Spectroscopic comparative study of the red giant binary system gamma Leonis A and B

Abstract

$\gamma$ Leo is a long-period visual binary system consisting of K0 iii (A) and G7 iii (B) giants, in which particular interest is attracted by the brighter A since the discovery of a planet around it. While detailed spectroscopic comparative study of both components would be worthwhile (e.g., for probing any impact of planet formation on chemical abundances), such a research seems to have been barely attempted as most available studies tend to be biased toward A. Given this situation, the physical properties of A and B along with their differences were investigated based on high-dispersion spectra in order to establish their stellar parameters, evolutionary status, and surface chemical compositions. The following results were obtained. (1) The masses were derived as $\sim 1.7$ $M_{\odot }$ and $\sim 1.6$ $M_{ \odot }$ for A and B, respectively, both of which are likely to be in the stage of red clump giants after He-ignition. The mass of the planet around A has also been revised as $m_{\mathrm{p}} \sin i_{\mathrm{p}} \simeq 10.7 M_{\mathrm{Jupiter}}$ (increased by $\sim 20\%$). (2) These are normal giants of subsolar metallicity ([Fe/H] $\sim -0.4$) belonging to the thin-disk population. (3) A as well as B show moderate C deficiency and N enrichment, which are in compatible with the prediction from the standard stellar evolution theory. (4) The chemical abundances of 26 elements are practically the same within $\lesssim 0.1$ dex for both components, which implies that the surface chemistry is not appreciably affected by the existence of a planet in A.

Appendix: impact of hyperfine splitting on abundance determination

In the determination of the abundances for heavier elements based on the equivalent widths described in Sect. 4.4, the conventional single-line treatment was adopted where the line opacity is represented by a symmetric Voigt function. While this assumption is valid for most cases, lines of some elements (especially odd-$Z$ elements around $Z \sim$ 20–30) are known to intricately split into sub-components, which is caused by nucleus–electron coupling of the angular momentum. Since this effect (hyper-fine splitting; abbreviated as “hfs”) acts as an extra broadening of the line opacity (while the total integrated opacity being kept unchanged) like the case of microturbulence, the equivalent width (of more or less saturated line) is increased by this splitting effect compared to the non-split case. As a result, the abundance derived from such a hfs-split line based on the usual single-component assumption tends to be overestimated unless the line is very weak.

The extents of overestimation caused by applying the single-component approximation were examined for the representative hfs lines of Sc ii ($Z=21$), V i ($Z=23$), Mn i ($Z=25$), Co i ($Z=27$), and Cu i ($Z=29$). Out of the 29 lines for these 5 species analyzed in Sect. 4.4, 22 lines were selected for this test (cf. Table 8), for which the relevant hfs data (wavelengths and relative strengths of subcomponents) are available in the “gfhyperall.dat” file downloaded from the Dr. R. L. Kurucz’s web site.⁹

Table 8 Hyperfine-splitting effect on the abundances of Sc, V, Mn, Co, and Cu.

By using the WIDTH9 program which was so modified as to enable incorporating the line-splitting effect by the spectrum-synthesis technique, two kinds of abundances [$A$(with hfs) and $A$(without hfs)] were obtained for given equivalent widths ($W_{\lambda}$), and the corresponding hfs corrections $\delta A$ [$\equiv A$(with hfs)$- A$(without hfs)] were computed for $\gamma$ Leo A and B along with the Sun. Similarly, its effect on [X/H]_∗ (abundance of element X relative to the Sun) could be evaluated as $\delta$[X/H]$_{*} \equiv \delta A_{*} - \delta A_{\odot}$. The results are summarized in Table 8, and in Fig. 8 are plotted these $\delta A$ as well as $\delta$[X/H] values against $W_{\lambda}$. An inspection of Fig. 8 reveals the following characteristics.

• The hfs corrections on the abundances ($\delta A$) are always negative, and $|\delta A|$ tends to be larger for stronger lines, as expected. However, their extents are considerably diversified from case to case depending on the detailed nature of line splitting. For example, even in the same strong-line regime ($W_{\lambda} \sim 100$ mÅ) for the case of $\gamma$ Leo A (Fig. 8a), $|\delta A|$ is almost negligible for Sc ii 5526.790 while significantly large ($\sim 0.3$ dex) for V i 5670.853.

  Fig. 8

  

  Corrections to the absolute ($A$) or relative ([X/H]) abundances due to the hyperfine-splitting effect (cf. Table 8) are plotted against the equivalent widths, where the open circles, filled circles, Greek crosses (+), half-filled triangles, and St. Andrew’s crosses (×) correspond to Sc, V, Mn, Co, and Cu, respectively. (a) Hfs corrections to $A$ for $\gamma$ Leo A (green) and the Sun (red). (b) Hfs corrections to [X/H] for $\gamma$ Leo A. (c) Hfs corrections to $A$ for $\gamma$ Leo B (blue) and the Sun (red). (d) Hfs corrections to [X/H] for $\gamma$ Leo B.

• Roughly speaking, the inequality relation $|\delta A_{\odot}| < |\delta A_{\mathrm{B}}| < |\delta A_{\mathrm{A}}|$ holds for the relative importance of hfs corrections between $\gamma$ Leo A and B and the Sun (Fig. 8a and Fig. 8c). Therefore, as to $|\delta$[X/H]| (generally smaller than $|\delta A|$ due to the subtraction of solar correction), $|\delta [{\mathrm{X}}/{\mathrm{H}}]_{\mathrm{B}}|$ is distinctly smaller than $|\delta [{\mathrm{X}}/{\mathrm{H}}]_{\mathrm{A}}|$. Actually, while $|\delta$[X/H]$_{ \mathrm{A}}|$ for $\gamma$ Leo A are still appreciable and significant (around $\sim 0.1$ dex on the average, though extending up to $\sim 0.3$ dex for some lines; cf. Figure 8b), $|\delta$[X/H]$_{\mathrm{B}}|$ for $\gamma$ Leo B is insignificant (confined within $\lesssim 0.05$ dex; cf. Figure 8d).

• As seen from the different extent of hfs correction between the three cases (Sun < $\gamma$ Leo B < $\gamma$ Leo A), $T_{\mathrm{eff}}$ is presumably the most critical factor determining the significance of hfs, because it affects (i) the equivalent width of a line and (ii) the thermal width of line opacity, both affecting the degree of saturation. Accordingly, we may generally state that the impact of hfs on abundance determinations becomes more significant as $T_{\mathrm{eff}}$ is lowered.

Then, how much hfs correction should be applied to the relevant abundance results of Sc, V, Mn, Co, ad Cu obtained in Sect. 4.4 (which were derived from equivalent widths based on the single-line assumption neglecting hfs)? As long as the lines presented in Table 8 are concerned, while the corrections ($\delta$[X/H]_B) for $\gamma$ Leo B are apparently insignificant (only a few hundredths dex in any case), appreciable downward corrections ranging from $\sim 0.0$ to $\sim 0.3$ dex (considerably differing from line to line) are expected for $\gamma$ Leo A as seen from the values of $\delta$[X/H]_A. Fortunately, even in the latter case of $\gamma$ Leo A, since the lines of large corrections (by ∼ 0.2–0.3 dex) belong to the species (i.e., V or Co) using a sufficient number of lines (8–9), their impact tends to be mitigated after averaging. By applying the $\delta$[X/H] corrections of 22 lines (Table 8) to the [X/H] values obtained in Sect. 4.4 (cf. “ewanalys_A.dat” and “ewanalys_B.dat” in the online material), new mean 〈[X/H]〉 values (with hfs included) were calculated (where the same [X/H] data were used unchanged for the 7 lines for which hfs data were unavailable).

The resulting differences (in dex) of 〈[X/H]〉(with hfs)−〈[X/H]〉(without hfs) are $-0.02|-0.02$ (Sc), $-0.07|0.00$ (V), $0.00|0.00$ (Mn), $-0.07|-0.02$ (Co), $-0.01|-0.01$ (Cu), for $\gamma$ Leo A|B, respectively. Accordingly, the hfs corrections on the final 〈[X/H]〉 results of Sc, V, Mn, Co, and Cu derived in Sect. 4.4 are only slight reductions by $\lesssim 0.1$ dex and thus not significant.