5.3 Solar abundance analysis

Due to their realistic nature and successful reproduction of key observational constraints, 3D hydrodynamical model atmospheres can be used for elemental abundance determinations. These will then hopefully be more reliable than corresponding 1D analyses since the traditional free parameters used in stellar/solar spectroscopy (mixing length parameters, micro- and macroturbulence) no longer enter into the line formation calculations and because line profile fitting may be routinely employed instead of relying on often uncertain equivalent width measurements. In a series of papers (Allende Prieto et al., 2001Jump To The Next Citation Point2002Asplund, 2000Jump To The Next Citation Point2004Jump To The Next Citation PointAsplund et al., 2000cJump To The Next Citation Point2004Jump To The Next Citation Point2005aJump To The Next Citation Point,bJump To The Next Citation PointScott et al., 2006Jump To The Next Citation Point), a re-analysis of the solar chemical composition was made, using a carefully constructed 3D solar convection simulation with the correct nominal solar effective temperature (Asplund et al., 2000bJump To The Next Citation Point). The 3D radiative transfer equation was solved at each time-step of the simulation using a realistic equation-of-state (Mihalas et al., 1988) and opacities (Gustafsson et al., 1975Kurucz, 1993) with the opacity binning technique (Nordlund, 1982). For most elements, LTE was assumed in the line formation calculations but for Li i and O i full 3D non-LTE calculations have been performed (Asplund et al., 20032004Jump To The Next Citation Point). In these studies special effort has been made to adopt the most reliable and up-to-date atomic and molecular input data, such as transition probabilities, partition functions, line broadening parameters and dissociation energies. In the comparison with observations, both disk-center and disk-integrated flux profiles have been used, which give nearly identical results. Similar solar abundance analyses for selected elements assuming LTE have been carried out using an independent 3D hydrodynamical solar model atmosphere computed with the co5bold code (Freytag et al., 2002) with in general good agreement with those presented by Asplund and collaborators when accounting for differences in the adopted atomic line data (Ludwig and Steffen, 2007Caffau and Ludwig, 2007Jump To The Next Citation PointCaffau et al., 2007aJump To The Next Citation Point,bJump To The Next Citation Point2008aJump To The Next Citation Point,bJump To The Next Citation PointMucciarelli et al., 2008Jump To The Next Citation Point).

5.3.1 Carbon

Of all elements carbon has the most diverse set of indicators that can be employed in deriving a solar elemental abundance. The diagnostics include both high-excitation permitted and low-excitation forbidden C i lines as well as a number of different molecular features, including CH vibration-rotation lines in the infrared, CH electronic lines and C2 electronic transitions in the optical (e.g., Lambert, 1978Jump To The Next Citation PointAsplund et al., 2005bJump To The Next Citation Point); CO vibration-rotation lines may also be used but it requires prior knowledge of the solar O abundance (Scott et al., 2006Jump To The Next Citation PointAyres et al., 2006Jump To The Next Citation Point). These are all formed in very different atmospheric layers and have distinct dependencies to the atmospheric conditions, in particular the temperature. As some lines are quite weak while others are partly saturated they also have different sensitivity to the predicted convective velocities. For these reasons, achieving consistent results from all different abundance indicators is challenging and provides a very stringent test of the appropriateness of the adopted model atmosphere, line formation calculations and input data for the transitions.

Asplund et al. (2005bJump To The Next Citation Point) carried out a solar C abundance analysis using a 3D hydrodynamical solar model atmosphere. Table 1 list their derived 3D-based C abundances as well as for two 1D model atmospheres often employed in solar/stellar abundance analyses: the theoretical marcs (Asplund et al., 1997Jump To The Next Citation Point) and the semi-empirical Holweger and Müller (1974Jump To The Next Citation Point) model atmospheres. Two things are particularly noteworthy. Firstly, only in 3D do the different indicators give consistent results while especially in the Holweger–Müller case there is a range of implied abundances differing by > 0.2 dex. Secondly, the 3D analysis result in significantly lower abundances than the Holweger–Müller, in particular for the molecular transitions. The latter is mainly due to the cooler temperatures in the optically thin layers in the 3D model compared with the 1D semi-empirical model as well as the presence of temperature inhomogeneities. Because of the great temperature sensitivity of molecule formation, both of these factors tend to strengthen the lines in 3D and thus require lower C abundances to explain the observed features. In the 3D case there are no significant abundance trends with wavelength, excitation or line strength, except for C i where there is a slight correlation with the equivalent widths of the lines; we suspect that this is a signature of underestimated non-LTE effects, maybe because here only 1D non-LTE calculations have been used (Fabbian et al., 2006).

The observed strong vibrational-rotational lines of CO in the Sun, in particular towards the limb, have for a long time been a challenge to model and has been argued to be inconsistent with the canonical temperature rise in the lower chromosphere (e.g., Ayres et al., 2006Jump To The Next Citation Point, and references therein). Departures from LTE in the line formation have been demonstrated to be unimportant and thus can not be invoked to explain the strong CO lines (Uitenbroek, 2000b). The presence of temperature atmosphere inhomogeneities in 3D hydrodynamical surface convection simulations on the other hand strengthens the predicted CO lines into better agreement with observations (Uitenbroek, 2000aScott et al., 2006Jump To The Next Citation Point); the typically cooler horizontally mean temperature stratification in 3D modeling than in the Holweger and Müller (1974Jump To The Next Citation Point) semi-empirical model is also conducive for molecular formation. Scott et al. (2006Jump To The Next Citation Point) have shown that the 3D-based C abundance from weak CO lines from the fundamental and first overtone bands are in excellent agreement with the other atomic and molecular C abundance indicators (Table 1). Although the situation is markedly better than with the Holweger and Müller (1974Jump To The Next Citation Point) model, the stronger low-excitation CO lines, however, are still predicted to be too weak with the 3D model, suggesting even lower temperatures around the heights of the nominal temperature minimum than the current generation of 3D models implies. In the solar photosphere up to heights of about 700 km above the optical surface, the time-dependent molecule formation of CO has been shown to proceed according to LTE expectations (Asensio Ramos et al., 2003Wedemeyer-Böhm et al., 2005), which will therefore not affect the derived abundances. The dynamical time-scale in the higher atmospheric layers are much shorter than the time-scale for radiative relaxation, which prevents a CO-driven self-amplified thermal instability to be operative (Wedemeyer-Böhm and Steffen, 2007).


Table 1: The derived solar C, N, and O abundances based on different atomic and molecular indicators using a 3D hydrodynamical model of the solar atmosphere (Asplund et al., 2004Jump To The Next Citation Point2005bJump To The Next Citation Point,aJump To The Next Citation PointScott et al., 2006Jump To The Next Citation Point, Asplund et al., in preparation), together with the corresponding 1D results for the theoretical marcs model atmosphere (Asplund et al., 1997) and the semi-empirical model of Holweger and Müller (1974Jump To The Next Citation Point). The quoted uncertainty is only the line-to-line scatter.
lines
log𝜖C,N,O
  3D HM marcs
[C i] 8.39 8.45 8.40
C i 8.36 ± 0.03 8.39 ± 0.03 8.35 ± 0.03
CH, Δv = 1 8.38 ± 0.04 8.53 ± 0.04 8.42 ± 0.04
CH, A-X 8.45 ± 0.04 8.59 ± 0.04 8.44 ± 0.04
C2 Swan 8.44 ± 0.03 8.53 ± 0.03 8.46 ± 0.03
CO, Δv = 1 8.40 ± 0.01 8.60 ± 0.01 8.55 ± 0.02
CO, Δv = 2 8.37 ± 0.01 8.69 ± 0.02 8.58 ± 0.02
N i 7.79 ± 0.08 7.90 ± 0.08 7.86 ± 0.08
NH Δv = 1 7.79 ± 0.05 8.01 ± 0.05 7.88 ± 0.05
CN 0–0 7.81 ± 0.04 8.03 ± 0.04 7.88 ± 0.04
[O i] 8.68 ± 0.01 8.76 ± 0.02 8.72 ± 0.01
O i 8.64 ± 0.02 8.64 ± 0.08 8.72 ± 0.03
OH, Δv = 0 8.65 ± 0.02 8.82 ± 0.01 8.83 ± 0.03
OH, Δv = 1 8.61 ± 0.03 8.87 ± 0.03 8.74 ± 0.03
OH, Δv = 2 8.57 ± 0.06 8.80 ± 0.06 8.61 ± 0.06

Since previously most trust has been put in the molecular lines, the study by Asplund et al. (2005bJump To The Next Citation Point) has resulted in a significant lowering of the recommended solar photospheric C abundance to log 𝜖C = 8.39 ± 0.05. Compared with the compilations of for example Anders and Grevesse (1989Jump To The Next Citation Point) and Grevesse and Sauval (1998Jump To The Next Citation Point) the new value is lower by 0.17 and 0.13 dex, respectively. While for the molecular lines the dominant factor is the use of a realistic 3D model instead of 1D model atmospheres, it should be emphasized that it is not the only factor causing this downward revision. Indeed, for the [C i] 872.7 nm line an improved transition probability is of equal importance while for the C i lines allowing for non-LTE effects is even more important than the 3D effects. The fact that after these significant improvements (3D model atmospheres, non-LTE line formation and better atomic/molecular line data) the derived abundances are in such excellent agreement is very encouraging. Finally, the derived carbon isotopic ratio (12C/13C = 87 ± 4) from CO lines using the same 3D model as above (Scott et al., 2006Jump To The Next Citation Point) is in excellent agreement with the terrestrial value (89 ± 1) while with 1D models the implied ratio is significantly lower (Scott et al., 2006Jump To The Next Citation PointAyres et al., 2006Jump To The Next Citation Point).

5.3.2 Nitrogen

Also for N there are both atomic and molecular lines that may be utilized in an abundance analysis, albeit not as many different indicators as for C or O (Asplund et al., 2005aJump To The Next Citation Point). The forbidden [N i] lines cannot be employed as they are all too weak in the solar spectrum but there are some 20 weak high-excitation N i lines that are suitable for the purpose. In addition there are both vibration-rotation and pure rotation lines of NH in the infrared as well as a multitude of CN transitions from various bands; in the latter case, however, one has to have prior knowledge of the C abundance from other diagnostics. The (still preliminary) results (Asplund, et al., in preparation) in terms of the solar N abundance are given in Table 1. Again, there is very satisfactory agreement between the different indicators in 3D although similar consistency is in fact achieved also with the 1D marcs model while the Holweger–Müller model returns somewhat larger discrepancies. The mean 3D-based abundance is significantly lower than in previous studies: log 𝜖N = 7.80 ± 0.05. This is 0.25 dex lower than the value recommended by Anders and Grevesse (1989Jump To The Next Citation Point) and is mainly due to the use of the 3D model with minor changes coming from non-LTE effects for N i, refined atomic/molecular line data and exact choice of lines.

5.3.3 Oxygen

Over the years a large number of studies have been devoted to estimate the solar O abundance, because of its importance in astrophysics stemming from its relatively large abundance, its significant contribution to the opacity in the stellar/solar interior and its diagnostics value for stellar nucleosynthesis and cosmic chemical evolution. In the solar case both atomic and molecular transitions are available for abundance analysis (e.g., Lambert, 1978Jump To The Next Citation PointAsplund et al., 2004Jump To The Next Citation Point). The high-excitation O i lines (including the well-known 777 nm triplet) are easily measured but are susceptible to significant departures from LTE (e.g., Altrock, 1968Kiselman, 1993Kiselman and Nordlund, 1995Asplund et al., 2004Jump To The Next Citation Point). The forbidden [O i] lines from the ground state at 630 and 636 nm do not suffer from non-LTE effects but are very weak and blended by other lines (Allende Prieto et al., 2001Jump To The Next Citation PointAsplund et al., 2004Jump To The Next Citation PointCaffau et al., 2008aJump To The Next Citation PointAyres, 2008Jump To The Next Citation Point). In the infrared there are numerous vibration-rotation as well as pure rotation lines of OH that can be employed (e.g., Sauval et al., 1984Grevesse et al., 1984Asplund et al., 2004Jump To The Next Citation PointMeléndez, 2004Jump To The Next Citation Point); the electronic OH lines in the UV are less suitable for abundance determinations due to the possibility of missing UV opacity (Asplund, 2004Jump To The Next Citation Point). Table 1 summarizes the results of Asplund et al. (2004Jump To The Next Citation Point) based on an analysis using a 3D hydrodynamical solar model atmosphere.

View Image

Figure 31: Upper panel: The observed (dots) feature 630 nm, which corresponds to the main forbidden [O i] line that is blended with a Ni i line. The solid line denote the best fitting 3D-profile consisting of contributions from both [O i] and Ni i (dashed lines). Lower panel: The same as above but ignoring the Ni line. Note that in this case the required O abundance is 0.13 dex higher but that neither the line shape nor the overall line shift of the feature is well explained (from Allende Prieto et al., 2001Jump To The Next Citation Point).

Allende Prieto et al. (2001Jump To The Next Citation Point) utilized the fact that the 3D model can predict the detailed line shapes and asymmetries to a remarkable degree (Section 5.2) to conclude that the [O i] 630 nm line must be blended by a Ni i line (Figure 31View Image), which was suspected already by Lambert (1978Jump To The Next Citation Point). In Allende Prieto et al. (2001Jump To The Next Citation Point) the product of the Ni abundance and the gf-value of the Ni blend was left as a free parameter in the fit of the [O i]+Ni i feature. It is noteworthy from their study that the most important difference compared with previous studies is the allowance of the Ni blend, which by itself lowers the derived O abundance by ≈ 0.13 dex, while the use of the 3D model causes a further 0.08 dex downward revision compared with the case with the Holweger and Müller (1974Jump To The Next Citation Point) model atmosphere. The presence of the Ni blend was subsequently confirmed experimentally by Johansson et al. (2003Jump To The Next Citation Point). Adopting the new laboratory transition probability for the Ni line together with the 3D-based solar Ni abundance (log 𝜖Ni = 6.17 ± 0.04, Scott et al., in preparation) would lead to a 0.12 dex higher loggf ⋅ 𝜖 Ni than estimated by Allende Prieto et al. (2001Jump To The Next Citation Point) and, hence, a lower left-over contribution of the 630 nm feature to be explained by O i. In terms of abundance this corresponds to a lowering of the O abundance by a further ≈ 0.04 dex compared with what is given in Table 1 at the expense of a degraded agreement with the observed line profile compared with Figure 31View Image.

Caffau et al. (2008aJump To The Next Citation Point) have recently performed an independent analysis of the 630 nm line using an alternative 3D hydrodynamical solar model atmosphere computed with the co5bold code. The two 3D models are based on essentially the same approximations, assumptions and input data but with different and completely independent numerical implementations. The resulting temperature structures are similar, although the co5bold model is slightly warmer in the line-forming region than the 3D model by Asplund et al. (2000bJump To The Next Citation Point). Caffau et al. (2008aJump To The Next Citation Point) predict the Ni contribution to the feature by adopting the Johansson et al. (2003) gf-value and the solar Ni abundance of Grevesse and Sauval (1998Jump To The Next Citation Point), which is 0.06 dex higher than the revised value of Scott et al. (in preparation). They find an essentially identical O abundance from this line as Allende Prieto et al. (2001Jump To The Next Citation Point) and Asplund et al. (2004Jump To The Next Citation Point): log 𝜖O = 8.68 ± 0.15. Ayres (2008) has carried out a similar study but based only on one snapshot of the co5bold 3D solar model. More importantly, he follows the procedure of Allende Prieto et al. (2001Jump To The Next Citation Point) to leave the Ni contribution as a free parameter when obtaining the best fitting line profile, in spite of the new accurate experimental transition probability. He concludes that the Ni line is only 70% as strong as would be expected based on the new gf-value and the Ni abundance of Grevesse and Sauval (1998Jump To The Next Citation Point), a difference which greatly exceeds the quoted uncertainties of these two values. As a result he arrives at a correspondingly higher O abundance: log 𝜖O = 8.81 ± 0.04.

Centeno and Socas-Navarro (2008Jump To The Next Citation Point) have used a novel alternative method, namely to analyze spectro-polarimetric observations of sunspots and the asymmetry of the Stokes V profile of the [O i] + Ni i blend. They derive an atomic ratio of O∕Ni = 210 ± 24, which according to their analysis corresponds to log𝜖O = 8.86 ± 0.07 after applying the Ni abundance of Grevesse and Sauval (1998Jump To The Next Citation Point) and correcting for the ∼ 50% of O locked up in CO in the cool environments of sunspots. The asymmetry of the Stokes V profile is relatively model-independent, but the derived oxygen abundance is of course still sensitive to the choice of gf-values and the C and Ni abundances. Correcting for the use of an outdated gf-value for the [O i] line and employing the new Ni abundance of Scott et al. (in preparation) revises their estimated atomic O abundance from log 𝜖O = 8.56 to log 𝜖OI = 8.43. If other molecules can be ignored, as supported by their calculations, the maximum possible total O abundance is obtained by assuming that all of C is tied up in CO. When adopting the solar C abundance of Grevesse and Sauval (1998Jump To The Next Citation Point) this leads to log𝜖O = 8.78 while using the value from Asplund et al. (2005bJump To The Next Citation Point) leads to log 𝜖O = 8.71, which is quite close to the values found by Allende Prieto et al. (2001) and Asplund et al. (2004Jump To The Next Citation Point). According to the analysis of Asplund et al. (2004Jump To The Next Citation Point), the even weaker [O i] 636 nm line gives results consistent with the 630 nm line, after allowance for two blending CN lines. This is not the case with the analysis of Caffau et al. (2008aJump To The Next Citation Point), in which the 636 nm line leads to a 0.10 dex higher abundance than the 630 nm line: log 𝜖O = 8.78 instead of log 𝜖O = 8.68. The exact reasons for this have not yet been established but it may be partly related to their use of a relatively high solar Ni abundance (Grevesse and Sauval, 1998Jump To The Next Citation Point), which under-estimates the O contribution to the 630 nm feature.

Meléndez and Asplund (2008Jump To The Next Citation Point) has performed a 3D-based analysis of the [O i] line at 557.7 nm not previously considered for abundance purposes. They argue that the significant blending due to two C2 lines can be rather accurately constrained by other nearby C2 lines from the same molecular band with essentially identical excitation potential, line strengths, and thus line formation properties. Using the same 3D solar atmosphere model as employed in the series of papers by Asplund and collaborators, Meléndez and Asplund (2008Jump To The Next Citation Point) find log 𝜖O = 8.70 ± 0.08. A range of 1D models give however very similar results (e.g., 8.73 with the Holweger and Müller, 1974Jump To The Next Citation Point model) with the mean value of the tested 3D and 1D models being log 𝜖O = 8.71 ± 0.02.

After careful inspection of the available permitted neutral oxygen lines, Asplund et al. (2004Jump To The Next Citation Point) selected six O i lines suitable for abundance determination. Full 3D non-LTE line formation calculations were performed, resulting in non-LTE abundance corrections (i.e., 3D non-LTE abundance minus the 3D LTE abundance) ranging from –0.03 to –0.24 dex for the different lines; the 777 nm triplet lines are the most affected in this respect; for the O i lines the main reason for the low estimated O abundance is non-LTE line formation with the effect of the 3D model being quite small. Accounting for departures from LTE greatly improves the agreement with the observed profile as well as the center-to-limb behavior for the 777 nm lines, as shown in Figure 32View Image. In the O atomic model, excitation and ionization from inelastic collisions with H atoms were not considered by Asplund et al. (2004Jump To The Next Citation Point) given the uncertainty surrounding these collisional cross-sections: for the few other elements where laboratory measurements or detailed quantum mechanical calculations exist the classical formula used for the purpose over-estimates the cross-sections by several orders of magnitude (see discussion in Asplund, 2005Jump To The Next Citation Point, and references therein). Allende Prieto et al. (2004) found that the agreement with the observed profiles close to the limb could be improved further by including inelastic H collisions. If correct, this would increase the derived O i abundance given in Table 1 by ≈ 0.06 dex. However, it should be noted that subsequently new quantum mechanical calculations for the electron collisional excitation of O i have been performed (Barklem, 2007a). These imply smaller cross-sections than employed in previous O i non-LTE works and thus one make the non-LTE effects more pronounced by ≈ 0.02 dex (Fabbian et al., 2009).

View Image

Figure 32: Center-to-limb variation of the O i 777 nm line strength. The observed behavior is shown as bands with estimated internal errors. The solid lines denote the 3D non-LTE case while the dashed lines correspond to the 3D LTE calculations. Note that in order to have the same disk-integrated equivalent widths, the 3D LTE calculations have been performed with a ≈ 0.2 dex higher O abundance than for the 3D non-LTE profiles (from Asplund et al., 2004Jump To The Next Citation Point).

An independent 3D-based analysis of the permitted O i lines has recently been performed by Caffau et al. (2008aJump To The Next Citation Point) using a co5bold solar model. In addition to the lines considered by Asplund et al. (2004Jump To The Next Citation Point) they also include the 1130.2 and 1316.4 nm transitions. They include non-LTE abundance corrections but only computed using 1D models, i.e., not full 3D non-LTE computations as in Asplund et al. (2004Jump To The Next Citation Point) . Their weighted mean of the eight O i and two [O i] lines is log 𝜖O = 8.76 ± 0.07, i.e., a value in between the recommended values of Asplund et al. (2005aJump To The Next Citation Point) and Grevesse and Sauval (1998Jump To The Next Citation Point). Most of the differences with the atomic-based results of Asplund et al. (2004Jump To The Next Citation Point) can be traced to Caffau et al. (2008aJump To The Next Citation Point) use of rather efficient H collisions for the 1D non-LTE calculations (Δ log 𝜖 = 0.03 dex O) and large adopted equivalent widths.3 Their measured equivalent widths are particularly large for the O i 777 nm triplet, indeed deviating by > 3σ compared with the eight most recent influential published solar abundance investigations starting from Lambert (1978). The reasons for these differences have not yet been established. Encouragingly, the particular choice of 3D model does not influence the results significantly. Somewhat earlier, Holweger (2001) obtained a similar O abundance based on an analysis taking multi-dimensional effects into account from a 2D solar granulation simulation and 1D non-LTE line formation: log 𝜖O = 8.74 ± 0.08.

Asplund et al. (2004Jump To The Next Citation Point) selected the best unblended 70 fundamental vibration-rotation (located around 3 μm) and 127 pure rotation lines (> 9 μm) of OH for abundance analysis. The resulting O abundances are much lower than previously thought from 1D studies: log 𝜖O = 8.61 and 8.65, respectively. This is a direct reflection of the great temperature sensitivity of the OH lines. There are no apparent abundance trends with wavelength, excitation potential or line strength for the vibration-rotation lines but there is a clear correlation with line strength for the strongest pure rotation lines in the 3D analysis. Since these lines are formed in very high atmospheric layers, this is probably a reflection of shortcomings of the 3D model atmospheres at those heights, such as too high temperatures. The derived low O abundance presented by Asplund et al. (2004Jump To The Next Citation Point) has been supported by a study of the extremely weak first overtone vibration-rotation lines of OH (Meléndez, 2004), which are also included in Table 1.

Asplund et al. (2004Jump To The Next Citation Point) argued that the mean 3D-based oxygen abundance from all the different abundance indicators is log𝜖O = 8.66 ± 0.05. The agreement between the different diagnostics is excellent in the 3D case (Δ ðœ– ≤ 0.1 dex) while the corresponding 1D results show quite discrepant results (Δ ðœ– ≥ 0.2 dex) with typically the molecular lines implying a higher abundance than the atomic due to the neglect of atmospheric inhomogeneities and the, in general warmer, mean temperature structure. The estimated abundance is 0.27 dex lower than recommended by Anders and Grevesse (1989Jump To The Next Citation Point), i.e., almost a factor of two downward revision. Given the recent flurry of studies devoted to the topic and the somewhat disparate results obtained, it is clear though that the solar O abundance issue has not yet been resolved once and for all. There are discouraging differences in terms of the observational data used, the collisional data required for the O i non-LTE calculations, the treatment of blending lines and the more reliable 3D atmospheric stratification, which urgently need to be addressed.

The estimated isotopic ratio (16O/18O = 479 ± 29) (Scott et al., 2006) from CO lines using a 3D solar model is in very good agreement with the terrestrial value (499 ± 1). In contrast, with 1D models the implied ratio is significantly lower than the terrestrial value (Ayres et al., 2006Jump To The Next Citation Point), which would be rather surprising.

5.3.4 Fe

Iron is a standard reference element for the overall metallicity of stars and galaxies and thus the solar Fe abundance is of fundamental importance for astronomy. In the 1980s and 1990s a debate raged whether the solar value was low (log 𝜖Fe ≈ 7.50, e.g., Holweger et al., 1995) or high (log𝜖Fe ≈ 7.65, e.g., Blackwell et al., 1995) which centered around the appropriate choices for the equivalent widths, microturbulence, pressure broadening constants, and transition probabilities. With the application of a 3D hydrodynamical solar model atmosphere the microturbulence parameter becomes obsolete (Asplund et al., 2000bJump To The Next Citation Point) while the excellent agreement between predicted and observed line shapes allows the use of profile fitting instead of relying on equivalent widths measurements. Asplund et al. (2000cJump To The Next Citation Point) performed a 3D LTE abundance analysis with the most up-to-date atomic data of both Fe i and Fe ii lines, in both cases finding a low abundance: log 𝜖 = 7.44 FeI and log 𝜖FeII = 7.45, respectively. There is, however, some evidence that departures from LTE are not insignificant for Fe i, mainly driven by over-ionization due to hot radiation field from below in the upflows (see discussion in Asplund, 2005Jump To The Next Citation Point, and references therein). As for O i lines, the main uncertainty in the available non-LTE calculations appears to be the treatment of inelastic collisions with H. Some calculations (e.g., Shchukina and Trujillo Bueno, 2001) which ignore these collisions altogether imply 1.5D non-LTE abundance corrections of ≈ +0.05 dex for Fe i for the Sun. On the other hand, Korn et al. (2003) find that the H collisions are indeed efficient in thermalizing the Fe i level populations and, hence, that the resulting 1D non-LTE abundance corrections are very small. The jury is still out regarding the H collisions but it is clear that the solar Fe abundance is low, log𝜖Fe ≤ 7.55, in particular since the solar Fe ii lines now have quite reliable gf-values and are little affected by the uncertainties surrounding the H collisions.

5.3.5 Other elements

To date at least a preliminary 3D-based abundance analysis of all elements up through Ni in the period table plus Zr, Eu, Hf, and Th has been performed; more elements are continually added to this inventory. For the vast majority of elements, solar spectoscopists have to settle for employing only various types of atomic transitions when attempting to estimate the solar abundances. Furthermore, for most elements only atomic lines from one ionization stage are available while often very few lines are suitable for abundance purposes (indeed, in several cases only a handful or fewer lines can be used). Finally, most of the time the appropriate atomic lines for a given element have quite similar sensitivity to the atmospheric conditions. It is therefore difficult to use the results as an indication of the appropriateness of the adopted model atmosphere and line formation calculations, as can be done for C, N, and O as described above, and the resulting 3D-based solar abundances must therefore be taken at face value.

Asplund (2000Jump To The Next Citation Point) found that the solar photospheric Si abundance only needed a 0.04 dex downward revision compared with previous studies. This is quite a significant finding nevertheless as it sets the absolute abundance scale of meteorites since those are depleted in all volatile elements, including hydrogen. In meteorites elemental abundances are therefore measured relative Si. As a consequence knowledge of the photospheric Si abundance is necessary to anchor the photospheric and meteoritic abundances to the same absolute scale. Of the other elements, Asplund et al. (2005aJump To The Next Citation Point) reported new abundances of the intermediate elements (Na-Ca) while a study of the Fe-peak elements (Sc-Ni) is currently ongoing (Scott et al., in preparation). Asplund (2004) estimated the amount of missing UV opacity from a comparison of the OH lines in the infrared and UV and from this could conclude that the solar photospheric Be abundance is not significantly depleted compared with the meteoritic value. Equipped with new transition probabilities Ljung et al. (2006) re-derived the solar Zr abundance with a 3D-analysis. The here mentioned works have all been based on the 3D solar model of Asplund et al. (2000c), which was also employed in the solar C, N, and O abundance analyses described in previous sections (Asplund et al., 2004Jump To The Next Citation Point2005bJump To The Next Citation Point,aJump To The Next Citation Point). For most atoms, the impact of 3D models compared with various often-used 1D models is relatively modest in general in contrast to the very model atmosphere-sensitive molecular lines. Typically the derived solar abundances are 0.02 – 0.1 dex lower than in a corresponding analysis with the Holweger and Müller (1974Jump To The Next Citation Point) model atmosphere when adopting the same input physics otherwise (Asplund et al., 2005aJump To The Next Citation Point); lines from a minority ionization stage are the most affected in this regard due to their greater temperature dependence (Steffen and Holweger, 2002Asplund, 2005). This is mainly a reflection of the steeper mean temperature gradient in the line forming region in the 3D model. For the elements for which two ionization stages can be employed, in general more consistent results are obtained with the 3D solar model compared with 1D model atmospheres, theoretical or semi-empirical. Furthermore, the agreement with the revised meteoritic abundance scale (Asplund, 2000) is typically improved, lending further support to the results.

Similar 3D-based determinations of the solar abundances using a co5bold 3D hydrodynamical solar model atmosphere have recently been carried out. Caffau and Ludwig (2007) and Caffau et al. (2007a) have revisited the solar S abundance and find a value in perfect agreement with that of Asplund et al. (2005aJump To The Next Citation Point). On the other hand, Caffau et al. (2007b) find a solar P abundance 0.1 dex higher than the preliminary analysis of Asplund et al. (2005aJump To The Next Citation Point); the exact reasons for this difference have not yet been established. In addition, Caffau et al. (2008b) and Mucciarelli et al. (2008) have determined the solar abundances of Eu, Hf, and Th, typically finding ≈ 0.02 dex lower values than the corresponding results with the Holweger and Müller (1974Jump To The Next Citation Point) 1D semi-empirical model; these elements have not yet been studied by Asplund and collaborators.

5.3.6 Implications and reliability of the new solar abundances

The recent revisions of the solar chemical composition based on 3D hydrodynamical model atmosphere, non-LTE line formation when necessary and improved atomic/molecular input data (e.g., Asplund et al., 2004Jump To The Next Citation Point2005b,aJump To The Next Citation Point) has some major implications, if true. First and foremost, due to the large changes of the solar C, N, and O (and by extension also to Ne and Ar4 abundances in particular, the overall photospheric metallicity is greatly reduced, from Z = 0.0194 (Anders and Grevesse, 1989Jump To The Next Citation Point) or Z = 0.0170 (Grevesse and Sauval, 1998Jump To The Next Citation Point) to Z = 0.0122 (Asplund et al., 2005aJump To The Next Citation Point). This relatively dramatic downward adjustment brings with it both good and bad news.

The new low solar abundances bring the Sun into agreement with the solar neighborhood as measured by nearby OB-type stars and the local interstellar medium (e.g., Turck-Chièze et al., 2004Esteban et al., 2005Przybilla et al., 2008), in particular when considering that the proto-solar abundances must have been 15% higher than the present-day photospheric values due to elemental diffusion (Turcotte et al., 1998). Furthermore, these abundances are consistent with existing models of the Galactic chemical evolution over the past 4.5 Gyr, which predicts that the oxygen abundance in the solar neighborhood has increased with ≈ 0.05 dex since the birth of the Sun. With the old C, N, and O abundances of Anders and Grevesse (1989) and Grevesse and Sauval (1998Jump To The Next Citation Point) there was a sharp conflict between the Sun and its surroundings.

However, the new abundances wreck havoc with the previous impressive agreement between the predicted solar interior sound speed and that measured with helioseismology (e.g., Delahaye and Pinsonneault, 2006Basu and Antia, 2008). Since in particular C, O, and Ne are significant opacity sources in the solar interior, the reduced abundances change the predicted temperature and density structure of the Sun based on standard solar interior models (e.g., Bahcall et al., 2006). The most noticeable disagreement occurs immediately below the convection zone, which also means that the predicted depth of the convection zone with the new abundances is inconsistent with the value inferred from helioseismology. A great number of possible explanations have been put forward in attempts to resolve the discrepancy, including missing opacity (Badnell et al., 2005), underestimated diffusion (Guzik et al., 2005), accretion of low-metallicity gas (Guzik et al., 2006), internal gravity waves (Young and Arnett, 2005Charbonnel and Talon, 2005) , and underestimated solar Ne abundance (Bahcall et al., 2005Drake and Testa, 2005) but to date no satisfactory solution has been found to this dilemma.

Another possibility is of course that the new solar abundances are not fully trustworthy and that the real solar C, N, and/or O abundances are significantly higher. Indeed with the values recommended by Grevesse and Sauval (1998Jump To The Next Citation Point) based on an analysis using the modified5 Holweger and Müller (1974Jump To The Next Citation Point) semi-empirical 1D model atmosphere this solar model problem largely disappears. The reasons for the lowering of the C, N, and O abundances are different for the various abundance indictors. As already mentioned, molecular transitions are particularly sensitive to the model atmosphere temperature structure and presence of inhomogeneities. The atomic lines are also dependent on the adopted model atmosphere but to a lesser extent. Instead the permitted lines such as O i are particularly vulnerable to non-LTE effects and thus the treatment of the poorly known inelastic H collisions but also the measurement of equivalent widths/fitting of line profiles. The forbidden lines are mostly dependent on how blends are accounted for. In all cases, improved atomic/molecular data and selection of lines also have played a role.

One of the key ingredients is the application of 3D, hydrodynamical models of the solar atmosphere instead of 1D hydrostatic models, either theoretical or semi-empirical ones. Such 3D models are still relatively new and thus the possibility of remaining problems with the predicted atmospheric structure in the line-forming region cannot yet be ruled out. As shown in this Section, theoretical 3D line profiles, including their shifts and asymmetries, agree almost perfectly with observations in spite of having no tunable free parameters in the modeling (Asplund et al., 2000bJump To The Next Citation Point). No 1D model comes close to achieving this. Furthermore, the predicted properties of the 3D simulations resemble very closely the observed solar granulation such as geometry, brightness contrast, velocities, both in terms of statistics and the temporal evolution. However, further confrontations with observational constraints are needed to remove lingering doubts about the 3D models’ appropriateness for abundance analysis purposes. For example, Ayres et al. (2006) argued on the basis of continuum center-to-limb variations and CO line strengths that the 3D model employed by Asplund and co-workers has an erroneous temperature structure. Their conclusion is based on their own calculations using the temporally and spatially averaged mean 3D model; full 3D calculations using the same opacities and equation-of-state used for the hydrodynamical convection simulation instead reveal smaller differences between the predicted and observed limb-darkening behavior by about a factor of two (see also discussion in Koesterke et al. (2008Jump To The Next Citation Point)). It is true though that the 3D model by Asplund et al. (2000b) is not perfect in this respect: in terms of the center-to-limb variation it performs better than theoretical 1D marcs and Kurucz models but not quite as well as the Holweger and Müller (1974Jump To The Next Citation Point) model, as shown by Koesterke et al. (2008) and Pereira et al. (in preparation). However, in the case of the solar hydrogen lines, which also trace the temperature structure in deep atmospheric layers, the 3D predictions agree better with observations than the Holweger–Müller model, which results in too shallow line wings (Pereira et al., in preparation), in particular when considering the possibility of non-LTE effects in the H line formation (Barklem, 2007b). The co5bold 3D solar model employed by for example Caffau et al. (2008aJump To The Next Citation Point) performs better in terms of continuum center-to-limb variation than the corresponding 3D model of Asplund et al. and, at least, as well as the Holweger–Müller model, yet it implies essentially the same solar oxygen abundance for atomic lines as advocated by Asplund et al. (2004Jump To The Next Citation Point) when allowing for differences in non-LTE corrections and adopted line strengths. The co5bold model has not yet been applied to molecular transitions but it is expected that it will yield somewhat higher abundances than estimated by Asplund et al. (2004), in which the molecular-based O abundances anyway are slightly lower than the atomic-based values. New 3D solar simulations are currently being carried out with an improved treatment of radiative transfer, including a selective (or sparse) opacity sampling technique rather than opacity binning and proper allowance of scattering (Trampedach et al., in preparation; Hayek et al., in preparation).

Finally, it must be emphasized that the application of a 3D solar model atmosphere is only one of the reasons for the recent downward revision of the solar C, N, and O abundances. Important in this respect are allowances of departures from LTE in the line formation for permitted atomic transitions, recognition of significant blends perturbing some weak lines and improved atomic and molecular input data. Even with the Holweger and Müller (1974) model with its shallow temperature gradient and high temperatures in the line-forming region quite low abundances are derived, as seen in Table 1; note that the molecular abundances are over-estimated in all 1D models on account of the neglect of temperature inhomogeneities.

As described above, there is today no clear consensus what the solar oxygen abundance is (unfortunately carbon and nitrogen have not received nearly as much attention). Asplund and collaborators are currently performing a re-analysis of the solar chemical composition for most accessible elements using a new improved 3D solar atmosphere simulation compared to the old 3D model applied in their previous works on the topic. Preliminary calculations reveal that the value recommended by Asplund et al. (2005a) may need to be revised upwards slightly to log 𝜖O ≈ 8.70 − 8.75. This would be in line with the recent estimates of Caffau et al. (2008a), Meléndez and Asplund (2008), and Centeno and Socas-Navarro (2008), when taking into account the recommended adjustments to the input data and analyses discussed in detail above. Such an O abundance would ease but not remove the discrepancy between solar interior models and helioseismology.


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