We included several CN and C
lines in the 615.8 nm region (Sauval 2008, private
communication). The line data are given in Table 5. These data
were obtained from from Sauval (2008, private communication). The
molecular line data is uncertain, especially wavelengths for
CN lines. With this uncertainty in mind, we adjusted some of
the wavelengths and
of the CN lines from Table 5. The two
(9, 4) band lines at 615.8522 and 615.8796 nm were
redshifted by 7.2 and 11.6 pm, respectively, so that
they match two features in the solar disk-centre spectrum. Furthermore,
the
values
of these two lines have been increased so that they fit the observed
features reasonably. For consistency the
values of the three other CN lines have been increased by the
same amount. For the 3D model this increase in
amounts to 0.35 dex, and we note that CN lines from
different bands do not necessarily require the same correction in
abundance or
.
However, we used the same
correction because the data for the different CN lines have
similar uncertainties. Additionally, the (10, 4) band line at
615.8223 nm has also been redshifted by 9.3 pm. As
detailed below, the inclusion of molecules is paramount for
understanding the solar spectrum at the limb.
Our synthetic profiles included a total of ten blends: the
three O I lines, the
strong Fe I line, and the
molecular lines outlined above. There are other atomic lines in the
region, not included because they are very weak.
The profile fits in Fig. 10 include
all these blends. In the lower left panel of Fig. 10 is shown
the synthetic spectrum of only O I
and Fe I compared with the
molecules, at the disk-centre and limb. At 10.741 eV, the
oxygen lines have a high excitation energy, making them very weak at
the higher layers of the atmosphere probed by the limb spectra when
compared to disk-centre. The molecules, on the other hand, are formed
in cooler regions and are thus significantly stronger at the limb than
at disk-centre. As is visible in the figure, at disk-centre the
molecules blended with oxygen have a very small contribution to the
total line strength, yet at the limb most of the line strength comes
from molecules. This type of blending can explain the observations
well. As seen in the top right panel of Fig. 10, the line
profile shape and strength using the oxygen abundance fitted at
disk-centre is very close to the observed profile.
Because the molecular lines to the blue of the oxygen line dominate at
the limb, the line centre is significantly blueshifted as is also
confirmed by the observations. (The wavelength calibration using the
strong Fe I line proved
important to establish this.) Furthermore, the variation in equivalent
width in Fig. 11
is another confirmation that models including the molecules reproduce
the observations satisfactory.
![]() |
Figure 11:
Equivalent width vs. |
Open with DEXTER |
![]() |
Figure 12:
Centre-to-limb variations of line equivalent widths. The 1D models were
computed with a microturbulence of |
Open with DEXTER |
The fitted oxygen abundances with the disk-centre FTS atlas were
(3D model), 8.72 (1D HM), 8.61 (1D MARCS).
For our own observations at disk-centre the abundance values were
higher by about 0.05 dex, difference that can be attributed to
the difficulty finding the continuum level. The carbon and nitrogen
abundances used to compute the molecular abundances were different for
the 3D and 1D models and consistent with the abundances
derived from each model from other molecular features. For 1D models
the macroturbulence was derived from nearby Fe I
lines, and a microturbulence of
was used.
The molecular blends can help to explain the centre-to-limb
variation in this spectral region. As seen in Fig. 11,
both 1D and 3D models can explain the variations
similarly well (although the fitted abundances at disk-centre vary).
However, the uncertainty of the molecular line data and the wavelength
shift of oxygen make this agreement less convincing. These
uncertainties do not allow us to reliably test the line formation
across the solar disk and the effects of different models. As for
O I 777 nm, we
also experimented with NLTE effects and different .
But for the 615 nm lines the NLTE effects are so weak
that with all the mentioned uncertainties, it is not possible at this
time to extract any reliable conclusions about, for example, the
H I collisional efficiency.
4.4 Lines from other species than O I
In Fig. 12 we present the centre-to-limb variation of the equivalent width for a few other lines than oxygen included in our observations. The properties of these lines are listed in Table 2. Nearby blends have been included for the Si I 615.57 nm and Ca I 616.60 nm. Their wings influence each other, so both of them have been included in each of their line profiles, as is a nearby strong Si I line at 615.51 nm. For the Ca I 616.60 nm line, we also include the very weak O I triplet at 615.60 nm, which influences the line slightly. Data for all the extra blending lines were extracted from the VALD database.
While the agreement between the 3D model and the lines in
Fig. 12
is generally worse than for the oxygen lines, it is in most cases an
improvement over the 1D models. For most of the Fe I
lines the 1D models predict a much weaker line at the limb, while the
3D model prediction usually follows the observations. What happens with
the Sc II 630.06 nm
is very similar with the figure for [O I]
630.03 nm. This is probably because this line of a ionized
rare element is not very sensitive to the local temperature. In the
case of Si I 615.57 nm,
blends are likely to influence the behaviour of the line. This line is
in a relatively crowded spectral region. For Fe I
615.93 nm from
to the limb the 1D models predict a decrease in line strength, while
the 3D model predicts an increase. The observations in this case seem
to follow neither and maintain a constant line strength. But it should
be noted that weak blending features on the wings of Fe I 615.93 nm
make the continuum level difficult to determine, hence the big
uncertainties in equivalent width. The Fe I 629.77
and 615.16 nm lines have a similar variation
with
,
which is reasonably reproduced by the 3D model while the
1D models show larger discrepancies and the wrong trend
with
.
At this time we refrain from drawing conclusions about NLTE effects in these lines. However, these may be addressed in the future if there is enough atomic data for these atoms.
5 Conclusions
The study of oxygen lines at different positions in the solar disk has
proven very fruitful. From departures of LTE to constraints in blends
and line data, the detailed line profiles for different values
give us a wealth of new information. The relevance of these tests is to
ascertain whether the temperature structure of the models can
reasonably explain the formation of these lines, and so can be
considered reliable for inferring the much debated solar oxygen
abundance. Although for abundance analysis the FTS atlases should be
the preferred choice, given their superior resolution and S/N,
our high-resolution spectra have proven decisive in identifying the
shapes and variations of lines and blends over a range of formation
temperatures.
Using detailed 3D NLTE radiative transfer, we computed the
level populations and synthetic profiles for oxygen lines. The
O I 777 nm
triplet is of particular interest. These lines suffer from NLTE
effects, the size of which is determined by inelastic collisions with
electrons and neutral hydrogen. Because of the lack of analytical or
experimental data regarding the efficiency of the neutral hydrogen
collisions, one has to treat it almost as a free parameter, which the
centre-to-limb variation of the lines helps for getting an empirical
estimate. In a similar approach to AAF04, we determined the empirical
value for the multiplication factor of the classical recipe for
hydrogen collisions, .
For the 3D model and the 1D Holwer-Müller model, the best fit is for
.
For the 3D model used by AAF04, we find a lower value. These
differences illustrate the model dependency of the centre-to-limb
derivation of
.
The 1D MARCS model does not even
reproduce the observed equivalent widths with any value of
.
A more decisive test of the 3D and other models for the
O I 777 nm lines will have
to wait until better data for hydrogen collisions is available.
Nevertheless, finding an
that describes the observations provides a self-consistent way of
determing the extent of the NLTE effects and to extract a reliable
value for the oxygen abundance. As seen in Table 3, the oxygen
abundance varies quickly with the chosen
,
especially for
,
making a self-consistent estimate of the hydrogen collisions of
paramount importance. The last remaining discrepancy with the
empirical
approach is that the best-fitting NLTE profiles at disk-centre are
slightly narrower and deeper than the observed. It is not clear that
this discrepancy can be improved on the model side or whether it is a
consequence of using the classical Drawin
(1968) formulæ.
The weak 615.81 nm O I line
also shows departures from LTE, albeit on a much smaller scale than the
777 nm counterparts. Unfortunately the weakness of the NLTE
effects and the presence of blends make it very difficult to
estimate
from the centre-to-limb variation of this line. When looking at the
line profiles, especially as one gets closer to the limb, we find a
line blueshift and strength that are inconsistent with the synthetic
spectra, when only oxygen is considered. With a high excitation energy,
synthetic models indicate that at the limb the oxygen line should be
much weaker than observed. However, if one includes a few molecular
blends present in the region, the line strength and blueshift effects
can almost be reproduced perfectly in the synthetic spectra. At the
limb the molecules blended with the oxygen are stronger than the oxygen
contribution. Uncertainties in the input data for the molecular lines
and continuum placement errors in the observations mean that the
results are not precise enough to discern between the different
for the weak NLTE effects.
Blends also play a determinant role in the [O I]
630.03 nm line. The unresolvable blend with Ni in
this line has been a major source of uncertainty in an otherwise good
indicator for the oxygen abundance (formed in LTE, relatively
independent of temperature). A good knowledge of the Ni I line
properties is essential. For that we use the recent measurement of its value
(Johansson et al. 2003)
and the recent determination of the nickel abundance for the 3D model (Asplund et al. 2009).
Establishing the correct contribution of nickel in the blend will not
guarantee a correct determination of the oxygen abundance. Because the
oxygen and nickel lines are so close together, a shift in their
wavelengths will affect the inferred oxygen abundance, because the
fitting procedure will compensate for the quantity of oxygen that best
matches the observations. It should be noted that because the nickel
abundance is kept fixed, the effect of the wavelength shift on the
oxygen abundance is not as significant as if it was allowed to vary
(e.g., ALA01): we estimate it to be less than 0.02 dex. In any
case, for this line, allowing a wavelength shift in the fitting is not
desirable, and a precise absolute wavelength calibration must be
obtained. Ayres (2008)
makes use of Fe I lines to
calibrate the wavelength scale, as the FTS atlas by itself is not
precise enough. In this work we used a similar approach of calibration
using Fe I lines to ensure
the accuracy of the results. The line profile fits for the FTS
intensity atlas using the 3D model agree remarkably between
model and observations, with less than 0.2% difference for
most of the line profile. Since it is not very sensitive to
temperature, this line displays a small centre-to-limb variation in
strength. Even with the observational uncertainties inherent in such a
weak line, we can see that the 3D model provides a very good
description of the observations. This agreement gives us confidence in
the 3D model, confirming its robustness at inferring the
oxygen abundance from this line.
Overall, we find that the 3D model reproduces the observations very well. Despite its one-dimensional nature not allowing for the most accurate shape of the observed profiles, the Holweger-Müller model also reproduces the observed equivalent widths, which is not surprising because it is semi-empirical. The 1D theoretical MARCS model falls short of its description of centre-to-limb variation of the O I 777 nm and [O I] 630.03 nm lines, probably because its temperature structure departs from the solar temperature structure.
Using the best fitting
and abundance results from disk-centre line profile fits, we infer an
oxygen abundance of 8.68 for the 3D model using the
777 nm lines. This value can be compared to the value
of 8.66 derived from the [O I]
630.03 nm line and the value of 8.62 derived from the
O I 615.82 nm
line (dependent on the assumed strength of the molecular lines). The
good performance of the 3D model in reproducing not only the
observed line shapes and shifts, but also the centre-to-limb variation
of the oxygen lines, is a good indicator of the quality of the inferred
abundances.
We would like to thank N. Grevesse and J. Sauval for fruitful discussions and for use of the molecular line database. T.M.D.P. acknowledges financial support from Fundação para a Ciência e Tecnologia (reference number SFRH/BD/21888/2005) and from the USO-SP International Graduate School for Solar Physics under a Marie Curie Early Stage Training Fellowship (project MEST-CT-2005-020395) from the European Commission. This research was partly funded by a grant from the Australian Research Council (DP0558836). The Swedish 1-m Solar Telescope is operated on the island of La Palma by the Institute for Solar Physics of the Royal Swedish Academy of Sciences in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias.
References
- Allende Prieto, C., Lambert, D. L., & Asplund, M. 2001, ApJ, 556, L63 [NASA ADS] [CrossRef] (ALA01)
- Allende Prieto, C., Asplund, M., & Fabiani Bendicho, P. 2004, A&A, 423, 1109 [NASA ADS] [EDP Sciences] [CrossRef] (AAF04)
- Altrock, R. C. 1968, Sol. Phys., 5, 260 [NASA ADS] [CrossRef]
- Anders, E., & Grevesse, N. 1989, Geochim. Cosmochim. Acta, 53, 197 [NASA ADS] [CrossRef]
- Anstee, S. D., & O'Mara, B. J. 1995, MNRAS, 276, 859 [NASA ADS]
- Asplund, M., Nordlund, Å., Trampedach, R., Allende Prieto, C., & Stein, R. F. 2000, A&A, 359, 729 [NASA ADS]
- Asplund, M., Carlsson, M., & Botnen, A. V. 2003, A&A, 399, L31 [NASA ADS] [EDP Sciences] [CrossRef]
- Asplund, M., Grevesse, N., Sauval, A. J., Allende Prieto, C., & Kiselman, D. 2004, A&A, 417, 751 [NASA ADS] [EDP Sciences] [CrossRef]
- Asplund, M., Grevesse, N., Sauval, J., & Scott, P. 2009, ARA&A, 47, 481 [CrossRef]
- Ayres, T. R. 2008, ApJ, 686, 731 [NASA ADS] [CrossRef]
- Barklem, P. S. 2007, A&A, 462, 781 [NASA ADS] [EDP Sciences] [CrossRef]
- Barklem, P. S., & O'Mara, B. J. 1997, MNRAS, 290, 102 [NASA ADS]
- Barklem, P. S., O'Mara, B. J., & Ross, J. E. 1998, MNRAS, 296, 1057 [NASA ADS] [CrossRef]
- Barklem, P. S., Belyaev, A. K., & Asplund, M. 2003, A&A, 409, L1 [NASA ADS] [EDP Sciences] [CrossRef]
- Botnen, A. 1997, Master's thesis, Inst. Theor. Astrophys. Oslo (1997)
- Brault, J. W., & Neckel, H. 1987, ftp://ftp.hs.uni-hamburg.de/pub/outgoing/FTS-Atlas
- Byrd, R. H., Lu, P., & Nocedal, J. 1995, SIAM Journal on Scientific and Statistical Computing, 16, 1190 [CrossRef]
- Caffau, E., Ludwig, H.-G., Steffen, M., et al. 2008, A&A, 488, 1031 [NASA ADS] [EDP Sciences] [CrossRef]
- Centeno, R., & Socas-Navarro, H. 2008, ApJ, 682, L61 [NASA ADS] [CrossRef]
- Cunto, W., Mendoza, C., Ochsenbein, F., & Zeippen, C. J. 1993, A&A, 275, L5 [NASA ADS]
- Drawin, H. W. 1968, Zeitschrift fur Physik, 211, 404 [NASA ADS] [CrossRef]
- Eriksson, K., & Toft, S. C. 1979, A&A, 71, 178 [NASA ADS]
- Eriksson, K. B. S. 1965, Ark. Fys., 30, 199
- Gustafsson, B., Edvardsson, B., Eriksson, K., et al. 2008, A&A, 486, 951 [NASA ADS] [EDP Sciences] [CrossRef]
- Holweger, H., & Müller, E. A. 1974, Sol. Phys., 39, 19 [NASA ADS] [CrossRef]
- Hummer, D. G., Berrington, K. A., Eissner, W., et al. 1993, A&A, 279, 298 [NASA ADS]
- Johansson, S., Litzén, U., Lundberg, H., & Zhang, Z. 2003, ApJ, 584, L107 [NASA ADS] [CrossRef]
- Kiselman, D. 1993, A&A, 275, 269 [NASA ADS]
- Kiselman, D., & Nordlund, Å. 1995, A&A, 302, 578 [NASA ADS]
- Kupka, F. G., Ryabchikova, T. A., Piskunov, N. E., Stempels, H. C., & Weiss, W. W. 2000, Baltic Astron., 9, 590 [NASA ADS]
- Lambert, D. L. 1978, MNRAS, 182, 249 [NASA ADS]
- Lambert, D. L. 1993, Phys. Scr. T, 47, 186 [NASA ADS] [CrossRef]
- Meléndez, J., & Asplund, M. 2008, A&A, 490, 817 [NASA ADS] [EDP Sciences] [CrossRef]
- Müller, E. A., Baschek, B., & Holweger, H. 1968, Sol. Phys., 3, 125 [NASA ADS] [CrossRef]
- Nave, G., Johansson, S., Learner, R. C. M., Thorne, A. P., & Brault, J. W. 1994, ApJS, 94, 221 [NASA ADS] [CrossRef]
- Nissen, P. E., Primas, F., Asplund, M., & Lambert, D. L. 2002, A&A, 390, 235 [NASA ADS] [EDP Sciences] [CrossRef]
- Pereira, T. M. D., Kiselman, D., & Asplund, M. 2009, A&A, 507, 417 [EDP Sciences] [CrossRef] (Paper I)
- Piskunov, N. E., Kupka, F., Ryabchikova, T. A., Weiss, W. W., & Jeffery, C. S. 1995, A&AS, 112, 525 [NASA ADS]
- Ralchenko, Y., Kramida, A., Reader, J., & NIST ASD Team. 2009, NIST Atomic Spectra Database (version 3.1.5), http://physics.nist.gov/asd3
- Rosman, K. J. R., & Taylor, P. D. P. 1998, Pure Appl. Chem., 70, 217 [CrossRef]
- Scott, P., Asplund, M., Grevesse, N., & Sauval, A. J. 2009, ApJ, 691, L119 [NASA ADS] [CrossRef]
- Socas-Navarro, H., & Norton, A. A. 2007, ApJ, 660, L153 [NASA ADS] [CrossRef]
- Steenbock, W., & Holweger, H. 1984, A&A, 130, 319 [NASA ADS]
- Storey, P. J., & Zeippen, C. J. 2000, MNRAS, 312, 813 [NASA ADS] [CrossRef]
- Unsöld, A. 1955, Physik der Sternatmospharen, MIT besonderer Berucksichtigung der Sonne (Berlin: Springer)
Footnotes
- ...
abundance
- SST spectra are available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/508/1403
- ... blends
- There are a few unknown blends visible in the disk-centre spectrum. Most notably, the feature at the ``knee'' of the wing of the 777.19 nm line. Their effects in the fit were minimized by limiting the profile-fitting region to parts not visibily affected by blends.
- ... profile
- The oxygen abundance was the only adjusted parameter in the disk-centre fit, and all other lines have the same abundance and parameters throughout the analysis.
All Tables
Table 1:
Equivalent widths for the lines included in this analysis, as a
function of .
Table 2: Lines studied in the present work and their parameters.
Table 3:
Derived disk-centre oxygen abundances (
)
from from the 3D model.
Table 4:
Ni I isotopes used and scaled
values.
Table 5: Molecular lines included in the 615.8 nm region.
All Figures
![]() |
Figure 1: Observed profiles at disk-centre and limb. For the weak 615.81 and 630.03 nm lines the location is indicated. In this figure the wavelengths for the limb spectra have been adjusted to compensate for solar rotation and other systematics. |
Open with DEXTER | |
In the text |
![]() |
Figure 2:
Equivalent width vs. |
Open with DEXTER | |
In the text |
![]() |
Figure 3: Comparison of the mean temperature structure of the new 3D model used in this work and the former 3D model of Asplund et al. (2000), plotted against the optical depth at 500 nm. |
Open with DEXTER | |
In the text |
![]() |
Figure 4:
Top panels: equivalent width vs. |
Open with DEXTER | |
In the text |
![]() |
Figure 5: Same as Fig. 4 but for the 1D models and only for the O I 777.41 nm line. |
Open with DEXTER | |
In the text |
![]() |
Figure 6:
Our observations (dots) and 3D synthetic line profiles (solid line).
Each panel shows the 777 nm triplet lines at disk-centre and |
Open with DEXTER | |
In the text |
![]() |
Figure 7:
Reduced |
Open with DEXTER | |
In the text |
![]() |
Figure 8:
Synthetic line profiles (solid lines) for the O I+Ni I
630.03 nm blend vs. observations (circles). Shaded regions
indicate the range over which the profiles were fitted. Left
panels: fit for FTS Intensity atlas, done over the wavelength
range of Allende-Prieto et al. (2001). Middle panels:
fit for our observations, disk-centre. Right panels:
our observations at |
Open with DEXTER | |
In the text |
![]() |
Figure 9:
Equivalent width vs. |
Open with DEXTER | |
In the text |
![]() |
Figure 10:
Synthetic LTE line profiles for the O I
615.81 nm lines (including blends from Fe I,
one C |
Open with DEXTER | |
In the text |
![]() |
Figure 11:
Equivalent width vs. |
Open with DEXTER | |
In the text |
![]() |
Figure 12:
Centre-to-limb variations of line equivalent widths. The 1D models were
computed with a microturbulence of |
Open with DEXTER | |
In the text |
Copyright ESO 2009
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.