N. Ryde 1,2 - D. L. Lambert 2
1 - Uppsala Astronomical Observatory,
Box 515,
751 20 Uppsala,
Sweden
2 - Department of Astronomy,
University of Texas,
Austin, TX 78712-1083,
USA
Received 21 May 2003 / Accepted 12 November 2003
Abstract
Sulfur
abundances have been determined for ten
stars
to resolve a debate in the literature on the Galactic chemical
evolution of sulfur in the halo phase of the Milky Way.
Our analysis is based on observations of the S I lines at
9212.9, 9228.1, and 9237.5 Å for stars for which the S
abundance was obtained previously from much weaker S I
lines at 8694.0 and 8694.6 Å. In contrast to the previous
results showing [S/Fe] to rise steadily with decreasing [Fe/H],
our results show that [S/Fe] is approximately constant for
metal-poor stars
(
)
at
.
Thus,
sulfur behaves in a
similar way to the other
elements, with an approximately constant [S/Fe] for
metallicities lower than
.
We suggest that the reason for the earlier claims of a
rise of [S/Fe] is partly due to the use of the weak S I 8694.0 and 8694.6 Å lines and
partly uncertainties in the determination of the metallicity
when using Fe I lines. The
S I 9212.9, 9228.1, and 9237.5 Å lines are preferred for an abundance analysis of sulfur for metal-poor stars.
Key words: stars: abundances - stars: atmospheres - stars: population II - Galaxy: abundances - Galaxy: evolution - Galaxy: halo
Galactic chemical evolution of the
elements (O, Ne, Mg,
Si, S, Ar, and Ca) might be expected to be similar from element to
element. It is thought that their production in the early Galaxy
was dominated by synthesis in massive stars and ejection into the
interstellar medium by supernovae (SN type II). Then, relative
abundances of
elements and of their abundances with
respect to iron reveal information about the yields from SN II and
the dependence of those yields on the initial metallicity. After
a passage of time, the Galactic gas was contaminated by ejecta of
type Ia supernovae (exploding white dwarfs). These produce little
of the
elements but large amounts of iron-group nuclei.
Thus, the relative abundance of
elements to iron
declined.
Accurate data on the abundances of
elements for stars
in the halo and disk
are essential if one
is to extract information about the nucleosynthesis of these
elements. First estimates of the S abundance in halo stars were
provided by Takada-Hidai et al. (2002) and Israelian & Rebolo (2001) who found that
[S/Fe] increased approximately linearly with decreasing [Fe/H]:
from the Sun (
)
to
, the metallicity limit of the
samples. In contrast, Nissen et al. (2003a) provide strong
evidence for a constant
for stars with
, and a quasi-linear rise to this value from
.
This discrepancy among the observational results for
deserves to be resolved before S abundances are added to the
observational inventory relevant to interpretations of Galactic
chemical evolution. This paper describes our attempt to resolve
the discrepancy.
A problem with obtaining the sulfur abundance of metal-poor stars
is the paucity of suitable atomic lines. Candidate lines of S I lie in the near-infrared (NIR): multiplets of
high-excitation lines occur near 8694 Å and at
9212-9238 Å. The drawback with the lines at 8694.0 Å and 8694.6 Å is their weakness in halo stars. Israelian & Rebolo (2001)
and Takada-Hidai et al. (2002) observed these lines. On the other hand, a
disadvantage with the much stronger triplet at 9212.9, 9228.1,
and 9237.5 Å is the heavy interference by the telluric H2O lines. Nissen et al. (2003a) observed these
lines and corrected for the H2O line
absorption.
In this project, we chose to observe the
lines in a number of the stars observed at
by Takada-Hidai et al. (2002, in the following
shortened as TH) and Israelian & Rebolo (2001, abbreviate as
I&R). Our stars sample the metallicity range down to
,
and consist of three from the sample of I&R, three from TH, and four from François (1988), whose
equivalent widths were reanalyzed by TH and I&R. Our primary goal
was to check the high [S/Fe] reported previously from the
lines. This check is executed using high
quality spectra of the
lines analyzed
using model atmospheres computed for the same effective
temperature and surface gravity as used in the pioneering studies
from which our star-list is made. As a secondary goal, we sought
to gain an indication of how [S/Fe] behaves among halo stars of
different metallicities.
The investigated stars, all lying in the northern sky, are presented in Table 1. I&R determined the sulfur abundance for 8 new stars, including two upper limits, with the 4.2 m William Herschel Telescope on La Palma. We have analyzed three of these, namely HD 2665, HD 19445, and HD 201889. TH made new determinations of the sulfur abundance in 6 stars (with one upper limit) using the HIRES spectrograph on the Keck telescope on Hawaii. Of these we have observed three (HD 84937, HD 88609, and HD 165195). Furthermore, we have observed HD 111721, HD 94028, HD 132475, and HD 201891, which were originally observed and analyzed by François (1988), and then reanalyzed both by TH and I&R.
The stars, which span the metallicity range of
,
were observed in observing runs from November 29 and 30, 2001 and
April 27, 2002 at the W. J. McDonald Observatory using the 2.7-m
Harlan J. Smith telescope with the high-resolution 2dcoudé
cross-dispersed echelle spectrograph (Tull et al. 1995). The
resolving power was approximately R= 60 000, a value determined
from the FWHM of thorium lines in the wavelength calibration
frames. Full spectral coverage from 3400 to 10 900 Å can
be obtained in two exposures. However, we observed every star in
only one setting of the echelle, thus retrieving the entire
wavelength range but with gaps. Our bandpass includes the sulfur
lines but not the
lines.
We used the TK3 detector, a
CCD with
m pixels.
The observing times, ranging from a half-an-hour to 3 hours for
the F, G, and K stars, are given in Table 1. To avoid a
large number of cosmic hits, individual exposures were limited to
a maximum of 30 min.
The observed CCD data was processed with the reduction package IRAF to retrieve one-dimensional, continuum normalized, and wavelength calibrated, pure stellar spectra. In the wavelength calibration a root-mean-square of the fit of less than 4 mÅ is achieved. Multiple exposures of the same star were added in the form of 1-dimensional spectra by weighting the different spectra by their mean count levels. When several frames are available a cosmic-ray-hit rejection algorithm was applied.
The local continua of the F, G, and K star spectra were fitted and normalized by a low-order Legendre function in order not to remove the wings of the stellar Paschen line. As can be seen in Fig. 1, one of the sulfur lines lies in the wing of this hydrogen line. The hydrogen lines in the dwarf spectra have wings stretching over a considerable wavelength range and we therefore have to proceed with caution when fitting the continuum.
![]() |
Figure 1:
In the upper panel, the full line displays the continuum-normalized
spectrum of our giant star HD 2665 (including telluric lines, mostly water vapor lines)
and, as dots,
the continuum-normalized spectrum of our rapidly rotating B-star,
which shows only telluric absorption lines.
In the lower panel,
the HD 2665 spectrum is divided by this telluric spectrum,
resulting in a pure stellar spectrum of HD 2665. The sulfur lines
and the Paschen ![]() |
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Table 1: Investigated stars.
![]() |
Figure 2:
Continuum-normalized spectra of our programme giants: HD 2665,
HD 88609, HD 111721, and HD 165195. Telluric absorption lines are ratioed out,
but some
residual signatures are visible.
In the spectra of HD 2665 and HD 111721 several
Fe I lines and a Mg II line are discernable and in the spectrum of
HD 165195 the most conspicuous Fe I line is detected. In the lower right panel in
Fig. 3 identifications of all observable metal lines in this
wavelength region can be found. Our best model spectra are also
plotted with full lines. See text for a comment on the bad fit of the hydrogen Paschen line
in the spectrum of HD 165195. After the names the star-model's temperature, ![]() |
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![]() |
Figure 3:
Continuum normalized spectra of our programme dwarfs: HD 19445, HD 84937,
HD 94028, HD 132475, HD 201891, and HD 201889. The telluric absorption lines are
removed as well as possible, but some residuals remain, most prominently in the
spectrum of
HD 19445 and HD 84937. Metal lines have been identified in the spectra of the four
lowest panels. In the spectrum of the most metal-rich star,
HD 201889, all the identified Fe I, Mg II, and S
I lines are marked. The full lines represent our modelled spectra.
After the names the star-model's temperature, ![]() |
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The 9200 Å region of interest here is marred by numerous
telluric absorption lines (Fig. 1). To eliminate
the telluric contribution to the spectra, we observed
fast-rotating-B-stars with
.
The intrinsic,
B-star spectra are featureless except for a more or less
pronounced, rotationally broadened Paschen
H I line
at 9229.02 Å, which means that they can be used as a template
for the telluric absorption lines. For these B-star spectra, we
used a spline function of high order to fit and normalize the
spectra, but also to eliminate the broad Paschen
H I
feature and occurring fringes. The hot stars were observed close
in time and at a similar airmass as the programme stars, and were
required to have a signal-to-noise ratio of several hundred. To
achieve this in the 9200 Å region, exposure times from tens of
seconds up to an hour were required, depending on the brightness
of the individual star and the specific spectral type. The reduced
B-star spectra achieved in this manner are assumed to contain
purely telluric absorption lines. The programme spectra were
subsequently divided by a scaled version of the "telluric''
spectra. The divided, reduced spectra are shown in Figs. 2 and 3. As can be seen in these
figures, the telluric lines are astonishingly well eliminated
while the stellar sulfur lines show up clearly. While our
procedure of eliminating the telluric lines adds to the noise, the
resultant signal-to-noise ratio of the ratioed stellar-spectra is
satisfactory for our purpose.
The equivalent widths of the sulfur lines at 9212.9 Å and
9237.5 Å, which are considered to be unblended, were measured
by Gaussian fits or by total integration of the line. The
equivalent width of the 9228.1 Å line is not measured (except
for HD 111721) since it lies in the stellar Paschen H
I line. The measured equivalent widths of the two (three) sulfur
lines, the equivalent widths of the S I 8694.6 Å line
supplied in the literature (I&R; TH), and our measured equivalent
widths of six Fe II lines (lying at 4416.8, 5264.8,
5284.1, 6149.3, 6432.7, and 6456.4 Å) are presented in
Table 2. We note that the measured equivalent widths of
the sulfur lines at 9212.9, (9228.1), and 9237.5 Å range
from approximately 10 to 100 mÅ, which is suitable for a
reliable abundance analysis. Observe also, that the equivalent
widths are an order of magnitude larger than those determined for
the line at 8694.6 Å. The 8694.0 Å line is a factor of
five weaker still and unmeasurable in all the metal-poor stars we
have been investigating, except HD 201889.
We note that the TK3 detector used consists of a thick chip, which is not severely affected by fringing. The existing fringing cancels well using a flat field - the top panel is Fig. 1 compares two such flat-fielded spectra. Fringing is eliminated to a high degree by using a hot star observed at the same time and the lower panel of Fig. 1 shows just such a spectrum.
In Figs. 2 and 3, there exist
low points which originate from the cancellation of the very
strongest telluric lines. None of these affect the SI lines. For
example, in the spectrum of HD 19445 in Fig. 3
only the 9212.9 Å line lies in a wing of a modestly strong
telluric line. The other ones are free. The abundance derived from
the free 9237.5 Å line is
(the
logarithmic number-abundance of sulfur relative to hydrogen,
,
normalized on a
scale where
), whereas the ratioed
9212.9 Å line gives 5.49. The synthetic spectrum which fits
these two lines, as well as the 9228.1 Å line is calculated
with an abundance of 5.50. The fact that the three sulfur lines
are synthesised well with one sulfur abundance shows that the
elimination of the telluric lines produces a reliable result,
clearly within the other uncertainties. We estimate the error in
the equivalent widths to be less than 5%, implying an uncertainty
in the derived sulfur abundance of the order of 0.05 dex, as
estimated from the individual measurements.
In some regions, for example around 9207 Å in the spectrum of HD 111721 in Fig. 2 and around 9245 Å in the spectrum of HD 132475 in Fig. 3, the elimination of the telluric lines is hampered due to closely lying telluric lines with wings blending with each other. The equivalent widths of the sulfur lines are, however, measured by drawing a local continuum which should reduce systematic errors due to this effect.
Table 2: Measured equivalent widths given in mÅ.
We analyze our data by modelling the stellar atmosphere and
requiring that the measured
equivalent widths are reproduced for the two unblended S I
and
lines. The mean sulfur abundance
yielded in this way is subsequently used in calculating a
synthetic spectrum for a given atmosphere of the entire region
(
9200-9500 Å). The synthetic spectrum is thereafter convolved
with a macroturbulence function in order to fit the shapes and
widths of the lines, see Figs. 2 and 3. In this section we will discuss the model
atmospheres, the stellar parameters including uncertainties, the
line data, and the spectrum synthesis.
I&R and TH used ATLAS9 model atmospheres whereas we use model atmospheres provided by the MARCS code. The MARCS code was first developed by Gustafsson et al. (1975) and has been successively updated ever since. These hydrostatic, plane-parallel model photospheres are computed on the assumptions of Local Thermodynamic Equilibrium (LTE), homogeneity and the conservation of the total flux (radiative plus convective; the convective flux being computed using the mixing length formulation). Data on absorption by atomic species are collected from the VALD database (Piskunov et al. 1995) and Kurucz (1995, private communication). Absorption by molecules is included but quite unimportant for our stars.
We have computed model atmospheres in plane-parallel geometry which is an excellent approximation for the dwarfs. To test the validity of the approximation for the giant stars we calculated a model atmosphere in spherical geometry for the giant HD 88609 and compared it with a plane-parallel model. The equivalent widths of the sulfur lines are changed by only a few percent. We have, therefore, calculated model atmospheres for all our stars in plane-parallel geometry.
In our model atmospheres the enhancement of C, O, Ne, Mg, Si, S,
Ar, Ca, and Ti (that is the elements) was assumed to be
except for HD 201889 for which it was
assumed to be
,
due to its higher
metallicity. The derived S abundance is quite insensitive to the
enhancement.
Using their equivalent widths, line parameters and set of fundamental stellar parameters, we are able to reproduce the derived abundances in I&R and TH. Our use of MARCS model atmospheres lowers the abundances by a few hundredths of a dex relative to those obtained from ATLAS9 models used previously. Clearly, the choice of ATLAS9 vs. MARCS is not an important factor affecting the derived abundances.
We have chosen the same stellar, fundamental parameters for the
model atmospheres (actually
,
,
and
)
as those determined in I&R and TH. However,
the metallicities of the stars (
)
we redetermined
from six singly ionized iron lines.
The fundamental stellar
parameters including our determined metallicities and are given in
Table 1.
As was noted above, the stars HD 111721, HD 94028, HD 132475, and HD 201891, which were originally observed and analyzed by François (1988), have been reanalyzed both by TH and I&R. For the determination of the effective temperatures and surface gravity, TH took into account interstellar reddening which resulted in noticeable adjustments of the parameters. We will use parameters determined by TH for the François (1988) stars.
TH determined the effective temperatures of HD 84937, HD 88609, HD 165195, and HD 111721 from the Alonso et al. (1999a) calibration, based on the infrared flux method ( IRFM), also taking the interstellar reddening into account. For the reanalysis of the dwarfs HD 94028, HD 132475, and HD 201891, TH used the empirical temperature scale for dwarfs as formulated by Alonso et al. (1996). Our new metallicities do not alter this temperature determination significantly.
Furthermore, TH calculated the surface gravity using Hipparcos parallaxes. The microturbulence was determined for HD 84937, HD 88609, and HD 165195 from Fe I lines. Microturbulence for HD 111721 is taken from Ryan & Lambert (1995), and for the dwarfs HD 94028, HD 132475, and HD 201891 it was calculated from the empirical formula provided by Edvardsson et al. (1993).
For the giant star HD 2665, the effective temperature was
determined by I&R based on the IRFM in Alonso et al. (1999b)
and the surface gravity ()
from a non-LTE study of iron
(for references see I&R). For HD 19445 and HD 201889 the
temperature is based on the IRFM (Israelian et al. 1998), and
from an non-LTE analysis of iron by Thévenin & Idiart (1999). The
microturbulence we have assumed to be
for these
three stars.
The high-excitation (
eV) S I lines used in this
paper are due to the multiplet
,
while the
lines at 8694.0 and 8694.6 Å are from the multiplet
.
The line parameters (wavelength, excitation
energy, line strength) of our S I lines and six Fe II
lines are provided in Table 3.
In the following, we have used a solar sulfur abundance of
(Chen et al. 2002) as a
reference point.
Table 3: Line parameters.
The sulfur abundance is originally found by reproducing the
equivalent widths of the unblended sulfur
and
lines. This is done with the radiative transfer
routines of the MARCS codes and yields a mean sulfur
abundance with a standard deviation of 0.01 to 0.1 dex. (This
gives an assessment of the random measuring uncertainties.)
Synthetic spectra around
9200-9250 Å are produced by
computations of the radiative transfer through the model
atmospheres, using the mean sulfur abundance and using our line
data for all three sulfur lines and the Paschen
H I
line. We calculate the radiative transfer for points in the
spectrum separated by
(corresponding to a resolution of
). We subsequently convolve
the spectra with a macro-broadening function, assuming a
Doppler-shift distribution for both radial and tangential velocity
components as specified by the "radial-tangential'' model for the
macroturbulence, for details see Gray (1992). The FWHM
velocities for the macroturbulence broadening are given in Table 1 and were derived by requiring that the shape and
widths of the sulfur lines should match the observations.
Note, that the sulfur
line, which lies in the
Paschen
H I line, will also be calculated (including
the hydrogen opacity) by the synthetic spectrum program. For a few
of the dwarfs the wings of the Paschen
H I line also
interfere, to various extents, with the two sulfur lines which
were assumed to be unblended. This means that the measured
equivalent widths could be wrong in these cases, underestimating
the sulfur abundance. Therefore, the sulfur abundances were
adjusted in order that the synthetic spectrum, including the
hydrogen-line wings, should fit the observations. The size of
these changes were, however, not more than approximately 0.05 dex
in the sulfur abundance.
In Figs. 2 and 3 we have plotted the final synthetic spectra together with our observations. The modelled spectra are shifted according to the observed radial velocities of the stars. From the figures, we see that all sulfur lines are synthesized convincingly. Thus, the information from all three sulfur lines has been used in determining the sulfur abundance. The synthetic spectra only take the sulfur lines and the hydrogen line into account. The other metal lines in the region were not included in the calculation.
The calculations of the wings of the hydrogen line yield a satisfactory match to the observations, which can be seen, in particular, in the dwarf spectra (see Fig. 3). Recall that the continuum normalization was made with a low order function only, in order to fit the continuum over a limited range, so spurious features (such as possible residual fringing) are not taken out. The hydrogen line cores are expected to be subject to departures from LTE, which could lead to poor fits. The unsatisfactory fit of the hydrogen-line core in the giant HD 165195, for example, could be improved but would require higher temperatures, of the order of 400 K.
The uncertainties in the fundamental parameters are adopted from
their sources: for HD 2665, HD 19445, and HD 201889 from I&R;
for HD 84937, HD 88609, and HD 165195 from TH; and for HD 111721,
HD 94028, HD 132475, and HD 201891 from the reanalysis of the
François (1988) data by
TH, see Table 1. For HD 2665, HD 19445 and
HD 201889, we assess the uncertainties in the microturbulence to
be of the same order as estimated in TH. Furthermore, we judge
the uncertainties in the macroturbulence to be of the same order,
that is
.
The uncertainties in our
new determination of the metallicity is assessed to be less than
0.15 dex.
The propagation of these uncertainties into the determination of the sulfur abundance is calculated by changing the fundamental parameters of the model atmosphere with the estimated uncertainties and then running the synthetic spectrum program to obtain the change in sulfur abundance for a given equivalent width. Table 4 shows the consequence of the uncertainties in the effective temperature, surface gravity, metallicity, and microturbulence on the [S/H] and [S/Fe] ratios for one giant and one dwarf. For the coolest stars (e.g. HD 165195), the dominant source of uncertainty is the 100 K estimate for the temperature error. The uncertainties in the sulfur abundance, due to temperature uncertainties, are of the order of 0.04 dex or less for the dwarfs, and for the giants, typically 0.1 dex.
Table 4:
Effects on logarithmic abundances derived when changing the fundamental
parameters of the model atmospheres. Two stars of different parameters are presented.
The parameters (
)
are, respectively:
(
)
and (
).
The total uncertainty in the [S/Fe] due to uncertainties in the fundamental parameters is, in general, of the order of 0.05, but could be as high as 0.08 in special cases. This is the same conclusion as Nissen et al. (2003a) arrive at in their investigation of the sulfur abundance in solar-type stars.
Table 5:
Abundances of Fe II and S I, the latter based on the
lines.
The resulting sulfur abundances for our stars are presented in
Table 5 as
,
the logarithmic abundance relative to the solar value of
,
i.e.
,
and the
logarithmic abundance relative to the solar value normalized to
the metallicity (
). Also, displayed in the Table
are the iron abundances calculated from the measured equivalent
widths of Fe II lines shown in Table 2. The total
uncertainty, including effects of statistical
measuring-uncertainties and uncertainties in the model parameters,
is estimated to be of the order of
0.15 dex.
In their non-LTE analysis of neutral sulfur in environments
relevant also in our study, TH find inconsequential effects for
the
lines, ranging from 0.00 to 0.08 dex
in the sulfur abundance. Nissen et al. (2003b) find in their
study of the sulfur abundance for similar stars, that the sulfur
abundance they derive from the
lines match
the abundance derived from the
lines very
well, indicating that departures from LTE should be small also for
the latter lines. It should be noted that neutral sulfur atoms
represent the main ionization state throughout most of the
atmosphere, and most importantly in the line-forming regions.
Thus, we judge that the NLTE effects should be small, justifying a
standard LTE analysis. Furthermore, Nissen et al. (2003a)
investigate and find that the 3D effects
for
dwarfs will not severely alter the [S/Fe] ratio (less than 0.05
dex). Therefore, we will neither make any corrections for non-LTE
effects nor for 3D effects. Our
values are
plotted versus [Fe II/H]
in Fig. 4. It is clear that departures
from LTE and the 3D effects have very similar (small) effects on the
abundance derived from the
9213-38 lines and
that from the
lines.
Table 6:
Sulfur abundances compared to those from the literature which are based on the
lines.
![]() |
Figure 4:
This figure shows the Galactic chemical evolution of
sulfur.
The iron and sulfur abundances,
as we have determined it from analyzing Fe II lines and sulfur lines in the NIR, are
presented with star symbols. Typical errorbars for our measurements of ![]() ![]() |
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Since sulfur abundances have been obtained previously for each of
our stars using the
lines, it is of
considerable interest to compare S (and Fe) abundances. This
comparison is made in Tables 6 and 7.
Table 7:
The iron and sulfur abundance ratios ([Fe/H], [S/H], and [S/Fe]) from our work and from the
literature for the
lines.
Three stars - one giant and two dwarfs - are in common with
I&R. Our sulfur abundances are systematically smaller:
(HD 2665), -0.47 (HD 19445), and -0.14 (HD 201889).
Recall that we have used the same stellar parameters. It is likely
to be significant that the agreement is best for the star
(HD 201889) for which the
lines are
strongest. The difference is in fact -0.14 dex also when the
abundance of I&R is corrected to the NIST gf-value
(abundance increased by 0.02 dex) and to the MARCS model
(abundance decreased by 0.02 dex). We suppose that the larger
differences for the two more metal-poor stars reflect the greater
uncertainty in measuring very weak S I
line
(equivalent widths of about 3 mÅ). Alternative choices of model
atmosphere parameters cannot erase the abundance difference
resulting from the choice of S I lines.
The
corresponding
for [Fe/H] are +0.26 (HD 2665), -0.02(HD 19445), and +0.23 (HD 201889). I&R indicate that the iron
abundance determination is
based on Fe I lines and a non-LTE analysis.
We greatly prefer to derive the Fe abundance from Fe II
lines, for which non-LTE effects are slight, than to use Fe
I lines and an uncertain non-LTE correction. Fe II lines
are, however, more sensitive than Fe I lines to
uncertainties in the surface gravity, but this is also true for
S I lines compared to S II. Thus, this sensitivity
should cancel out in the S I/Fe II ratio.
There are large differences in the [S/Fe] ratios obtained by us and I&R: 0.14 vs. 0.69 (HD 2665), 0.20 vs. 0.65 (HD 19445), and 0.20 vs. 0.57 (HD 201889) arising from a higher S abundance in each case and a lower Fe abundance in two cases. In short, we do not confirm the high [S/Fe] proposed by I&R.
Three of our stars were observed and analyzed previously by
TH. For HD 88609, the most metal-poor star (
)
of the trio,
their upper limit to the S abundance is a safe
0.7 dex higher than our measured abundance. For HD 84937 with
,
the sulfur abundance derived by TH is 0.45 dex
larger than ours but this difference is probably due to the
uncertain equivalent width of the
line; TH note that
their spectrum is of low signal-to-noise ratio and marred by
residual fringing. In the case of HD 165195, our and their S
abundances agree well. These comparisons use LTE abundances
derived by TH; the corrections for non-LTE effects are small. The LTE Fe abundances derived by TH from a set of Fe II lines
are in good agreement with ours:
s are -0.12, +0.12,
and +0.05. The [S/Fe] values for the two stars for which TH
detected the
line in the sense ours vs. theirs, are 0.52 vs. 0.64 (HD 165195) and 0.13 vs. 0.60 (HD 84937).
TH detected the
lines in
three stars not observed by us. Their detections appear quite
secure. We note that the [S/Fe] ratio inferred by TH for these
stars, with
,
average about 0.2 and fit well
with our suggested run of [S/Fe] with [Fe/H], see Fig. 4.
We chose four stars from François (1988). This quartet was
reanalysed by TH and I&R using equivalent widths of the
line reported by François (1988). Table 6 shows that, for the dwarfs, these reanalyses and our
abundance from the NIR lines are in good agreement. The agreement
extends to [S/Fe], cf. Table 7. The typical total
uncertainties quoted by TH, for their dwarfs, for the [S/Fe]
ratio is 0.15 dex. However, for their analysis of HD 111721 the
uncertainty is larger (0.4 dex).
Our observations show that the S I NIR lines are detectable
and S abundances determinable to
,
and, thus,
confirm the conclusions of Nissen et al. (2003a) from their
VLT/UVES observations of the same lines in southern dwarfs and
subgiants. In Fig. 4, we show our results with
those of Nissen et al. (2003a) for halo stars, also based on the
9213-38 lines,
and Chen et al. (2002) for disk stars. Chen et al. (2002) used the
lines and also lines at 6046, 6053, and 6757 Å, but for their
chosen disk stars these lines provide readily measurable lines in
high-resolution spectra.
In Fig. 4, our values for the stars in common
with I&R and TH are connected with theirs to guide the eye. For
the stars we have in common with TH, we have, for consistency,
chosen their [Fe II/H]
and [S/Fe
II]
values.
The figure illustrates the comparisons between our and the
8694-95-based abundances discussed in the
previous section.
There is no evidence in our data for the rise of [S/Fe] with
decreasing [Fe/H] earlier proposed by I&R and TH. I&R claimed a
linear trend such that
at
,
and TH put the slope lower so that
at
.
We have suggested that the lower [S/Fe] now being obtained are due to a combination of
overestimates of the strength of the very weak
lines in the most metal-poor stars, and of underestimates
of the Fe abundances by I&R. We reiterate that the adopted
effective temperatures and surface gravities are those used by
I&R and TH. Our primary goal was to check the latter authors' S
abundances,
as directly as possible, by using
9213-38
lines rather than the
8694-95 lines used by
them.
Definition of the run of [S/Fe] with [Fe/H] was a secondary goal whose
full achievement demands additional stars.
As can be seen in Fig. 4, the
evidence that [S/Fe] is nearly independent of [Fe/H] for
is greatly strengthened on adding the sulfur abundances
derived by Nissen et al. (2003a), who find a constant value of
dex.
There is a hint in Fig. 4 that our [S/Fe] estimates may be systematically about 0.1 dex lower than those of Nissen et al. (2003a). This difference could be the result of an accumulation of minor differences in effective temperature scales, surface gravity determinations, Fe II gf-values, and others. We also note, that Nissen et al. (2003a) derive a solar iron abundance 0.03 dex larger than the one we apply. Considering this fact would diminish the discrepancy.
Many studies of abundance of
elements in halo stars have
shown that [
/Fe] at a fixed [Fe/H] is largely without
cosmic scatter. The S abundances of Nissen et al. (2003a) confirm
that this result may now be extended to sulfur.
In our small sample, HD 165195 appears to
depart from the constant [S/Fe] indicated by other stars. This
departure may possibly be due to adoption of incorrect atmospheric
parameters. We note that TH remark that the determination of the
effective temperature for HD 165195 is uncertain. They consider a
range of temperatures (
4131-4507 K) in which their adopted
temperature (and therefore the one used by us) is at the lower end
of this range. Observe, that the sulfur abundances determined for
this star are the most sensitive to the effective temperature of
our entire sample, which can be seen in Table 4. A
temperature increase of 300 K would yield a [S/Fe] ratio close to
our mean value. Therefore, our value might be seen as a
determination which could be on the high side. We note, in
passing, that an increase in temperature would also make the
modelled hydrogen-line fit the observed line better.
The exact run of the abundances with metallicity has consequences
for theories and our understanding of Galactic chemical evolution
and for the sites of formation of the elements. So, what are the
sites where sulfur was synthesized during the first few billion
years of the Universe? -capture elements are thought to be
formed during explosions of supernovae (SNe) type II. Owing to
the short life-times of high-mass stars, the progenitors of SNe
type II, the abundances of elements synthesized by them and
ejected into the interstellar medium, quickly reach a steady state
and show a constant over-abundance in the ordinary [S/Fe] vs.
[Fe/H] diagram. However, based on their data, TH and I&R discern
a linear rise of the
-capture element sulfur for the halo
phase of the Milky Way, thus showing a divergent behaviour
compared to other
-capture elements, except possibly
oxygen. If there is a rise in the abundances with decreasing
metallicity, other processes for their formation have to be
invoked. TH and I&R suggest a sulfur contribution from
hypernovae in the early galaxy as an explanation of the high
values. Hypernovae are thought to be the explosion of an extremely
massive star (several 100
). Another mechanism that could
lead to a divergent evolutionary behaviour of oxygen and sulfur as
compared to the other
-capture elements, is the fact that
these two elements are volatile elements as opposed to the others
which are refractory elements. This is important in the modelling
of the transport and mixing of supernovae ejecta into the
interstellar medium, with volatile elements experiencing a mixing
time-scale, more than an order of magnitude faster. However,
considering the results that Nissen et al. (2003a) and we find,
there does not seem to be a need for a distinct evolutionary
scenario for sulfur as compared to the other
elements.
We have shown that reliable abundances of sulfur down to
metallicities of
are obtainable using
the S I lines lying at 9212.9, 9228.1, and 9237.5 Å. In an attempt to resolve the discrepancy found in the
literature, about the Galactic chemical evolution of sulfur for
metallicities lower than
,
we have observed
an ensemble of ten stars, both dwarfs and giants, previously
analyzed with a different and weaker diagnostic; the S I
lines at 8694.0 and 8694.6 Å. These previous investigations
of the 10 stars claimed a rise of the
ratio with
decreasing metallicity. We are not able to confirm this rise. Our
conclusion is instead that we corroborate the finding by
Nissen et al. (2003a) indicating a similar behaviour of sulfur to
the other
elements.
We suggest that the reasons for the difference in determined
sulfur abundances and [S/Fe] are the strength of the lines
analyzed and the way the metallicity is determined. First, we have
used lines which are stronger by a factor of ten as compared to
those used earlier. This is critical for metal-poor stars. Thus,
we conclude that the smallest equivalent widths for the weaker
line must have been overestimated in the previous
studies, leading to an overestimation of the [S/H] ratio by up to 0.5 dex. Second, we have determined the metallicity from
Fe II lines which should give a better determination of the
metallicities than an non-LTE analysis of Fe I lines.
We also show that in spite of the numerous telluric, water-vapor lines in the 9200 Å spectral region, a careful reduction of the data can provide clean spectra. We conclude that the 9212.9, 9228.1, and 9237.5 Å lines are the preferred ones to be used for abundance analyses of sulfur of halo stars.
Acknowledgements
We should like to thank Drs. C. Allende Prieto, B. Gustafsson, K. Eriksson, B. Edvardsson, A. Kron, and N. Piskunov for valuable discussions and comments. This research has been supported in part by the Swedish Research Council, Stiftelsen Blanceflor Boncompagni-Ludovisi, née Bildt, the Swedish Foundation for International Cooperation in Research and Higher Education, and the Robert A. Welch Foundation of Houston, Texas.