MOLECULAR LINE FORMATION IN THE EXTREMELY METAL-POOR STAR BD+44° 493^*

We apply model atmospheres of the ATLAS NEWODF grid (Castelli et al. 1997) to our 1D/LTE analysis as done by Ito et al. (2013). Atmospheric parameters derived by Ito et al. (2013) are adopted: ${T}_{\mathrm{eff}}$ = 5430 K, $\mathrm{log}\;g\;=\;3.4$, [Fe/H]$\;=\;-3.8$, and ${v}_{\mathrm{micro}}$ $\;=\;1.3$ km s⁻¹. We also examine the effect of the changes of ${T}_{\mathrm{eff}}$ and ${v}_{\mathrm{micro}}$ on the results below.

Figure 3 depicts the O abundances derived from individual OH lines as a function of their excitation potential. The results from different systems are shown by different symbols. The derived abundances exhibit a clear dependence on the excitation potential. A least square fit to the data points indicates the slope of $d\mathrm{log}\;\epsilon /d\chi =-0.23\pm 0.03$ dex eV⁻¹. A similar result is obtained even if the analysis is limited to the lines of the $A-X$ 0–0 system: the slope is $-0.24\pm 0.03$ dex eV⁻¹. The null hypothesis that there is no correlation between the two values is rejected by the regression analysis at the 99.9% confidence level. The slope derived from the 1–1 system is $-0.15\pm 0.08$ dex eV⁻¹. Although the correlation derived from the 1–1 system alone is slightly weaker, the confidence level is still 95% by the same analysis.

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The correlation between the derived oxygen abundances and the excitation potentials is dependent on the adopted stellar parameters, in particular, the effective temperature and the micro-turbulent velocity. If a lower effective temperature is adopted, the spectral lines with larger excitation potentials become weaker, resulting in higher abundances derived from these lines to explain the observed line absorption. Indeed, the slope in the diagram of the oxygen abundance and excitation potential is $-0.16\pm 0.03$ dex eV⁻¹ for the analysis assuming ${T}_{\mathrm{eff}}$ $\;=\;5230$ K (Figure 4(b)). Although the correlation is weaker than that derived for the effective temperature we adopt (${T}_{\mathrm{eff}}$ $\;=\;5430$ K), it is still statistically significant. We note that the oxygen abundance derived for ${T}_{\mathrm{eff}}$ $\;=\;5230$ K on average is about 0.4 dex lower than that for ${T}_{\mathrm{eff}}$ $\;=\;5430$ K.

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The slope is also dependent on the assumed micro-turbulent velocity. The micro-turbulent velocity is determined as the elemental abundances derived from individual lines show no dependence on the line strengths. The micro-turbulent velocity of this object, ${v}_{\mathrm{micro}}$ $\;=\;1.3$ km s⁻¹, is determined by the analysis of Fe i lines (Ito et al. 2013). Adopting this value, a correlation between the oxygen abundances and the strengths of OH lines is found (Figure 4(d)). This is, however, attributed to the fact that lines with smaller excitation potentials are stronger in general (Figure 4(f)). There are four exceptionally weak lines ($\mathrm{log}\;W/\lambda \sim -5.5$) among those with small excitation potential ($\chi \lesssim 0.3$ eV). The oxygen abundances derived from these four lines are as high as the value obtained from stronger lines ($\mathrm{log}\;\epsilon$(O) ∼ 6.5), supporting our interpretation that the apparent correlation between the oxygen abundances and the strengths of OH lines is due to the dependence of the derived abundances on the excitation potentials of the OH lines. The slope $d\mathrm{log}\;\epsilon /d\chi$ obtained for ${v}_{\mathrm{micro}}$ $\;=\;2.3$ km s⁻¹ and ${T}_{\mathrm{eff}}$ $\;=\;5430$ K is $-0.12\pm 0.03$ (Figure 4(c)).

We note for completeness that, although a weak correlation is found between the derived abundances and wavelengths of the lines (Figure 4(e)), it is also explained by the fact that most of the lines with smaller excitation potentials, from which higher abundances are derived, exist at shorter wavelengths.

A similar analysis is made for CH lines as done for OH lines. The results are shown in Figure 5(a). A clear correlation between the carbon abundances derived from individual CH lines and their excitation potentials is found as for OH lines. The null hypothesis that there is no correlation between the two values is rejected by the regression analysis at the 99.9% confidence level. The slope $d\mathrm{log}\;\epsilon /d\chi$ is $-0.15\pm 0.01$ dex eV⁻¹ (Figure 5(a)). The slope is slightly shallower, $d\mathrm{log}\;\epsilon /d\chi =-0.14\pm 0.01$ and $-0.11\pm 0.01$ dex eV⁻¹ if larger micro-turbulent velocity (${v}_{\mathrm{micro}}$ $\;=\;2.3$ km s⁻¹) and lower effective temperature (${T}_{\mathrm{eff}}$ $\;=\;5230$ K), respectively, are adopted (Figure 5(b), (c)).

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In the panels (d) and (e) of Figure 5, no clear correlation between the derived carbon abundances and wavelengths of CH lines, nor line strengths, is found. This would be due to the fact that the correlation between the wavelength and excitation potentials of CH lines is not as clear as those of OH lines (Figure 5(f)).

Our 1D-LTE abundance analysis for OH and CH molecular lines for the EMP star BD+44°493 demonstrates that the derived oxygen and carbon abundances are dependent on the excitation potential with slopes of $d\mathrm{log}\;\epsilon /d\chi =-0.15\sim -0.2$ (dex eV⁻¹). This suggests that the spectral lines with smaller excitation potentials are enhanced by the existence of a cool layer in the atmosphere that is not reproduced by the current 1D models. 3D atmosphere models predict that the upper layer of the photosphere is significantly cooler than that of the 1D models. Frebel et al. (2008) report the correction of oxygen and carbon abundances measured from OH and CH molecular lines using 3D model atmospheres as a function of excitation potentials. They estimate that the abundances derived from 3D models are lower than those from 1D models by ∼0.75 dex and by ∼0.55 dex for lines with $\chi \sim 0.0$ and 1.0 dex, respectively. Namely, the 3D corrections explain the slopes of $d\mathrm{log}\;\epsilon /d\chi \sim -0.2$ dex eV⁻¹ found by our 1D analysis.

Dobrovolskas et al. (2013) also investigated line formation for molecules including OH and CH based on the 3D model atmospheres for red giants with ${T}_{\mathrm{eff}}$ ∼ 5000 K. Their models for [Fe/H]$\;=\;-3$ also predict trends of 3D corrections, as a function of excitation potentials, for these molecules that are similar to those of Frebel et al. (2008). More quantitatively, the correction for CH lines with $\chi \sim 0$ shown in Figure 9 of Dobrovolskas et al. (2013) is smaller than those of Frebel et al. (2008). This difference might be partially due to the difference of the effective temperature and metallicity studied by the two works. The shallower slope found for CH than for OH in our result supports the prediction by Dobrovolskas et al. (2013).

A similar dependence of the derived abundances on excitation potentials of spectral lines is also expected for Fe lines. Collet et al. (2007) estimate that the correction reaches $-1.0$ dex for low excitation lines of Fe i, and the slope $d\mathrm{log}\;\epsilon /d\chi$ could be about $-0.2$ dex eV⁻¹ for very metal-poor stars. Such a clear trend is, however, not found in our previous measurements of Fe lines (Figure 5 of Ito et al. 2013). A weaker trend, $d\mathrm{log}\;\epsilon /d\chi \sim -0.05$ dex eV⁻¹, is found in the derived Fe abundances from Fe i lines. This trend, however, almost disappears if a slightly low ${T}_{\mathrm{eff}}$ is adopted in the analysis (Ito et al. 2013).

Figure 6 shows the Fe abundances derived from individual Fe i lines as functions of excitation potentials and equivalent widths. Large scatter is found in Fe abundances derived from lines with small excitation potentials shown by filled and open circles in the figure. Abundances from these lines show some dependence on line strengths: results from lines with equivalent widths larger than 80 mÅ exhibit lower abundances. Such trends suggest that spectral line formation is not well described by 1D LTE models.

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The recent study by Dobrovolskas et al. (2013) predicts smaller corrections for Fe abundances derived from Fe i lines than that of Collet et al. (2007): their corrections are smaller than 0.2 dex for lines with $\chi \geqslant 2$ eV. The correction for Fe abundances from Fe i lines with $\chi =0$ eV is, however, predicted to be still as large as 0.6 dex. The abundances derived from lines with $\chi \sim 0$ eV for BD+44°493 show scatter as large as 0.4 dex (Ito et al. 2013). The large scatter of abundances from low excitation Fe i lines might indicate that these lines are particularly affected by the 3D effect. These lines could also be affected by NLTE effects. Bergemann et al. (2012) conducted NLTE analyses for Fe lines of metal-poor stars using the spatial and temporal average stratification from 3D hydrodynamic models, as well as 1D static model atmospheres. They demonstrated for the cases of metal-poor stars like the subgiant HD 140283 that the analysis with the mean 3D models obtains lower Fe abundances on average, with smaller scatter of Fe abundances from individual Fe i lines, than those obtained from 1D models. On the other hand, the NLTE analysis using the 3D models derives higher Fe abundances than those obtained by an LTE analysis. If similar effects are working in the subgiant with lower metallicity like BD+44°493, the averaged Fe abundances derived by the 1D LTE analysis is not significantly corrected by the 3D NLTE analysis, whereas the scatter found in abundances from individual lines with small excitation potentials becomes smaller.

We note that the Fe abundance obtained from Fe ii lines by our analysis agrees well with that from Fe i lines even if we adopt the gravity ($\mathrm{log}\;g=3.3$) estimated adopting the parallax of this star to be 4.88 mas that is independent of the spectroscopic analysis of Fe lines (Ito et al. 2013). The NLTE and 3D effects estimated for Fe ii lines are much smaller than those for neutral lines in general (Collet et al. 2007; Bergemann et al. 2012; Dobrovolskas et al. 2013). The agreement of Fe abundances obtained from lines of the two ionization stages using the 1D model suggests that the corrections by 3D NLTE analysis for Fe i lines is not as large as those estimated by 3D LTE models.

The carbon and oxygen abundances of BD+44°493 derived from the lines with relatively large excitation potentials ($\chi \sim 1.0$) are $\mathrm{log}\;\epsilon$(C) = 5.8 and $\mathrm{log}\;\epsilon$(O) = 6.3, respectively (Figures 4 and 5). Adopting the solar abundances $\mathrm{log}\;\epsilon$(C)${}_{\odot }$ = 8.43 and $\mathrm{log}\;\epsilon$(O)${}_{\odot }$ = 8.69 (Asplund et al. 2009) as well as [Fe/H]$\;=\;-3.8$ for BD+44°493, the abundance ratios are [C/Fe]$\;=\;+1.2$ and [O/Fe]$\;=\;+1.4$. The difference of oxygen abundances obtained from OH lines with $\chi =1.0$ (eV) by 3D and 1D model atmospheres (${{\rm{\Delta }}}_{3{\rm{D}}-1{\rm{D}}}$) is approximately $-0.4$ dex (Figure 9 of Dobrovolskas et al. 2013). Similarly, the ${{\rm{\Delta }}}_{3{\rm{D}}-1{\rm{D}}}$ of carbon abundances from CH lines with $\chi =0.0$ and 1.0 (eV) are $-0.2$ to $-0.1$ dex. Including these corrections, [C/Fe] and [O/Fe] of BD+44°493 are about 1.0 dex, indicating that carbon and oxygen are clearly enhanced in this object. We note that the C/O ratio obtained from CH and OH molecular lines estimated by 1D model atmospheres is robust.

The carbon abundance of BD+44°493 is measured using the C i lines at 1.068–1.069 μm by an NLTE analysis based on a 1D model atmosphere by Takeda & Takada-Hidai (2013), obtaining $\mathrm{log}\;\epsilon$(C)$\;=\;5.69$. This is slightly lower than the carbon abundance obtained from CH lines with 1D models, but agrees well with the value corrected for the 3D effects (see above). Takeda & Takada-Hidai (2013) mentioned, however, that the derived carbon abundance from the C i lines is sensitive to the treatment of NLTE effects. Hence, we cannot conclude that the estimate of the 3D effects for the carbon abundances from CH lines are quantitatively correct from the comparison with the carbon abundance from the C i lines. However, the agreement of the abundances within 0.1–0.2 dex from CH and C i lines is supportive for the reliable estimates of carbon abundance of this object.