Solar Chemical Abundances Determined with a CO5BOLD 3D Model Atmosphere

Introduction

Since the pioneering work of \inlineciterussell29, the study of the chemical composition of the solar photosphere has been an important topic in astronomy. Russell, measuring the strength of the absorption lines in the observed solar spectrum, determined the abundance of 56 elements and six molecules. After this work many other astronomers analysed the solar spectrum in order to deduce the detailed pattern of photospheric abundances. The accurate determination of the solar chemical abundances is a major topic, because:

the knowledge of the elemental abundances in the present solar photosphere is the basis to infer the chemical composition of the initial Sun, and allows one to reconstruct the past and future evolution of the Sun, including its physical and chemical internal structure;

the comparison of the chemical abundances in the solar photosphere and in meteoritic samples provides important information about the formation and chemical evolution of the solar system;

the construction of detailed models of the solar atmosphere requires the knowledge of its chemical composition;

the knowledge of the solar photospheric chemical abundance allows the empirical determination of the oscillator strength of any spectral line of this element observable in the solar spectrum;

the solar abundances serve as a reference for the chemical analysis of other stars in the Galaxy, of the interstellar medium, and of the stellar populations of external galaxies.

In our analysis of the solar photosphere we are mainly interested in the first and third point.

For our work on the solar abundance determinations, we rely on a CO5BOLD 3D model of the solar photosphere. We were interested to understand if the presence of horizontal fluctuations (the solar granulation) has a systematic effect on the abundances derived from the 3D model with respect to what is obtained by 1D models which ignore granulation.

We find that the effects of granular fluctuations can lead to both positive and negative abundance corrections, depending on the properties of the individual spectral line under consideration. However, the granulation effect is relevant only in a few particular cases. 3D effects are not responsible for the systematic lowering of the solar abundances in recent years.

In the following sections we summarise the investigations of some elements we have already published, and present a new analysis of some other elements (Li, K, Fe, and Os). For a complete overview of the solar abundance determinations we recommend the review by \inlinecitelodders09 as a very detailed and complete work.

Model Atmospheres

the semi-empirical Holweger-Müller solar model (Holweger 1967, Holweger and Müller 1974, hereafter HM);

the ATLAS-9 model computed by F. Castelli [http://wwwuser.oats.inaf.it/castelli/sun/ap00t5777g44377k1asp.dat] with the solar abundances of \inlinecitesunabboasp.

3D Corrections

For some of the weak lines that we investigated (e.g. the C i line at 538 nm), we compared the 3D correction $\Delta^{(1)}$ with the results of \inlinecitemst02, which are based on a 2D hydrodynamical simulation, and find a close agreement. Summarising our analysis, we can say that the total 3D correction $\Delta^{(2)}$ is positive for the majority of the relevant spectral lines, except for a few weak, high-excitation lines (mostly Nitrogen) for which both $\Delta^{(1)}$ and $\Delta^{(2)}$ are negative. However, the 3D corrections are small in general.

The abundances presented in this work have been derived directly from the 3D model, in line with our previous publications. We trust in the temperature structure of our 3D-CO5BOLD model, because it is able to reproduce the centre-to-limb variation of the continuum intensity even somewhat better than the HM model Ludwig et al. (2009). However, we plan to compute abundances also with the alternative approach, i.e. from the HM model and correcting by $\Delta^{(1)}(\xi_{\rm mic})$, in future investigations. While it is not entirely clear which of the two approaches gives the more reliable results, we propose the abundance differences between the two methods to be considered as a measure of the systematic uncertainty of the abundance analysis.

Observational Data

Our analysis is based on mainly four high resolution, high signal-to-noise ratio [S/N] spectra, two for disc centre, and two for the integrated disc. For most elements we use more than one solar spectrum, because we realised that the abundance derived from different spectra do not always agree within one $\sigma$. The observed spectra we considered are:

the integrated disc spectrum based on fifty solar FTS scans taken by J. Brault and L. Testerman at Kitt Peak between 1981 and 1984 Kurucz (2005);

the two absolutely calibrated FTS spectra obtained at Kitt Peak in the 1980s, covering the range 330 nm to 1250 nm for the integrated disc and disc centre Neckel and Labs (1984); Neckel (1999);

the disc centre intensity spectrum in the range 300 nm to 1000 nm observed from the Jungfraujoch Delbouille, Roland, and Neven (1973), and in the range from 1000 nm to 5400 nm observed from Kitt Peak Delbouille el at. (1981).

Chemical Abundances

Lithium is widely studied in metal-poor stars. The Li i resonance doublet at 670.7 nm is also observable in the solar spectrum and in the spectra of F–K main sequence stars. In metal-poor stars, this region is very clean, and the Lithium feature is not blended. This is not the case in solar-metallicity stars, where atomic and molecular lines contaminate the region. Good atomic data for these blending lines are not readily available in databases, but there are a few published line lists that have been used for the abundance analysis of the solar photosphere. For our own analysis of Li in the solar photosphere, we took into account both granulation and 3D-NLTENLTE stands for Non Local Thermodynamic Equilibrium effects in computing the contribution of the Li doublet, while 3D-LTE line formation calculations were performed for the other blend components.

Considering the four solar atlases described above to investigate lithium, we realise that the two observed intensity spectra are significantly different (see Figure \ireffig:liint). We have no explanation for this disagreement. The easiest way to explain it would be to invoke telluric absorption, but this spectral range has been carefully scrutinised in the context of the Li isotopic ratio in metal-poor stars, and it seems unlikely that a telluric absorption could have gone unnoticed. We decided to discard the Delbouille disc centre atlas, and to work only with the other three atlases for the Li abundance determination. The reason for discarding the Delbouille disc centre atlas is that we cannot reproduce the profile with synthetic spectra, while we can in the case of the other three solar atlases, and obtain Li abundances that agree closely.

The two lists of blending lines that can reproduce the solar spectrum in this region reasonably well are those from \inlineciteghezzi09 and from \inlinecitereddy02. To obtain the Li abundance, we fit the observed line profile, interpolating in a grid of 3D synthetic spectra, in which NLTE effects are taken into account for Li. We obtain $A$(Li)${}_{\rm 3D-NLTE}=1.03\pm 0.03$, fitting the three observed line profiles using the \inlineciteghezzi09 line list. Fortunately, the solar Lithium abundance is not very sensitive to the choice between the two line lists: when using the \inlinecitereddy02 list, we obtain $A$(Li)${}_{\rm 3D-NLTE}=1.01$.

2 Carbon

3 Nitrogen

4 Oxygen

5 Phosphorus

We considered five infrared P i lines of Multiplet 1 for the photospheric abundance determination Caffau et al. (2007b). Our photospheric Phosphorus abundance of $A$(P)$=5.46\pm 0.04$ is in perfect agreement with the meteoritic value Lodders et al. (2009). The Phosphorus abundance in \inlineciteasplund09 is 0.06 dex larger with respect to the value of $A$(P)$=5.35\pm 0.04$ given in \inlinecitesunabboasp. It is unclear whether this upward revision is related to their new 3D model or to a change in the line list, in the $\log\,gf$ values, and/or the adopted equivalent widths.

6 Sulphur

In \inlinecitelodders09 the photospheric Sulphur abundance is given as $A$(S)$=7.14\pm 0.01$ and the meteoritic one as $A$(S)$=7.17\pm 0.02$. We have studied several S i lines in the solar spectrum. From the weak forbidden line at 1082 nm we obtain $A$(S)$=7.15\pm\left(0.01\right)_{\rm stat}\pm\left(0.05\right)_{\rm sys}$ Caffau and Ludwig (2007). \inlineciteasplund09 criticise both the measured equivalent widths as being too small, and the $\log\,gf$ we (and also \inlineciteryde06) use as being obsolete, claiming that updated values should be used. As no further details are given, it is impossible to judge whether their equivalent widths and $\log\,gf$ values are better. We considered also the permitted lines of Multiplet 3, Multiplet 6, and Multiplet 8, discarding the strong lines of Multiplet 1 at 920 nm, because they are blended with telluric absorption Caffau et al. (2007a). Both lines of Multiplet 6 and Multiplet 8 are weak and close to LTE. The abundance we find is $A$(S)$=7.14$ from the line of Multiplet 8, and $A$(S)$=7.11$ from the two lines of Multiplet 6. The lines of Multiplet 3 at 1045 nm are affected by departures from LTE. If we take this effect into account, using the NLTE correction of \inlinecitetakeda05, we obtain $A$(S)$=7.30$. This value becomes $A$(S)$=7.28$ when using the NLTE corrections computed by S. Andrievsky and S. Korotin with the Sulphur model atom described in \inlinecitekorotin08 and \inlinecitekorotin09. The simple average over all of the multiplets would give $A$(S)$=7.17\pm 0.07$, where $\sigma$ is the root-mean-square deviation. Giving twice the weight to the [SI] lines and the lines of Multiplet 8 because they are unaffected by NLTE, we obtain $A$(S)$=7.16\pm 0.05$, which we recommend as the solar photospheric value.

7 Potassium

In the solar spectrum, Potassium is observed through lines of the neutral species, K i. As for other alkalines, the strongest lines are those of the resonance doublet of K i at 766.4 nm and 769.8 nm, the only observable lines in metal poor stars. In fact, the other K i lines are much weaker. Unfortunately, the strongest K i line at 766.4 nm is heavily blended in the solar spectrum by strong telluric O2 absorption.

delareza75 performed the first detailed study of the K i 769.8 nm doublet component in the solar photosphere, analysing its centre-to-limb variation and computing the K abundance in NLTE.

Among the few excited K i lines, the one at 404.4 nm is often used in old solar abundance analyses; but this line is significantly blended and the $f$ value is uncertain so that it is excluded by \inlinecitedelareza75. Also \inlinecitelambert78b suggest that a wrong $f$ value could be the reason for the exceedingly low abundance derived from this line.

takeda96 obtain a good fit of the solar flux spectrum with their synthetic profile of the line at 769.8 nm with a multi-parameter fitting method. They also studied the dependence of the K abundance upon the atomic parameters, the microturbulence, and the adopted model atmosphere (see their Table 4). The NLTE correction for this line is estimated by them to be about $-0.4$ dex.

zhang06 consider seven lines: the line at 693.8 nm, the resonance doublet, plus four lines in common with \inlinecitelambert78b. These authors derive the Potassium abundance by line profile fitting of the integrated disc solar spectrum with a NLTE synthetic profile. The NLTE corrections provided in this paper are applied to our LTE analysis (see below). \inlinecitetakeda96 select eight weak K lines, adding to the list of \inlinecitezhang06 the lines at 404.7, 533.9, and 583.1 nm, while they ignore the 1243.2 nm line, which is included by \inlinecitezhang06. According to \inlineciteivanova00 NLTE corrections are small for the 693.8 nm line, important for the 1252.2, 1243.2, and 1176.9 nm lines, and very important for the 769.8 nm line.

Our adopted value is $A$(K)${}_{\rm 3D-NLTE}=5.11\pm 0.09$, which is obtained by applying the NLTE corrections of \inlinecitezhang06 to the results from the 3D-LTE analysis for the integrated disc spectrum. The 3D-LTE results from disc centre and integrated disc agree very closely, the latter being 0.03 dex higher. This tiny difference is probably due to different NLTE corrections.

8 Iron

Iron is a complex atom with a very rich spectrum of atomic lines, especially from the neutral and singly ionised stage. Many scientists devoted time to the determination of the Iron abundance in the solar photosphere, both from Fe i (which accounts for most of the lines in the solar spectrum) and from Fe ii (which is the dominant ionisation stage of Iron in the photosphere).

The Iron abundance was continuously decreasing from the value given by \inlineciterussell29 until the 1960s. The correction of the transition probabilities produced an increasing solar abundance by about one order of magnitude until the 1990s. Since then, $A$(Fe) has experienced a smooth decrease (see Figure 1 in \inlinecitegrevesse99). We recall some important developments in this field: Corliss and his group investigated the Iron abundance, with their transition probability Corliss and Warner (1966); Corliss and Tech (1968); Bridges and coworkers applied their new $gf$-scale to the abundance determination Bridges and Wiese (1970); Bridges and Kornblith (1974). Between 1980–1990, there was a long debate between Holweger and the Blackwell group, advocating a low ($A$(Fe)$=7.50$) and a high ($A$(Fe)$=7.63$) Iron abundance, respectively Biemont et al. (1991); Blackwell, Lynas-Gray, and Smith (1995); Holweger, Kock, and Bard (1995); Blackwell, Smith, and Lynas-Gray (1995); Kostik, Shchukina, and Rutten (1996). \inlinecitekostik96 pointed out the necessity to perform a 3D-NLTE analysis, which was impossible at the time for the lack of computer power and atomic-physics data.

To investigate the Iron abundance in the solar photosphere, we selected 15 Fe ii lines and measured their equivalent widths with the IRAF task splot (see Table \ireftbl:feiilines). We presume that transitions from the dominant ionisation stage of Iron, Fe ii, are close to LTE condition Gehren et al. (2001). This is not the case for Fe i, for which NLTE-effects are important, at the level of $\approx 0.1$ dex, as shown by Gehren et al. (2001; 2001) using hydrostatic 1D model atmospheres, and by \inlineciteST01 using a single snapshot of a 3D hydrodynamical simulation.

For the disc centre and integrated disc spectra, the 3D abundance we find is $A$(Fe)$=7.525\pm 0.057$ and $A$(Fe)$=7.512\pm 0.062$, respectively, when using the $\log\,gf$ from \inlinecitemelendez09. When we use the $\log\,gf$ from \inlinecitehannaford92, the line-to-line scatter increases and the abundances become $A$(Fe)$=7.530\pm 0.110$ and $A$(Fe)$=7.516\pm 0.109$, respectively. If we remove the 744.9 nm line, which shows an exceptionally low $A$(Fe) value, we slightly reduce the $\sigma$: $A$(Fe)$=7.550\pm 0.082$ and $A$(Fe)$=7.532\pm 0.093$, respectively. Thirteen of our selected Fe ii lines are in common with those for which \inlineciteSchnabel have measured oscillator strengths. Using their set of $\log\,gf$ values we obtain, for these 13 lines, $A$(Fe)${}_{\rm 3D}=7.50\pm 0.11$ and $A$(Fe)${}_{\rm 3D}=7.49\pm 0.11$ for the for the disc centre and integrated disc spectra, respectively. We conclude that the different sets of oscillator strengths provide highly consistent Iron abundances. However, the line-to-line scatter is considerably smaller when adopting the \inlinecitemelendez09 $\log\,gf$ values. Therefore, considering both disc centre and integrated disc spectra, we recommend $A$(Fe)$=7.52\pm 0.06$ for the photospheric solar Iron abundance. As a consequence of the problem in representing the turbulent motions on small scales in the hydrodynamical simulations, described in Steffen et al. (2009), there is a small slope of abundance with equivalent width of the line, which amounts to 0.02 dex/pm.

From our analysis, the recommended solar Iron abundance is A(Fe) = $7.52\pm 0.06$.

9 Europium

Basing our 3D LTE analysis Mucciarelli et al. (2008) on the five Eu ii lines from \inlinecitelawler01, we obtain $A$(Eu)$=0.52\pm 0.02$. The isotopic ratio of 151Eu/(151Eu + 153Eu) derived from disc centre and integrated disc spectra is $(49\pm 2.3)$% and $(50\pm 2.3)$%, respectively. We are in perfect agreement with the results of \inlinecitelodders09.

10 Hafnium

For the abundance determination of Hafnium Caffau et al. (2008b), we considered four Hf ii lines, suggested by \inlinecitelawler07. The lines are weak and blended, making the abundance determination a difficult task. Our abundance determination, $A$(Hf)$=0.87\pm 0.04$, is in close agreement with the photospheric value of \inlinecitelodders09, but larger than their meteoritic value of $0.73\pm 0.02$.

11 Osmium

Osmium and Iridium are among the heaviest stable elements and as such are reliable reference elements for measuring the decay of the radioactive nuclei 238U and 232Th. Therefore Os is important in radioactive cosmochronology.

The determination of the solar Os abundance is not an easy task: the suitable Os i lines lie mostly in the crowded violet and near UV range, and the transition probabilities have been revised several times in the last decades. Improved centre-of-gravity wavelength are given by \inlineciteivarsson03, who recall also that Os has seven stable isotopes; the even isotopes which account for more than 80% of all Osmium have no hyperfine structure. However, according to the analysis of \inlinecitequinet06, the isotopic splitting and the hyperfine structure of the odd isotopes have no influence on the Os abundance determination.

ivarsson03 determined a new set of $\log\,gf$ for 18 Os i lines and compared them with previous values, finding a good agreement of their experimental results with previous determinations for the three strongest lines (290.9, 305.8, and 330.1 nm). However, a substantial disagreement is found for other lines with offset and dispersion increasing for the weaker lines. The comparison with theoretical results shows an even larger scatter. \inlineciteivarsson03 did not study the solar Os abundance, but applied their new $\log\,gf$ values to the analysis of the metal poor giant CS 31082-001, previously analysed by \inlinecitehill02.

The solar abundance of Os has been determined by \inlinecitejacoby76 from three Os i lines (305.8706, 330.1579, and 442.0460 nm), using $\log\,gf$ from \inlineciteCB, to obtain $A$(Os)=0.70. Owing to the large errors often present in the \inlineciteCB data, a new determination of the lifetimes of nine transitions of Osmium, including the three lines used by \inlinecitejacoby76, has been done by \inlinecitekwiatkowski84. These new $\log\,gf$ are systematically lower than those by \inlineciteCB (by about 0.5 dex) leading to $A$(Os)$=1.45\pm 0.10$ from the equivalent widths of nine lines measured in the solar atlas of \inlinecitedelbouille, and using the HM model. This abundance agrees within one $\sigma$ with the Os abundance in meteorites of $A$(Os)$=1.37\pm 0.03$ Lodders et al. (2009).

The most recent transition probabilities and solar Osmium abundance are due to \inlinecitequinet06, who also give all of the possible contaminations of each Os i line in the Sun or in metal-poor stars. New $\log\,gf$ are determined by these authors for 11 Os i lines and the difference with respect to the previous results is less than 0.1 dex for all but the two lines at 397.2 nm and 442.0 nm. Their newly determined $\log\,gf$ value for the 442.0 nm line differs by 0.33 from the previous value; the new $\log\,gf$ value of $-1.20$ produces an Os abundance in better agreement with that from other Os i lines in the star CS 31082-001. They determine the Os abundance using SYNTHE Kurucz (1993) with HM and MARCS models, but do not specify which observational data are used. They discarded not only the heavily blended lines, but also the weakest ones (EW$<0.2$ pm) because they are faint, sensitive to blends, and more affected by uncertainties in the $\log\,gf$ values. In the end, \inlinecitequinet06 retained only three lines (326.7945, 330.1559, and 442.0468 nm) that give the abundances $A$(Os)= 1.40, 1.30, and 1.15, respectively, with the HM model, and $A$(Os)= 1.30, 1.25, and 1.10 with a MARCS model. Their final Os abundance is $A$(OS)$=1.25\pm 0.11$.

We adopted the equivalent widths of the Os i lines from \inlinecitekwiatkowski84 and derived the abundances interpolating in theoretical curves-of-growth (see Table \ireftbl:osilines). We adopted the partition function from \inlineciteAllen. If we weight the abundances from the individual lines as in their analysis, we obtain an abundance of $A$(Os)${}_{\rm 3D}=1.36\pm 0.19$. The straight average gives $A$(Os)${}_{\rm 3D}=1.35\pm 0.21$. The $\log\,gf$ values that we use are from \inlinecitequinet06 for all lines except for the 409 nm, 442 nm, and 463 nm lines for which we use the $\log\,gf$ values from \inlinecitekwiatkowski84. If we restrict our selection to the three lines considered most reliable by \inlinecitequinet06 (330.1 nm, 409.1 nm, and 455.0 nm) we obtain a very similar value for the average ($A$(Os)=1.37) with an improved but still very large line-to-line scatter ($\sigma$=0.16). For this reason we recommend the result from the complete sample of lines.

12 Thorium

The only line of Thorium in the solar spectrum that can be used for abundance determination is the Th ii resonance line at 401.9 nm Caffau et al. (2008b). This weak absorption lies on the red wing of a stronger Fe-Ni feature and is blended with weaker lines. We performed a line profile fitting analysis with a 3D synthetic profile, in order to take into account the convection-induced asymmetry, of the Fe-Ni blend. Giving higher weight to the results from the disc centre data, which resolve the line profile better, we obtained $A$(Th)$=0.08\pm 0.03$ Caffau et al. (2008b). This result is in perfect agreement with the meteoritic value Lodders et al. (2009).

Conclusions

The abundances of the solar photosphere, based on our CO5BOLD solar model atmosphere, are reported in Table \ireftbl:abbo. We find that 3D corrections are small in general, and not responsible for the systematic lowering of the solar abundances over the past years. With the abundances given in Table \ireftbl:abbo, and the abundances from \inlinecitelodders09, photospheric where available, for the elements that we did not analyse, we obtain a solar metallicity of $Z=0.0153$, and $Z/X=0.0209$. This value can be compared to $Z=0.0141$, and $Z/X=0.0191$ of \inlinecitelodders09 and $Z=0.0134$, and $Z/X=0.0181$ of \inlineciteasplund09.

Our spectroscopic abundances of O and Fe are in agreement, within the indicated mutual errors, with what is derived from helioseismic constraints: $A$(O)$=8.86\pm 0.045$, $A$(Fe)$=7.50\pm 0.048$ Delahaye and Pinsonneault (2006). There is also a good agreement for the key elements C, N and O, with the most likely spectroscopic abundances recommended by \inlinecitePD09: $A$(C)$=8.44\pm 0.06$, $A$(N)$=7.96\pm 0.10$, $A$(O)$=8.75\pm 0.08$.

We conclude that our derived solar metallicity goes in the direction of reconciling atmospheric abundances with helioseismic data. According to Turcotte and Wimmer-Schweingruber (2002), the abundance of metals in the solar photosphere may have decreased by up to 0.04 dex by diffusion during the solar lifetime. This would improve the correspondence between spectroscopic and helioseismic results even further.

We thank Rosanna Faraggiana for her constant support and precious advise. We are grateful to Sergei Andrievsky and Sergei Korotin for NLTE computations and useful discussions. We acknowledge support from EU contract MEXT-CT-2004-014265 (CIFIST).

References