Issue |
A&A
Volume 519, September 2010
|
|
---|---|---|
Article Number | A46 | |
Number of page(s) | 10 | |
Section | Stellar atmospheres | |
DOI | https://doi.org/10.1051/0004-6361/201014397 | |
Published online | 10 September 2010 |
Galactic evolution of oxygen
OH lines in 3D hydrodynamical model atmospheres
J. I. González Hernández1,2,3 - P. Bonifacio2,3,4 - H.-G. Ludwig2,3,5 - E. Caffau3 - N. T. Behara2,3,6 - B. Freytag7,8
1 - Dpto. de Astrofísica y Ciencias de la Atmósfera, Facultad de
Ciencias Físicas, Universidad Complutense de Madrid, 28040
Madrid, Spain
2 - Cosmological Impact of the First STars (CIFIST) Marie Curie
Excellence
Team http://cifist.obspm.fr, France
3 - GEPI, Observatoire de Paris, CNRS, Université Paris Diderot, Place
Jules Janssen, 92190
Meudon, France
4 - Istituto Nazionale di Astrofisica - Osservatorio Astronomico di
Trieste, via Tiepolo 11, 34143 Trieste, Italy
5 - Zentrum für Astronomie der Universität Heidelberg,
Landessternwarte, Königstuhl 12, 69117 Heidelberg, Germany
6 - Institut d'Astronomie et d'Astrophysique, Université Libre de
Bruxelles, 1050 Bruxelles, Belgium
7 - CRAL,UMR 5574: CNRS, Université de Lyon, École Normale Supérieure
de Lyon, 46 allée d'Italie, 69364 Lyon Cedex 7, France
8 - Istituto Nazionale di Astrofisica - Osservatorio Astronomico di
Capodimonte, via Moiariello 16, 80131 Napels, Italy
Received 10 March 2010 / Accepted 17 May 2010
Abstract
Context. Oxygen is the third most common element in
the Universe. The measurement of oxygen lines in metal-poor unevolved
stars, in particular near-UV OH lines, can provide invaluable
information about the properties of the Early Galaxy.
Aims. Near-UV OH lines constitute an important tool
to derive oxygen abundances in metal-poor dwarf stars. Therefore, it is
important to correctly model the line formation of OH lines,
especially in metal-poor stars, where 3D hydrodynamical models
commonly predict cooler temperatures than plane-parallel hydrostatic
models in the upper photosphere.
Methods. We have made use of a grid of
52 3D hydrodynamical model atmospheres for dwarf stars
computed with the code ,
extracted from the more extended CIFIST grid. The 52 models
cover the effective temperature range 5000-6500 K, the surface
gravity range 3.5-4.5 and the metallicity range
.
Results. We determine 3D-LTE abundance corrections
in all 52 3D models for several OH lines and Fe I lines
of different excitation potentials. These 3D-LTE corrections are
generally negative and reach values of roughly -1 dex (for the
OH 3167 with excitation potential of approximately
1 eV) for the higher temperatures and surface gravities.
Conclusions. We apply these 3D-LTE corrections to
the individual O abundances derived from OH lines of
a sample the metal-poor dwarf stars reported in Israelian
et al. (1998, ApJ, 507, 805), Israelian et al. (2001,
ApJ, 551, 833) and Boesgaard et al. (1999, AJ, 117, 492) by
interpolating the stellar parameters of the dwarfs in the grid of
3D-LTE corrections. The new 3D-LTE [O/Fe] ratio still keeps a similar
trend as the 1D-LTE, i.e., increasing towards lower [Fe/H] values. We
applied 1D-NLTE corrections to 3D Fe I
abundances and still see an increasing [O/Fe] ratio towards lower
metallicites. However, the Galactic [O/Fe] ratio must be revisited once
3D-NLTE corrections become available for OH and Fe lines for a grid of
3D hydrodynamical model atmospheres.
Key words: nuclear reactions, nucleosynthesis, abundances - stars: abundances - stars: Population II - Galaxy: halo - Galaxy: evolution - line: formation
1 Introduction
The metal-poor stars of the Galactic halo provide the fossil record of the early Galaxy's composition. Dwarf halo stars are particularly relevant, because their atmospheres are not significantly altered by internal mixing and provide a unique tracer to constrain Galactic chemical evolutionary models. Oxygen is a key element in this scenario, because it is the most abundant element in stars after H and He. It is produced in the interiors of massive stars by hydrostatic burning and its content is modified during the explosive nucleosynthesis in type II supernovae (SNe) and hypernovae (HNe) and returned into the interstellar medium. On the other hand, iron is created by both type II and type I SN explosions. However, type I SNe progenitors have longer lifetimes, which is why the abundance ratio of [O/Fe I] can be used to constrain the chemical evolution of the Galaxy.
There have been numerous studies of the oxygen abundance in
halo
stars. Despite considerable observational and theoretical efforts, the
trend of [O/Fe] ratio
versus [Fe/H]
is still unclear. The analysis of the forbidden line O I
6300 Å
in giants shows a plateau with [O/Fe
in the
metallicity range
(Barbuy 1988) and
[O/Fe
for
(Cayrel et al. 2004).
A similar behaviour is seen for metal-poor subgiant stars in the range
0.4-0.5,][]gar06.
However, García Pérez et al.
(2006) already noted that by plotting all
measurements from the [OI] line for dwarfs (Nissen
et al. 2002), subgiants
(García Pérez et al. 2006)
and giants (Cayrel et al. 2004),
the picture changes and an
increasing trend [O/Fe] towards lower metallicities clearly appears.
The near infrared (IR) triplet O I
7771-5 Å in metal-poor dwarfs and
subgiants (Abia
& Rebolo 1989; García Pérez et al. 2006; Israelian
et al. 2001) points towards increasing [O/Fe]
values with decreasing [Fe/H], although the O abundances derived from
the near-IR triplet are typically 0.4-0.7 higher than those
derived from the forbidden O I line
(Fulbright & Johnson 2003).
The OH A-X
electronic lines in the near ultraviolet (UV) provide also higher
[O/Fe] ratios towards lower [Fe/H] values in dwarf stars
(González
Hernández et al. 2008; Boesgaard et al. 1999; Israelian
et al. 1998,2001). However, García
Pérez et al. (2006) found a
quasi-plateau of [O/Fe] for subgiant stars in the range
,
using Fe abundances determined from
Fe II lines. The [O/Fe] ratio
shows a negative slope if one instead uses the Fe abundances estimated
from Fe I lines, although
with lower [O/Fe] values than those determined for metal-poor dwarfs.
It is advisable to use Fe I lines
instead of Fe II lines
to derive the [O/Fe] ratio because of its similar sensitivity
to the
surface gravity.
These O-abundance indicators present different complications.
The
near-IR O I triplet is susceptible
to non-local
thermodynamical equilibrium (NLTE) effects
(Kiselman 2001, and references
therein), with abundance corrections
below 0.2 dex, and is quite sensitive to the adopted .
The [OI] is not sensitive to departures from LTE, but it is
essentially
undetectable in dwarfs with
.
The near-UV OH lines are strongly sensitive to the temperature
structure and inhomoginities
(González
Hernández et al. 2008; Asplund & García Pérez 2001).
In addition, Fe I lines suffer
from severe NLTE effects in metal-poor stars (see e.g. Thévenin & Idiart 1999). We
note that
Shchukina et al. (2005)
have performed NLTE computations for the metal-poor
subgiant HD 140283 (
)
with a single
snapshot of a 3D hydrodynamical simulation (Asplund
et al. 1999), and found NLTE-LTE corrections of +0.9
and +0.4 for Fe I
and Fe II lines, respectively.
Finally, the oxygen abundance in the Sun is still a matter of
debate.
We will adopt throughout this work the value of ,
which was determined through
3-dimensional (3D) hydrodynamical models (Caffau
et al. 2008).
We have used a subset of the CIFIST grid of 3D hydrodynamical model atmospheres (Ludwig et al. 2009) to investigate the 3D-LTE and 3D-NLTE [O/Fe] and [O/H] trends in metal-poor dwarf stars.
Table 1:
Details of the 3D hydrodynamical
model atmospheres.
2 3D hydrodynamical simulations
The 3D hydrodynamical model atmospheres
(see Ludwig et al. 2009,
for further details)
were computed with the code
(Wedemeyer
et al. 2004; Freytag et al. 2002). Each
model consists of a
representative set of snapshots sampling the temporal evolution of the
photospheric flow. In Table 1
we provide
a summary of the 3D models used in this paper. The evolutionary time
scale and the spatial scale of the convective surface flows roughly
scale inversely proportional to the surface gravity. Following this
scaling behaviour, we tried to ensure that the duration of each model
sequence corresponds to at least 3600 s of solar-equivalent
time.
Moreover, we also scaled the size of the computational domain leading
to about the same total number of convective cells in each model.
The spatial resolution was typically ,
with a constant grid spacing in the
(horizontal) x- and y-directions
and a variable spacing in z-direction. Our
standard solar model - actually not part of the grid used here, but
mentioned for reference - has a horizontal
size of 5600 km. The total height is 2250 km, from z=-1380 km
below optical
depth unity to z=870 km above, located in
the low chromosphere. The
computational time step was typically 0.1-0.2 s.
![]() |
Figure 1:
3D temperature structure of the 3D |
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The description of the radiative energy exchange is important
for the resulting temperature structure of a model. Here we provide
some
details about the binning-scheme which we applied when modelling the
wavelength dependence of the radiative transfer. The wavelength
dependence is represented by 5 multi-group bins in solar
metallicity
models and 6 bins at sub-solar metallicities following the
procedure originally laid out by Nordlund
(1982) and subsequently
refined by Ludwig
et al. (1994); Vögler et al. (2004);
Ludwig (1992).
For test purposes we calculated a few models with 12 bins.
Different from the original implementation of Nordlund
(1982), the bin-averaged opacities were calculated
explicitely from
the run of the monochromatic opacity within a particular bin. No
scaling among the bins was assumed. The sorting
into wavelength groups was done applying thresholds in logarithmic
Rosseland optical depth
for the 5-bin, and
for the 6-bin schemes. For the 12 bins we used
as thresholds
-0.75, -1.5, -2.25,
;
in addition, each of the first three
continuum-like bins were split into 2 bins according to wavelength
at 550, 600, and 650 nm. In all but one bin a
switching between
Rosseland and Planck averages was performed at a band-averaged
Rosseland optical depth of 0.35; in the bin gathering the
largest line
opacities the Rosseland mean opacity was used throughout. The
decisions about the number of bins, and sorting thresholds are
motivated
by comparing radiative fluxes and heating rates obtained by the binned
opacities in comparison to high wavelength resolution. In
comparison to the models of Asplund
& García Pérez (2001), who worked with
Stein-Nordlund models (Stein &
Nordlund 1998) and used 4 opacity bins, our
treatment of the wavelength dependence of the radiation field puts
extra emphasis on the continuum-forming layers.
![]() |
Figure 2:
Same as Fig. 1
but for the 3D model |
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2.1 3D temperature structure
In Figs. 1
and 2
we depict the temperature
structure of two 3D hydrodynamical simulations for two different
effective temperatures, 5850 and 6270 K, and the same surface
gravity,
,
and metallicity,
.
The main difference between these two 3D models is the temperature
inhomogeneities which are larger in the hotter model.
These strong temperature fluctuations are typically present for
effective temperatures hotter than 5900 K and surface
gravities lower
than 4.
The 3D models displayed in Figs. 1 and 2 show an
overcooling effect in the outer layers of the star with respect
to 1D models. This is particularly
relevant in all models with metallicities [Fe/H]=-3 and -2. 3D
models with metallicities [Fe/H]=-1 and 0 do not show a
pronounced
overcooling effect and the line formation is dominated by the
temperature
fluctuations. We note that the overcooling of the higher photospheric
layers is the dominant 3D effect, but in the deep photosphere,
at ,
3D models are always slightly hotter than a
corresponding hydrostatic 1D model in radiative-convective
equilibrium.
The comparison of 3D versus 1D models depends on
which particular 1D model is
chosen. We compared each of our full 3D models to a
corresponding (in
,
,
and metallicity) standard hydrostatic 1D model
atmosphere (hereafter denoted as 1D
)
and a 1D model
obtained from the temporal and horizontal average of the
3D structure
over surfaces of equal (Rosseland) optical depth (hereafter denoted as
3D
). The 1D
model is calculated
with a 1D atmosphere code called LHD. It assumes plane-parallel
geometry and
employs the same micro-physics (equation-of-state, opacities) as
.
Convection is described by mixing-length theory. See
Caffau et al. (2007)
for further details. Note that the 1D
model depends on the choice of
the mixing-length parameter, the
3D
model on details of the averaging procedure. The temperature of the
3D
model
is indeed obtained by
averaging the fourth power of the 3D temperature field. The
choice was
motivated by the property that this kind of averaging largely preserves
the radiative flux (Steffen
et al. 1995).
We adopted a mixing-length parameter
in
the LHD models. However, this parameter only affects lines that are
formed at optical depth
.
As we will see in the next
section, the OH lines in metal-poor 1D models form at
optical depth
.
We compute the curves of growth of the OH lines and Fe I lines,
for both 1D and 3D models with the spectral synthesis
code Linfor3D.
It is necessary to assume a value of the micro-turbulence for the
spectral synthesis of the 1D models. We have adopted a
= 1
.
![]() |
Figure 3:
Contribution functions to the equivalent width of the OH
3123 Å line computed with |
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2.2 Line formation
In Fig. 3
we display the contribution functions (CFs) to
the equivalent width (EW) of the disc centre of the
OH lines at 3123 Å and 3167 Å according to
the 3D model
with given stellar parameters and metallicity
.
These two features have different excitation
potentials (
and 1.1 eV for the OH 3123 Å and
3167 Å lines, respectively) and their contribution
functions look similar in shape but different in strength. These
molecular lines tend to form in the outer layers of the
3D model
atmosphere, at
between
-2.8
and
-2.2, where
the 3D model is cooler than the 1D
model. Thus this
line is significantly weaker in the 1D
model and forms in
the inner layers of the star. Because of the sensitivity of
OH lines to the temperature, the line appears much stronger
in 3D than in 1D.
![]() |
Figure 4: Same as Fig. 3 but for the Fe I 3849 Å and 3852 Å lines. |
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![]() |
Figure 5:
Line profiles of the Fe I 3849 Å
and 3852 Å
lines computed with |
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This effect is usually found in metal-poor atmospheres
(see Asplund et al. 1999)
and is particularly important for the oxygen
abundances derived from OH molecules, as the differences are large in
the layers where these lines are formed. The result is that the oxygen
abundances become lower in the 3D formulation than in
the 1D. We
quantify this effect through the 3D correction (see
Sect. 2.3).
In hotter 3D models (
K)
this
effect becomes more severe, making the 3D corrections larger.
We display the CFs to the EW of the Fe I lines
at 3849 Å and 3852 Å in Fig. 4. These lines have
different excitation
potentials (
and 2.2 eV for the Fe I 3849 Å
and
3852 Å lines) and their CFs are different in both
strength and
shape. The Fe I
3849 Å line extends from
to
almost 0, whereas the Fe I 3852 Å line,
due to the higher excitation potential, goes from
to 0. Nevertheless, the main contribution is located at
for the Fe I
3849 Å line and at
for the
Fe I 3852 Å line. This
means that the Fe I 3849 line
is mostly formed in the outer layers of the 3D atmospheric
model, and the equivalent width is larger than in the 1D
model. Although the
Fe I 3852 Å line is
mainly formed in the inner layers, the EW computed
for this 3D model is still larger than in 1D, due to
the contribution of the outer layers. Therefore, this line still
provides negative 3D corrections. In addition, although they
have very similar excitation potentials, the
ratio EW(3D)/EW(1D
)
of the Fe I 3849 Å line
is
smaller than that of the OH 3167 Å line. This is
probably caused
by the stronger sensitivity of the OH line to the temperature
structure of the 3D model.
In Fig. 5
we display the line profiles of the
Fe I 3849 Å
and 3852 Å lines for the same 3D
and
1D
models with stellar parameters and metallicity
.
The 3D profiles of both lines are more broadened than the 1D
profiles in part because these 1D profiles were not
been convolved with a macroturbulent velocity, whereas
in the 3D profiles the broadening effect due to macroturbulence is
naturally included.
In addition, the 3D profiles are slightly
asymmetric due to the convective motions in the hydrodynamical
simulations included in the 3D model atmosphere. It is quite
clear
that the 3D profile of the Fe I 3849 Å line
is stronger
than the 1D
profile. This is not as evident for the
Fe I 3852 Å line,
where the line core is deeper in the
1D
profile but the line wings are tighter. The ratios
EW(3D)/EW(1D
)
of these lines in these 3D and 1D
models are 1.59 and 1.25 for the Fe I
3849 Å
and 3852 Å lines, respectively. As a
comparison, the ratios
EW(3D)/EW(1D
)
of the OH 3123 Å
and 3167 Å lines
are 20.2 and 8.2, respectively. Therefore, it is
expected that all
these lines should provide different 3D corrections. We will
discuss quantitatively these abundance
corrections in Sect. 2.3.
![]() |
Figure 6:
3D-1D
|
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2.3 3D corrections
The spectral synthesis code Linfor3D produces three curves of growth:
full 3D, 3D
and 1D
(Caffau
et al. 2009,2010). This allows us to estimate
abundance corrections through the EW(3D) of the 3D
model abundance to derive the corresponding abundances in the
3D
and 1D
models.
Two main effects distinguish 3D from 1D models: the
average temperature profile and the horizontal temperature
fluctuations. We quantify the contribution of these two main effects by
introducing the 3D correction as 3D-1D
.
The first and the
second effect can also be separately estimated with the
3D
-1D
and 3D-
3D
corrections, respectively. The velocity fluctuations (i.e. intrinsic
velocity fluctuations and microturbulence) are other
effects that also play a role, but their influence on the derived
abundance, although not negligible, is not as relevant.
In Fig. 6
we display the 3D-1D
abundance corrections of the
OH 3167 Å line for different effective temperatures
and
metallicities, and
= 4.
The 3D models with metallicities
[Fe/H]=-1 and 0 show very small and mainly positive 3D-1D
corrections, whereas 3D models with [Fe/H]=-3 and -2 show
strong,
negative corrections. The 3D-1D
generally increases towards hotter 3D models and lower
metallicites.
We note here that the behaviour of other OH lines is practically the
same although for slightly different values for the 3D-1D
abundance
corrections.
In Figs. 7
and 8
we show the 3D-1D
abundance
corrections of the Fe I 3849 Å
and 3852 Å lines for different effective
temperatures and metallicities, and
= 4. The
behaviour of the Fe I
3849 Å line is quite similar to
that of the OH 3167 Å line, although with
smaller 3D-1D
values.
On the other hand, the Fe I 3852 Å line
behaves in a completely different way, and the 3D-1D
corrections depend on whether the
line formation occurs mainly in the outer or inner region of the
atmosphere of a given 3D model at a given temperature and
metallicity.
In Fig. 9
we depict the 3D
-1D
corrections of the OH 3167 Å line for
different effective temperatures and
metallicities, and
= 4.
The
3D
-1D
corrections reflect how important these cooling effects are in the
3D models. Thus, the strongest correction is found for the
3D model with metallicity
[Fe/H]=-3 and
.
One also realizes by comparing
Figs. 6
and 9
that the 3D models with
metallicities [Fe/H]=-3 and -2 and
> 5900
have large
temperature fluctuations that account for a significant fraction of
the total 3D-1D
correction.
The sensitivity of the 3D-1D
corrections to the surface gravity is
less relevant (see Fig. 10).
The derived 3D-1D
corrections
are typically larger in 3D models with larger surface gravities,
although only variations of
0.2 dex are expected
from
= 3.5
to 4.5.
![]() |
Figure 7: Same as Fig. 6 but for the Fe I 3849 Å. |
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![]() |
Figure 8: Same as Fig. 6 but for the Fe I 3852 Å. |
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![]() |
Figure 9:
|
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![]() |
Figure 10:
3D-1D
|
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![]() |
Figure 11:
3D-1D
|
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The excitation potential determines the layer of the
3D model
atmosphere where the line forms. Thus, it is expected that a line of
the given molecule or atom forms further out if the excitation
potential is lower. In the case of OH molecular lines, further
out
means lower temperature and therefore enhanced molecule formation.
This is exactly what it is displayed in Fig. 11, the lower the
excitation potential of a OH line is, the larger negative
3D-1D
corrections it provides.
All in all, the dependence of the abundance corrections on metallicity shows a kind of threshold behaviour. Noticeable corrections indicating sizable temperature differences between 1D and 3D models set in rather abruptly at metallicities below -1. Ludwig et al. (2008) have argued that this can be expected on general grounds emerging from the temperature and metallicity sensitivity of the radiative relaxation time scale.
2.4 Dependence on carbon abundance
The molecular equilibrium of OH lines also involves the
molecules CO, CH and C2. Thus, the C
abundance surely affects the contribution function to the EW
of the OH lines.
The CO molecule is the most tightly bound and has the tendency to get
hold of all available O atoms, to the detriment
of OH.
Behara et al. (2010)
have already checked this effect in C-enhanced metal-poor stars,
showing that if the C abundance is large enough, the
3D-1D
abundance corrections become much smaller, reaching values
of the order of -0.2 if the carbon-to-oxygen ratio is as high
as
[C/O]
1.
In Table 3
we provide the 3D-1D
corrections to the O abundance derived from an
OH line with excitation potential
0.1 eV, for several
values of [C/O], which have been computed only for testing purposes
with the 3D model with parameters
.
For these low ratios [C/O], the 3D-1D
corrections are similar and within 0.15 dex. In addition,
looking at
these corrections in detail one realizes that (i) when [C/O] is low
enough, the 3D-1D
correction to the O abundance derived from OH
lines is only slightly dependent on the C abundance with
changes
0.05 dex;
(ii) when the [C/O] is
near the value zero, the C abundance starts to become relevant,
with changes
0.20 dex;
(iii) only when [C/O] is large
enough, the 3D-1D
correction becomes negligible.
In our computations we assumed that the carbon abundance
scales with
metallicity, [C/Fe] = 0. In models with metallicities
lower than
-1 dex, we have assumed the -elements enhanced by a factor
of [
/Fe] = 0.4.
Therefore, the [C/O] = -0.4, which means that
at the lowest metallicities, i.e. at [Fe/H] = -2
and -3, where the
observed abundances can reach values of [O/Fe]
0.5-1.0
(see Sect. 3)
and [C/Fe]
0
(e.g. Lai et al. 2007),
our estimated 3D-1D
corrections might have to be corrected downwards
by 0.06-0.12 dex.
This small effect has not been taken into
account and goes in the direction of slightly increasing the strength
of the 3D-1D
corrections.
Table 2:
3D abundance corrections for several OH lines using 3D
models with 6 and 12 opacity bins with the parameters
and
6240/4/-3, respectively.
2.5 Dependence on opacity binning
We tested a few 3D hydrodynamical models
with 12 opacity bins and found that the cooling effect at
is less pronounced than in our standard 6 bin
models. From this result we expect that in the next generation of
3D models, using a refined opacity binning, the 3D-1D
abundance corrections would come out smaller for OH lines and
Fe lines with excitation potentials below 1.5 eV.
Therefore, the corrections presented here for these lines can be
considered as upper limits.
In Table 2
we provide a comparison between the 3D-1D
corrections in the 6-bin and 12-bin 3D models. The 6-bin model produces
larger corrections for these three OH lines, between
-0.36
and -0.23 dex, with excitation potentials
between 0.2 and 1.1 eV. In addition, the 12-bin model
has stronger temperature fluctuations than the 6-bin model, since the
3D-
3D
is larger for the 12-bin model. This difference explains some of the
larger scatter in oxygen abundances obtained from different lines when
using 3D models than in the 1D case (see
Sect. 3).
3 Applications to the Galactic oxygen abundance
The aim of this study is to apply our grid of the 3D-1D
corrections
to a sample of metal-poor dwarf stars with available
O abundances
derived from near-UV OH lines. This sample was obtained from the
studies of
Boesgaard et al. (1999),
Israelian
et al. (1998,2001), and the most metal-poor dwarf
stars
of the binary CS 22876-032 from González
Hernández et al. (2008). We adopted the stellar
parameters and the O and Fe I abundances
of the dwarf stars provided in those works.
In Fig. 13
we display the 1D-LTE [O/H] and 1D-NLTE
[O/Fe I] ratios versus 1D-NLTE [Fe I/H]
in metal-poor
dwarf stars.
Table 3:
3D-1D
O abundance corrections for several [C/O] ratios
from the OH line 3106 Å with an excitation potential equal to
0.1 eV, using the 3D model with the parameters
.
We applied the same formula given in Israelian
et al. (2001) to correct
the 1D Fe I abundances for NLTE.
This formula was derived by these authors by fiting the 1D NLTE-LTE
corrections
provided by Thévenin & Idiart
(1999) as a function of metallicity. They also noted that
these NLTE corrections were not significantly sensitive to the stellar
parameters in their sample of metal-poor stars. This formula provides
corrections of +0.25 and +0.37 at [Fe/H] -2
and -4,
respectively. In the literature
there are other studies of the NLTE effect on Fe lines
(e.g. Shchukina
et al. 2005; Mashonkina et al. 2010; Korn et al.
2003) in metal-poor stars, but none of them provides a
similar table with NLTE-LTE corrections for a grid of models at
different metallicities.
NLTE effects on the OH lines may be also significant. Asplund & García Pérez (2001)
tried to investigate this effect using a two-level OH molecule and
found NLTE corrections up to +0.25 dex at metallicities
below -2. We
note here that in this study we have not taken into account any
possible NLTE effect on the OH lines.
The trend displayed in Fig. 13
clearly shows an increasing
[O/Fe I] ratio towards lower metallicities.
The error bars in
this figure only show the dispersion of the abundance measurements
using 1D models. We derived the slope of a linear fit to
all data points shown in the lower panel in Fig. 13,
providing
.
This value may be compared the slope of the 1D-NLTE [O/Fe] ratio
reported in Israelian et al.
(2001), whose
value is
.
The difference is likely related to the
fact that Israelian et al.
(2001) used data points from Israelian et al. (1998,2001), Boesgaard et al. (1999) and
Edvardsson et al. (1993).
We determined for all 3D models in Table 1 the 3D-1D
abundance corrections for the OH and Fe I lines
given in
Table 4.
The Fe I lines have three
different
excitation potentials from roughly 1 to 3 eV. We
chose some stars in the sample of Israelian et al. (1998,2001),
for which we have near-UV spectra to check if the selected Fe I
lines provide appropriate [Fe/H] values. For this estimate we used the
code 1D LTE MOOG (Sneden 1973)
and LTE model atmospheres
with
-elements
enhanced, by +0.4 dex, computed
with the Linux version (Sbordone
et al. 2004) of the ATLAS code
(Kurucz 1993). We used the new
opacity distribution functions (ODFs)
of Castelli & Kurucz (2003)
with the corresponding metallicity.
In Table 5
we give
the 1D LTE Fe abundances from these Fe I lines.
The Fe I 3849 Å line
is quite strong and starts to be in the saturation
regime for metallicities above -2. If one takes into account
that the 3D-LTE corrections for Fe I lines
of different excitation potentials are different, one should obtain
different abundances when using 1D models, according to
Fig. 11.
We hardly see this strong effect in the values given in Table 5. In Fig. 12 we depict these Fe
I abundances for different values of
microturbulent velocities for three of the stars in Table 5. As soon as one
goes to higher metallicities and lower excitation potentials, the
Fe I is more sensitive to the adopted
microturbulence. However,
at the lowest metallicities, the Fe I line
at 3 eV provides
more uncertain results because the EW is very low
and therefore more
sensitive to the quality of the observed spectra. We believe that our
choice of microturbulent velocity equal to 1
is
a reasonable
assumption, although the hottest stars, with
6300 K,
in our sample may require a slightly higher microturbulence.
Table 4: Selected lines for the abundance analysis.
![]() |
Figure 12: 1D LTE [Fe/H] abundances of some the stars in Table 5 excitation potential of the Fe I line, for three different microturbulent velocities adopted in each computation. |
Open with DEXTER |
In order to derive 3D abundances, we interpolated within the
grid of 3D-1D
corrections using the stellar parameters and
metallicities of the sample stars. For OH lines, we applied individual
abundance
3D-1D
corrections to the O abundance derived from each OH line and
finally computed the average 3D O abundance of all
available lines in
each star. The error of the [O/H] abundance is then estimated from the
dispersion of the 3D-LTE abundances of all OH lines.
![]() |
Figure 13: 1D [O/Fe I] ratio versus 1D Fe I abundances in metal-poor dwarf stars computed with 1D-LTE models using OH lines from Boesgaard et al. (1999, triangles), Israelian et al. (1998, 2001, diamonds). The circles represent the most metal-poor dwarf stars of the binary CS 22876-032 from González Hernández et al. (2008). The stars labeled ``A'' and ``B'' represent the primary and secondary star in this binary. |
Open with DEXTER |
![]() |
Figure 14: 3D-LTE [O/H] and 3D-NLTE [O/Fe I] ratios versus 3D-NLTE Fe I abundances computed with 3D-LTE models. The symbols are the same as Fig. 13. |
Open with DEXTER |
For Fe I we used a different
recipe. The papers by Israelian
et al. (1998) and Boesgaard
et al. (1999) do
not provide the Fe I lines used to
determine the
metallicity. On the other hand, the paper by Israelian
et al. (2001) gives a few Fe I lines
in the near-UV spectral region where the OH lines form. The excitation
potential of these Fe I lines is
eV.
However, these Fe I line are too
strong and gets saturated in stars with [Fe/H]>-2. Therefore, we
decided to adopt the following strategy:
(i) for stars with [Fe/H]<-2 we only used the Fe I
3849 Å
line to apply a 3D-1D
correction to the 1D metallicities; and (ii)
for stars with [Fe/H]>-2 we derived an average correction with
the
two other Fe I lines
at 3843 and 3852 Å. For [Fe/H]>-2,
we estimated the error of the 3D-LTE [Fe I/H]
by adding
quadratically the dispersion of the 3D-1D
corrections and the dispersion of the 1D-LTE abundances. For
[Fe/H]<-2,
we adopted ad hoc a dispersion of 0.3 dex in the 3D-1D
abundance corrections because we were only using one Fe I line.
In Sect. 2.3
we discussed the expected differences in the
3D-LTE 3D-1D
correction between the Fe I 3849 Å
and
3852 Å lines for models with [Fe/H]<-2. Thus,
it is clear that if one would use both Fe I lines
to estimate the 3D-1D
correction for stars with [Fe/H]<-2, one would get smaller
corrections, but the error bar associated to these corrections would be
very large.
As a first approximation, we corrected our values for the 3D-LTE Fe I abundances for NLTE effects with the 1D-NLTE corrections already applied before to the 1D case. Finally, we determined the 3D-NLTE [O/Fe I] ratio by computing the difference between the 3D-LTE O abundance and the 3D-NLTE Fe I abundance in all dwarf stars of the sample. We are aware that these NLTE corrections may be too small, but we also know that our 3D-LTE corrections in both OH and Fe lines may be also overestimated because of the opacity binning used to compute our grid of 3D models (see Sect. 2.5). In addition, the carbon abundance may be another factor to take into account (see Sect. 2.4). We see that these effects tend to go in opposite directions when trying to define the slope, if it exists, of the ratio [O/Fe] versus [Fe/H] at the lowest metallicities.
Table 5: 1D Fe abundances for six stars in the sample of Israelian et al. (1998,2001), from three Fe I lines of different excitation potentials.
In Fig. 14
we depict the 3D-LTE [O/H] and 3D-NLTE
[O/Fe I] trend in metal-poor dwarf stars.
The slope of the linear fit to the 3D-NLTE [O/Fe I]
trend
is smaller in absolute value, ,
but still negative and
relatively significant, at least under the assumptions made in this
work.
The error bars are larger in this figure than in Fig. 13
because we added quadratically the standard deviation on the OH and
Fe abundances, and the dispersion on the 3D-1D
abundance corrections from different OH and Fe lines.
There is also a larger scatter in the almost linear relation
between the 3D-NLTE [O/Fe] and [Fe/H] ratios. The reason may
be that the 3D corrections applied to the stars depend not only on the
metallicity of the star, but also on the stellar parameters. Therefore,
when we
apply the 3D-1D
corrections, different stars move to different
directions in the plane [O/Fe] versus [Fe/H]. As we stated in
Sect. 1,
large and positive 3D-NLTE
corrections for Fe I lines are
expected in metal-poor 3D models (Shchukina
et al. 2005), but this needs to be done for the
whole grid of 3D hydrodynamical models to see how the picture changes.
We also
note here that the computations done by Shchukina
et al. (2005) do not consider
the inelastic collisions with neutral hydrogen atoms, because there is
at present no reliable values for the collisional rates, and
the classical Drawin formula leads to uncertain estimates.
They also pointed out that inelastic collisions with neutral hydrogen
atoms would tend to alleviate the NLTE effects, and therefore, the
difference between the NLTE and LTE may be considered as the maximum
effect that inelastic collisions might produce.
Figure 15
shows the 3D-NLTE [O/Fe I] ratio
versus
effective temperature of the star. There is no clear trend with
effective temperature, except that due to selection
effects, most of the dwarf stars with higher 3D-NLTE [O/Fe I] values
are hot stars (
> 5900),
with the exception of very
few cases.
Finally, we remark here that after all these corrections, the trend in [O/Fe I] obtained from near-UV OH lines in metal-poor dwarf stars is consistent with [O/Fe] ratios obtained from the forbidden [O I] in metal-poor giant stars for which the 3D corrections are expected to be negligible (González Hernández et al. 2008).
![]() |
Figure 15: 3D [O/Fe I] ratio versus effective temperature. The symbols are the same as Fig. 13. |
Open with DEXTER |
4 Summary
The large grid of 3D hydrodynamical model atmospheres of dwarf stars
quite captivated our attention during the last
three years (Ludwig et al. 2009).
It took thousands of hours in computing time to build such a grid. We
have used 52 3D models extracted from this grid with the
following stellar parameters and metallicities: = 5000,
5500, 5900, 6300 and 6500 K,
= 3.5, 4
and 4.5, and [Fe/H]=0, -1, -2 and -3. The main difference with
the ``classical'' 1D models is that 3D models show temperature
inhomogeneities and a cooler average
temperature profile in models with [Fe/H]<-1.
This allowed us for the first time to compute 3D abundance corrections of several near-UV OH and Fe I lines. These 3D corrections are generally larger for higher effective temperatures, larger surface gravities, and lower metallicities. In addition, lines with lower excitation potentials show stronger 3D corrections.
We applied this grid of 3D corrections to a sample of metal-poor dwarf stars from Israelian et al. (1998,2001), Boesgaard et al. (1999) and the most metal-poor dwarf stars of the binary CS 22876-032 from González Hernández et al. (2008). We interpolated within this grid, using the stellar parameters and metallicities of these stars.
Finally, we are able to display a new trend with the 3D-NLTE [O/Fe I] ratio versus metallicity and this trend still increases towards lower metallicities, as the 1D-NLTE, but with a smaller slope in absolute value. However, we caution that some assumptions (as e.g. the restriction to a 6-bin scheme in most 3D models and NLTE corrections only in 1D), which we believe to be reasonable, have been adopted to achieve this result and that therefore, this result should be taken with that in mind. A full 3D-NLTE study of all 3D model atmospheres presented in this paper must be performed for both near-UV OH lines and Fe I lines to see if this trend changes.
J.I.G.H., P.B., H.-G.L. and N.B. acknowledge support from the EU contract MEXT-CT-2004-014265 (CIFIST). J.I.G.H. also thanks support from the project AYA2008-00695 of the Spanish Ministry of Education and Science. B.F. acknowledges financial support from the Agence Nationale de la Recherche (ANR), and the ``Programme National de Physique Stellaire'' (PNPS) of CNRS/INSU, France. We are also grateful to the supercomputing centre CINECA, which has granted us time to compute part of the hydrodynamical models used in this investigation, through the INAF-CINECA agreement 2006, 2007.
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Footnotes
- ... ratio
-
.
- ... Linfor3D
- More information on Linfor3D can be found in the following link: http://www.aip.de/ mst/Linfor3D/linfor_3D_manual.pdf
All Tables
Table 1:
Details of the 3D hydrodynamical
model atmospheres.
Table 2:
3D abundance corrections for several OH lines using 3D
models with 6 and 12 opacity bins with the parameters
and
6240/4/-3, respectively.
Table 3:
3D-1D
O abundance corrections for several [C/O] ratios
from the OH line 3106 Å with an excitation potential equal to
0.1 eV, using the 3D model with the parameters
.
Table 4: Selected lines for the abundance analysis.
Table 5: 1D Fe abundances for six stars in the sample of Israelian et al. (1998,2001), from three Fe I lines of different excitation potentials.
All Figures
![]() |
Figure 1:
3D temperature structure of the 3D |
Open with DEXTER | |
In the text |
![]() |
Figure 2:
Same as Fig. 1
but for the 3D model |
Open with DEXTER | |
In the text |
![]() |
Figure 3:
Contribution functions to the equivalent width of the OH
3123 Å line computed with |
Open with DEXTER | |
In the text |
![]() |
Figure 4: Same as Fig. 3 but for the Fe I 3849 Å and 3852 Å lines. |
Open with DEXTER | |
In the text |
![]() |
Figure 5:
Line profiles of the Fe I 3849 Å
and 3852 Å
lines computed with |
Open with DEXTER | |
In the text |
![]() |
Figure 6:
3D-1D
|
Open with DEXTER | |
In the text |
![]() |
Figure 7: Same as Fig. 6 but for the Fe I 3849 Å. |
Open with DEXTER | |
In the text |
![]() |
Figure 8: Same as Fig. 6 but for the Fe I 3852 Å. |
Open with DEXTER | |
In the text |
![]() |
Figure 9:
|
Open with DEXTER | |
In the text |
![]() |
Figure 10:
3D-1D
|
Open with DEXTER | |
In the text |
![]() |
Figure 11:
3D-1D
|
Open with DEXTER | |
In the text |
![]() |
Figure 12: 1D LTE [Fe/H] abundances of some the stars in Table 5 excitation potential of the Fe I line, for three different microturbulent velocities adopted in each computation. |
Open with DEXTER | |
In the text |
![]() |
Figure 13: 1D [O/Fe I] ratio versus 1D Fe I abundances in metal-poor dwarf stars computed with 1D-LTE models using OH lines from Boesgaard et al. (1999, triangles), Israelian et al. (1998, 2001, diamonds). The circles represent the most metal-poor dwarf stars of the binary CS 22876-032 from González Hernández et al. (2008). The stars labeled ``A'' and ``B'' represent the primary and secondary star in this binary. |
Open with DEXTER | |
In the text |
![]() |
Figure 14: 3D-LTE [O/H] and 3D-NLTE [O/Fe I] ratios versus 3D-NLTE Fe I abundances computed with 3D-LTE models. The symbols are the same as Fig. 13. |
Open with DEXTER | |
In the text |
![]() |
Figure 15: 3D [O/Fe I] ratio versus effective temperature. The symbols are the same as Fig. 13. |
Open with DEXTER | |
In the text |
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