Revisiting the Iron Abundance in the Hyper Iron-poor Star HE 1327–2326 with UV COS/HST Data^*

The equivalent widths (EWs) of Fe ii lines in the UV spectrum were measured by convolving the COS line-spread functions (Ghavamian et al. 2009) with Gaussian profiles following Roederer et al. (2016) and fitting them to the lines. The uncertainties on the EWs and abundance measurements were determined by altering the continuum placement and the FWHM of the corresponding lines by ±1σ and recording the corresponding abundance changes. The significance of the detections were assessed by dividing the EW of each line by its uncertainty. Four Fe ii lines at 2327, 2332, 2338, and 2343 Å were detected with >3σ significance, and one Fe ii line at 2331 Å was detected with 2.1σ. The Fe ii lines as well as the 1σ, 2σ, and 3σ detection limits are shown in Figure 1. The atomic properties of the Fe ii lines (excitation potential, oscillator strengths $\mathrm{log}{gf}$) and measured EWs are listed in Table 1.

Table 1.  Atomic Properties of the Fe ii Absorption Lines Detected in the UV Spectrum of HE 1327−2326, Including the Excitation Potentials of Their Lower Energy Levels (χ), Oscillator Strengths ($\mathrm{log}{gf}$), Equivalent Widths with their Uncertainties (EW and σ EW), as well as Their Detection Significance (see Section 4.1 for Details)

Absorption	λ	χ	$\mathrm{log}{gf}$	EW	$\sigma \,\mathrm{EW}$	Detection	$\mathrm{log}\,\epsilon$(X)
Line	(Å)	(eV)		(mÅ)	(mÅ)	Significance	(dex)
Fe ii	2327.39	0.08	−0.67	30.8	7.8	3.9σ	1.65
Fe ii	2331.30	0.23	−0.68	18.0	8.5	2.1σ	1.43
Fe ii	2332.79	0.04	−0.19	33.7	8.7	3.9σ	1.34
Fe ii	2338.00	0.10	−0.43	32.5	8.8	3.7σ	1.46
Fe ii	2343.49	0.00	+0.06	53.8	10.3	5.2σ	1.56

Note. The last column shows our result for the determined line abundances (in LTE) at $\mathrm{log}g$ = 3.7.

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Line-by-line iron abundances for HE 1327−2326 were then calculated using the 2017 version of the LTE radiative transfer code MOOG (Sneden 1973), which includes Rayleigh scattering treatment as described by Sobeck et al. (2011). Custom spectroscopic analysis software was first described in Casey (2014). From the four Fe ii lines with >3σ detections, we determine an average Fe ii abundance of [Fe ii/H](LTE) = −5.99 ± 0.25 in LTE and [Fe ii/H](NLTE) = −6.01 ± 0.25 in NLTE. The abundance uncertainties were derived following the same procedure as that used to derive the EW uncertainties. The abundances (here and throughout the rest of this paper) are reported relative to the reference solar abundances from Asplund et al. (2009).

Using 10 Fe i lines measured in a high-resolution VLT/UVES⁴ spectrum, Frebel et al. (2008) determined an Fe i abundance of [Fe i/H] = −5.71 ± 0.2 for $\mathrm{log}g$ = 3.7. They also obtained [Fe i/H] = −6.01 ± 0.2 from a 3D LTE analysis, following (Collet et al. 2005). In Ezzeddine et al. (2017), 1D LTE and 1D NLTE analyses were performed for HE 1327−2326, from which [Fe i/H](NLTE) = −5.20 ± 0.20 and [Fe i/H](LTE) = −5.80 ± 0.16 were obtained using the same lines as Frebel et al. (2008). The LTE optical Fe i abundance agrees within uncertainties (∼0.15 dex) with our new UV LTE Fe ii abundance, suggesting no offset as a function of a wavelength when considering LTE.

Our NLTE "abundance correction" obtained for Fe ii, defined by the difference between the average NLTE abundance and the corresponding average LTE abundance, ${{\rm{\Delta }}}_{\mathrm{corr}}=\mathrm{log}\,\epsilon (\mathrm{NLTE})-\mathrm{log}\,\epsilon (\mathrm{LTE})$, is negligible (${{\rm{\Delta }}}_{\mathrm{corr}}=-0.02$ dex). This result is in line with previous studies (Mashonkina et al. 2011; Bergemann et al. 2012; Amarsi et al. 2016; Ezzeddine et al. 2017), as NLTE line strengths and abundances of dominant species, i.e., Fe ii, are not theoretically expected to significantly deviate from the LTE assumption.

Comparing this NLTE Fe ii abundance with the NLTE optical Fe i result reveals it to be higher than that inferred from the UV Fe ii lines, by Δ(log (Fe i, NLTE) − log (Fe ii,NLTE)) = 0.81 dex. This difference between the optical and UV abundances in NLTE is largely due to the significant deviations of the NLTE Fe i abundance from the LTE assumption, namely, by ${{\rm{\Delta }}}_{\mathrm{corr}}\sim 0.6$ dex (Ezzeddine et al. 2017). Such a large discrepancy between Fe i and Fe ii cannot possibly be compensated by increasing $\mathrm{log}g$ to attain ionization equilibrium, as it would lead to nonphysical surface gravity values, i.e., $\mathrm{log}g\sim 6$.

Discrepancies between the optical and UV abundances of the same species have been reported in previous studies (Roederer et al. 2012, 2014a, 2014b, 2014c; Lawler et al. 2013). These studies found that the abundances of individual UV lines show larger scatter than those of the optical lines (up to ±0.4 dex around the mean), and that the mean UV Fe abundances are slightly lower in the UV than in the optical (i.e., slight negative trends with decreasing wavelengths). Roederer et al. (2012), for example, studied the LTE iron abundances in the UV and optical spectra of four reference metal-poor stars with ${\rm{[Fe/H]}}\gt -3.1$. They found lower average abundances down to −0.2 dex for lines lying between ∼3100 and 3700 Å, compared with those at $\lambda \gt 4000\,\mathring{\rm A}$.

In most of these studies, however, the Fe i lines did not continuously cover the entire wavelength range from the UV to the optical, especially toward the lowest λ ∼ 2000 Å, to draw firm conclusions. It was suggested that the source of these discrepancies and decreasing abundance trends toward UV wavelengths (for the same chemical species) might be due to either NLTE effects or the underestimation of the H i contribution to the continuum opacities, which becomes important toward the lower UV wavelengths at λ < 3500 Å. For more details on these suggestions, we refer the reader to Figure 11 in Roederer et al. (2012). However, as we show above, NLTE abundances only appear to make any discrepancies even larger.

We principally investigate the origin of the abundance discrepancies between lines found in the optical and UV wavelength range in HE 1327−2326 and previous studies. For that, we performed new, detailed LTE and NLTE abundance analyses of two well-studied extremely metal-poor stars, G64−12 and BD +44°493. Both stars have sufficient Fe i and Fe ii lines available across large regions of the optical and UV spectra. For G64−12, we used EW measurements of UV and optical Fe lines obtained from HST/STIS⁵ and VLT/UVES spectra,⁶ respectively (Roederer et al. 2018). We adopt ${T}_{\mathrm{eff}}$ = 6492 K and $\mathrm{log}g=4.4$ as well as [Fe/H] = −3.2 and ξ_t = 1.5 km s⁻¹ for input stellar parameters from Roederer et al. (2018). Their ${T}_{\mathrm{eff}}$ agrees well with the infrared flux method (IRFM) (Casagrande et al. 2010) value of 6464 ± 150 K. Their surface gravity also agrees, within uncertainties, to that derived from the Gaia DR2 parallax (3.7625 ± 0.0855 mas) of $\mathrm{log}g=4.1\pm 0.3$.

For BD +44°493, we used published EW measurements for UV and optical Fe lines from Ito et al. (2013) and Placco et al. (2014), respectively. We adopt stellar atmospheric parameters from Ito et al. (2013), with ${T}_{\mathrm{eff}}$ = 5430 K determined from the IRFM (Casagrande et al. 2010) and $\mathrm{log}g$ = 3.4, [Fe/H] = −3.8, and ξ_t = 1.3 km s⁻¹ from a spectroscopic Fe i/Fe ii abundance analysis. The Gaia DR2 parallax (4.7595 ± 0.0659 mas) yields a surface gravity of $\mathrm{log}g=3.5\pm 0.3$, which is in very good agreement with the value from Ito et al. (2013).

NLTE calculations were performed following the same procedure in Ezzeddine et al. (2017), where the NLTE radiative transfer code MULTI2.3 (Carlsson 1986, 1992) was used with the MARCS (Gustafsson et al. 1975, 2008; Plez 2012) model atmospheres interpolated to the corresponding stellar parameters. The LTE abundances were also calculated using the same code and atmospheric models. The average abundance results obtained for G64−12, BD +44°493, and HE 1327−2326 from optical and UV Fe i and Fe ii lines (whenever possible) are displayed in Table 2. Line-by-line abundances as a function of wavelengths are also shown for the three stars in Figure 2.

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In LTE, no systematic differences are found between the abundances derived from the UV and optical lines or those derived from Fe i and Fe ii lines for BD +44°493, G64−12, and HE 1327−2326. Any small differences are within the abundance uncertainties of the three stars. In NLTE, however, the abundances obtained from both optical and UV Fe i lines are systematically higher than those from the Fe ii lines from either region (when available). The Fe i–Fe ii discrepancies are +0.30 dex for BD +44°493, +0.33 dex for G64−12, and +0.80 dex for HE 1327−2326. It is important to note, though, that the abundances inferred from UV Fe ii lines show larger scatter (±0.2 dex for G64−12 and BD +44°493) around the mean values as compared to those inferred from optical Fe ii lines (±0.14 dex for BD +44°493 and ±0.05 dex for G64−12), or UV and optical Fe i lines (∼±0.15 dex). The same large scatter is obtained in both LTE and NLTE analyses. This is in line with previous LTE Fe abundance studies based on UV lines (e.g., Roederer et al. 2012).

In order to further understand this discrepancy, we considered other studies on, e.g., G64−12. Amarsi et al. (2016) performed a full 3D NLTE abundance analysis for G64−12 and three other well-studied metal-poor stars. As part of their work, they found their 1D NLTE abundances for G64−12 to be higher than the 1D LTE values, up to 0.23 dex for Fe i, but they are, of course, negligible for Fe ii. This is very similar to our findings (Δ_corr = 0.25 dex), albeit using a slightly lower $\mathrm{log}g$ value by 0.14 dex than ours.

Also, Amarsi et al. (2016) compared 3D NLTE and 1D NLTE abundances in G64−12. They found non-negligible positive abundance corrections of +0.16 dex for Fe ii and ∼+0.11 dex for Fe i due to 3D effects in G64−12. Interestingly, both these 3D NLTE Fe i and Fe ii abundances are increased (although not at the same level) compared to the 1D NLTE case. This differential increase of both Fe i and Fe ii abundances brings them into agreement with each other, to within ∼0.1 dex, when abundance uncertainties are also ∼0.1 dex.

The abundances derived in this combined 3D NLTE framework furthermore suggests Fe i and Fe ii corrections to increase even more toward lower metallicities relative to just 1D NLTE (Amarsi et al. 2016; Nordlander et al. 2017). This behavior has already been documented as part of the full 3D NLTE analysis of the most iron-poor giant star SMSS 0313−6708 with [Fe/H] < −7.0 (Nordlander et al. 2017). "Residual" 3D corrections of ${{\rm{\Delta }}}^{3{\rm{D}}}=\mathrm{log}\,\epsilon (3{\rm{D}},\mathrm{NLTE})-\mathrm{log}\epsilon (1{\rm{D}},\mathrm{NLTE})=0.2$ dex were determined for a putative Fe i line in this star. Moreover, the corresponding residual 3D correction for Fe ii lines in SMSS 0313−6708 is expected to be larger than that for Fe i (Amarsi et al. 2016), although, unfortunately, no explicit calculations were reported for SMSS 0313−6708. In addition, they report a 1D NLTE effect of Δ_corr = 0.6 (compared to 1D LTE). This is larger than the residual 3D correction, but comparable to what we find for HE 1327−2326 in the present study. Finally, Nordlander et al. (2017) found that the 3D LTE framework can heavily underestimate the Fe i abundances by ∼1 dex compared to the full 3D NLTE case.

Consequently, they deduced that the 3D NLTE Fe i abundance (${\rm{[Fe/H]}}\lt -6.53\pm 0.5$) is the best avenue for determining the iron abundance of this star, but if a 3D analysis is not possible, the 1D NLTE case (${\rm{[Fe/H]}}\lt -6.73\pm 0.2$) provides a robust estimate of the Fe abundance instead. This will be the case for most analyses, given that full 3D NLTE calculations are based on complex and lengthy computational requirements.

By analogy, we thus conclude that the discrepancies observed in HE 1327−2326 between the UV Fe ii line and the optical Fe i line abundances may well be due to these unaccounted 3D residual corrections. Further exploration of the issue in terms of 3D modeling is warranted, but beyond the scope of the present study.

Our investigation into understanding the differences obtained between the abundances of Fe i and Fe ii arising from LTE, NLTE, and 3D calculations for G64−12, BD +44°493 and SMSS 0313−6708 yielded that the 1D NLTE Fe i abundance is presently the most robust indicator to use if a full 3D NLTE calculation is not available (Amarsi et al. 2016; Nordlander et al. 2017).

Guided by these results, for HE 1327−2326, we thus adopt the 1D NLTE abundance of ${\rm{[Fe/H]}}$ = −5.20 ± 0.12 inferred from optical Fe i lines as our final [Fe/H] value. This new result is slightly higher than what was previously adopted ${\rm{[Fe/H]}}$ = −5.4 (Frebel et al. 2005), which was an LTE value corrected with an arbitrarily chosen NLTE correction of 0.2 dex. A value of ${\rm{[Fe/H]}}$ = −5.2 should be more physically meaningful for any interpretation of the origin of this star and its abundance pattern than any other values. Performing a computationally challenging full 3D NLTE abundance analysis in the future would hopefully show agreement between the abundances of both Fe i and Fe ii species, within uncertainties.