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

γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\gamma $\end{document} Leo is a long-period visual binary system consisting of K0 iii (A) and G7 iii (B) giants, in which particular interest is attracted by the brighter A since the discovery of a planet around it. While detailed spectroscopic comparative study of both components would be worthwhile (e.g., for probing any impact of planet formation on chemical abundances), such a research seems to have been barely attempted as most available studies tend to be biased toward A. Given this situation, the physical properties of A and B along with their differences were investigated based on high-dispersion spectra in order to establish their stellar parameters, evolutionary status, and surface chemical compositions. The following results were obtained. (1) The masses were derived as ∼1.7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sim 1.7$\end{document} M⊙\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M_{\odot }$\end{document} and ∼1.6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sim 1.6$\end{document} M⊙\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M_{ \odot }$\end{document} for A and B, respectively, both of which are likely to be in the stage of red clump giants after He-ignition. The mass of the planet around A has also been revised as mpsinip≃10.7MJupiter\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$m_{\mathrm{p}} \sin i_{\mathrm{p}} \simeq 10.7 M_{\mathrm{Jupiter}}$\end{document} (increased by ∼20%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sim 20\%$\end{document}). (2) These are normal giants of subsolar metallicity ([Fe/H] ∼−0.4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sim -0.4$\end{document}) belonging to the thin-disk population. (3) A as well as B show moderate C deficiency and N enrichment, which are in compatible with the prediction from the standard stellar evolution theory. (4) The chemical abundances of 26 elements are practically the same within ≲0.1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lesssim 0.1$\end{document} dex for both components, which implies that the surface chemistry is not appreciably affected by the existence of a planet in A.


Introduction
The star γ Leo (Algieba)1 is a well-known 2ndmagnitude star in the constellation Leo, which is known to be a visual binary consisting of two rather similar orange-yellowish stars (the brighter component γ Leo A = γ 1 Leo = HD 89484 = HR 4057 with V = 2.37 mag and the fainter component γ Leo B = γ 2 Leo = HD 89485 = HR 4058 with V = 3.64 mag) separated by a few arcseconds after the discovery of Sir William Herschel in 1782.Since this system has a highly eccentric orbit (eccentricity as large as e ∼ 0.9) with very long period (several centuries), even half of its orbit has not been completed (neither periastron nor apoastron has been reached) over the past 240 years, which means that its orbital elements still suffer considerable uncertainties.
Modern astronomical spectroscopy revealed that these component stars are red giants classified as K0 iii (A) and G7 iii (B); that is, the brighter former is somewhat redder than the fainter latter.As these are apparently ordinary red giant stars like many others, this system was not of particular astrophysical interest for a long time, despite that it has been popular among amateur astronomers challenging to resolve it into two stars and to enjoy the delicate contrast of colors by using small home telescopes or binoculars.
However, a significant feature was recognized in this star about a decade ago, when Han et al. (2010) reported (based on the radial velocity method) the detection of a planetary companion with a mass of m p sin i p = 8.78M Jupiter orbiting around γ Leo A with a period of 429 days.This is an important finding because it is presumably the first planet-hosting visual binary of two similar red giants which are separately observable. 2enerally speaking, a binary system in which only one component harbors a planet (while the other does not) is potentially an important testing bench for investigating the impact of planet formation on the host star, if the spectra of both stars are independently obtainable and their spectral types are not very different.That is, if any difference in the chemical abundances could be detected between the two, it would provide us with valuable information on the star-planet connection (e.g., accretion of proto-planetary materials), since they should have formed from gas with the same composition.
Although not a few such comparative studies of chemical abundances for the planet-host and nonplanet-host components of visual binaries have been conducted so far, they are restricted to solar-type dwarfs such as 16 Cyg A+B and HD 219542 A+B (see, e.g., Ryabchikova et al. 2022 and the references therein).In this sense, it is worth determining the chemical abundances of many elements for γ Leo A and B, in order to check whether any significant difference exists between these giant stars.
However, few such chemical abundance studies directed to both of γ Leo A and B have been published.That is, most investigations on γ Leo tend to be biased toward the brighter A, while little attention has been paid to the fainter B. As a matter of fact, as summarized in Table 1, only two rather old studies are available that included γ Leo B (and also γ Leo A) as one of the targets: (i) Lambert & Ries's (1981) work on the CNO(+Fe) abundances of 32 G-K giants, and (ii) McWilliam's (1990) abundance determinations of ∼ 10 comparatively heavier elements (Si through Eu) for an extensive sample of 671 GK giants.
Our group has so far published a series of papers focusing the abundances of various elements for a large sample of red giant stars: Takeda et al. (2008; hereinafter referred to as T08) [atmospheric parameters and abundances of many elements], Takeda & Tajitsu (2014;T14) [Be abundances], Takeda et al. (2015;T15) [C, O, and Na abundances], Takeda et al. (2016;T16) [S and Zn abundances], Takeda & Tajitsu (2017;T17) [Li abundances], and Takeda et al. (2019;T19) [ 12 C/ 13 C ratios and N abundances].However, neither γ Leo A nor B were included in our previous targets.Therefore, this unsatisfactory situation motivated the author to newly carry out a detailed spectroscopic comparative study of both γ Leo A and B in order to compare the chemical abundances for a number of elements (volatile as well as refractory elements) between these planethost and non-planet-host components, while making good use of our past experiences.This was the first motivation of this investigation.
Besides, by taking this opportunity, we intend to clarify the stellar parameters and the properties (e.g., activity level, kinematic information, etc.) of these two binary components, because they are not necessarily well established.Especially, although information of the stellar mass is important (which controls the stellar evolution and directly affects the mass evaluation for the orbiting planet), published results are rather diversified (M of γ Leo A ranges from ∼ 1.2M to ∼ 1.8M ; cf.Table 1).It should thus be worthwhile to determine the masses of both A and B as precisely as possible, such as attempted recently by Takeda (2022).for giants in the Kepler field.
In addition, we can also check the nature of internal mixing in γ Leo based on the surface abundances of light elements (especially C, N, O, and Na).Our previous studies (T15 and T19) suggested that the surface abundance characteristics of mid-G to early-K giants (i.e., moderate deficiency in C, near-normal O, enrichment in N, mild overabundance in Na) are almost consistent with the results of recent theoretical simulations for red giants having experienced the first dredge-up (e.g., Lagarde et al. 2012).Meanwhile, some previous work on γ Leo A done in 1990s reported that the surface abundances of the relevant light elements are anomalous and in conflict with the standard theory.That is, nitrogen is nearly normal ([N/Fe] ∼ −0.1; Shavrina et al. 1996a) and carbon is even somewhat overabundant ([C/Fe] ∼ +0.2; Shavrina et al. 1996b); this tendency is apparently incompatible with the results corroborated in our past papers.Is γ Leo A a peculiar star in comparison with other red giant stars in general?To clarify this point is also counted as one of the tasks of this investigation.

Observational data
The observational data (high-dispersion spectra) employed in this study were obtained in two observatories: Okayama Astrophysical Observatory (OAO) and Subaru Telescope (Subaru).Actually, most of the analysis was done based on the former OAO spectra covering the visible (and near IR) wavelength region, while the latter Subaru spectra in the violet-UV region were subsidiarily used only for the specific purposes of Be abundance 52 Summarized here are the effective temperature (in K), logarithmic surface gravity in c.g.s unit (in dex), microturbulence (in km s −1 ), Fe abundance relative to the Sun, and mass (in M ) taken from various previous studies.a Although the star is labeled as HD 89485 (which literally means γ Leo B) in their table, it is suspected to be a mistype of HD 89484 (γ Leo A) as judged from the given T eff value as low as 4500 K. Besides, it seems rather unnatural to do an analysis only for the fainter B without touching the brighter A. Therefore, it is tentatively assumed that these data should be understood as those of γ Leo A. b Although the star is labeled simply as HIP 50583, this number in the Hipparcos catalogue corresponds to γ Leo A+B system as a whole (not the individual components).Therefore, it is assumed here that these data are those of the brighter γ Leo A. c Presumably, some kind of error is involved in this mass value, which is too low.determination (from Be ii 3131) and measurement of Ca ii 3934 core emission.

OAO observation
The spectroscopic observations of γ Leo A and B in the visible to photographic IR wavelength region were done in 2010 May 3 (UT) by using HIDES (HIgh Dispersion Echelle Spectrograph) placed at the coudé focus of the 188 cm reflector at Okayama Astrophysical Observatory.The exposure times were 300 s (A) and 1200 s (B).Equipped with three mosaicked 4K×2K CCD detectors at the camera focus, HIDES enabled us to obtain an echellogram covering ∼ 5100-8800 Å with a resolving power of R ∼ 67000 (with the slit width of 200 µm).

Subaru observation
The Subaru observations of γ Leo A and B were carried out on 2010 May 25 (UT) with HDS (High Dispersion Spectrograph) placed at the Nasmyth platform of the 8.2-m Subaru Telescope, by which high-dispersion spectra covering ∼ 3000-4600 Å could be obtained with two CCDs of 2K×4K pixels in the standard Ub setting with the blue cross disperser.The spectrum resolving power was R 60000 with the slit width set at 0. 6 (300 µm) and a binning of 2×2 pixels.The integrated exposure times were 35 s (A) and 80 s (B), while the star lights were considerably reduced with the help of a neutral density filter in order to avoid saturation.

Data reduction
The reduction of the spectra (bias subtraction, flatfielding, scattered-light subtraction, spectrum extraction, wavelength calibration, and continuum normalization) was performed by using the "echelle" package of the software IRAF3 in a standard manner.

Atmospheric parameters
The atmospheric parameters [effective temperature (T eff ), surface gravity (log g, where g is in cm s −2 ), and microturbulence (v t ) were spectroscopically determined in the same manner as in T08 (see Sect. 3.1 therein for the details) based on the equivalent widths (W λ ) of Fe i and Fe ii lines measured on the OAO spectra covering ∼ 5100-8800 Å.The resulting parameters for γ Leo A / γ Leo B are 4457(±23) / 4969(±15) K, 1.89(±0.10)/ 2.53(±0.05)dex, and 1.44(±0.10)/ 1.39(±0.08)km s −1 , where ± values in parentheses are internal statistical errors (cf.Sect.5.2 in Takeda et al. 2002).The Fe abundances (A Fe )4 corresponding to the final solutions are plotted against W λ and χ low in Fig. 1, where we can see that there is no systematic dependence as required.The detailed W λ and A Fe data for each star are given in "feabunds.dat" of the supplementary material.The mean Fe abundances ( A Fe ) for A / B are 7.09(±0.03)/ 7.12(±0.02),where ± values in parentheses are the mean errors ( ≡ σ/ √ N ; σ is the standard deviation and N is the number of lines).The corresponding values of metallicity ([Fe/H])5 are −0.41 (A) and −0.38 (B).The model atmosphere for each star to be used in this study was generated by interpolating Kurucz's (1993) ATLAS9 model grid in terms of T eff , log g, and [Fe/H].

Mass and age
The absolute magnitude (M V ) or luminosity (L) are determinable from the apparent magnitude (V ) and the parallax (π) with appropriate corrections, Then, since the position on the theoretical HR diagram is established in combination with T eff , the mass (M ) as well as stellar age (age) can be evaluated with the help of theoretical evolutionary tracks.For this purpose, the open software tool PARAM version 1.36 (da Silva et al. 2006) was employed as done by Takeda (2022), which requires T eff , [Fe/H], V 0 (≡ V − A V ), and π (along with their errors) as input parameters (see Table 2).The uncertainty in V − A V was assumed to be 0.05 mag (that of A V ).The output results of M , age, R (radius), and log g M R (gravity from M and R) are also summarized in Table 2.
For the sake of confirming these solutions, the positions of γ Leo A and B on the log T eff vs. log L diagram are compared with the theoretical evolutionary tracks in Fig. 2, and the PARAM results of age vs. M relation are illustrated in Fig. 3.
Regarding the evolutionary status of these two stars, although it is difficult to discriminate based on these figures whether they are in the H-burning phase (ascending the red giant branch) or in the post-He-ignition phase (red clump giants), the latter would be more likely for both, because of the sign of advanced first dredge-up (such as the low 12 C/ 13 C ratio around ∼ 10; cf.Sect.5.1.2).  2012) PARSEC tracks computed for z = 0.006 (moderately metal-deficient by −0.37 dex lower than the solar metallicity) and various M values (1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, and 2.3 M ; thick lines for the cases of integer masses, otherwise thin lines) are overplotted for comparison.These theoretical tracks are depicted in different colors corresponding to their evolutionary stages: Red • • • shell-H-burning phase before He ignition (Red Giant phase or RG). Green • • • M ≤ 1.8 M stars at the He-burning phase (1st Red Clump giant phase or RC1).Blue • • • M > 1.8 M stars at the He-burning phase (2nd Red Clump phase or RC2).(3932.8-3934.6 Å), where integration was done for evaluating the emission strength, is indicated by a horizontal bar.The wavelength scale is adjusted to the laboratory frame by correcting the radial velocity shift.

Stellar activity and rotation
In order to estimate the chromospheric activity, the activity index log R Kp was evaluated from the Subaru spectra by following the procedure described in Sect. 3 of Takeda et al. (2012) where R Kp is the ratio of the chromospheric core emission flux of the Ca ii resonance line at 3933.663 Å (after subtraction of the photospheric flux computed from the classical model atmosphere) to the total bolometric flux.Fig. 4 displays the appearance of the spectra in the relevant core region of Ca ii 3934 line.The resulting log R Kp values are −5.11(A) and −5.07 (B).
The projected rotational velocity (v e sin i), which is closely related to stellar activity, was determined from the spectrum fitting analysis in the 6080-6089 Å region (cf.Fig. 5a and the top row of Table 3), as detailed in Sect.4.2 of T08.The v e sin i results for γ Leo A and B are 1.41 and 1.62 km s −1 , respectively.
Comparing these values of log R Kp and v e sin i with the trends shown in Fig. 6c-e of T17, we can see that both γ Leo A and B are typical red giant stars of low activity for their low rotational velocities.

Kinematic parameters
The velocity components of a star and the properties of its orbital motion in the Galaxy are important to understand the stellar population.These kinematic parameters for the γ Leo system (A and B do not need to be distinguished here) were obtained by following the procedure described in Sect.2.2 of Takeda (2007), and the results are summarized in the last section of Table 2.
Plotting the resulting values of V LSR (+11.7 km s −1 ) and z max (0.063 kpc) on the z max vs. V LSR diagram (cf.Fig. 5a of T17), we can state that γ Leo belongs to the ordinary thin-disk population.This conclusion was also confirmed by applying the U LSR , V LSR and W LSR values to Bensby et al.'s (2005) kinematical criteria (cf.Appendix A therein), which yields T D/D = 0.05 satisfying the criterion of 0 < T D/D < 1 for thin-disk population.

Basic policy
In this study, larger weight is put to comparatively lighter elements (rather than heavier ones), because important volatile species or mixing-sensitive elements are included in this group.Therefore, abundances of such lighter elements are derived based on the spectrumfitting method by taking the non-LTE effect into account, while abundance determinations for heavier elements are done by the conventional manner using equivalent widths with the assumption of LTE.
We exclusively focus on the relative abundances of γ Leo A and B in comparison with the Sun7

Spectrum fitting analysis
Such as was conducted in T17, the abundances of 7 elements (Li, Be, C, O, Na, S, and Zn; either important lighter elements or volatile species) for γ Leo A and B (as well as for the Sun) were determined by applying the spectrum-fitting technique, followed by a non-LTE analysis (except for several cases where LTE was assumed) based on the equivalent widths inversely derived reported in their high-precision differential study of nearby solar twins in comparison with the Sun that the solar abundances of refractory elements (such as Fe group) are slightly deficient relative to the volatile ones (such as CNO), which might be associated with the formation mechanism of our solar system (especially rocky terrestrial planets).However, we do not need to care about this problem in this study, since the magnitude of this effect (on the order of several hundredths dex) is not significant as compared to the typical precision of abundance determination ( 0.1 dex).
from the best-fit abundance solutions (see Sect. 7-9 in T17 for more explanations of the procedures).Likewise, CN abundances (usable to obtain the abundances of N) and 12 C/ 13 C ratios were derived by the synthetic fitting method as done in T19.Specific information (wavelength range, varied abundances, reference sources of the line data) regarding these spectrum fitting analyses is summarized in Table 3, and the atomic data for the representative key lines in each of the wavelength regions are presented in Table 4. Regarding the spectra for the Sun (to be used for deriving the reference solar abundances), the OAO spectra of Moon in the visible-near IR region (as in T15) and the Subaru spectra of Vesta in the UV-violet region (as in T17) were adopted.
How the theoretical and observed spectra match each other is displayed for each region in Fig. 5, and the results of the analysis (equivalent widths, non-LTE correction, elemental abundances, and differential abundances relative to the Sun) are summarized in Table 5.

Derivation of C and N abundances
The role played by C is especially significant because it directly affects the abundance of N determinable from CN.In this study, C abundanes were derived for 4 lines (C i 5052, C i 5380, C i 8335, and [C i] 8727).An inspection of the abundance difference between A and B   In columns 3-5 are presented the atomic line data of λ (air wavelength), χ low (lower excitation potential) and log gf (logarithm of statistical weight times oscillator strength), respectively.See Table 3 for the reference sources of these data.
(δ ≡ A A − A B ) revealed that only that for C i 5380 is appreciably large by δ ∼ +0.25 dex while those for the other three lines are as small as |δ| 0.05 dex (cf.Table 5).Since this suggests that the C i 5380 line is likely to be contaminated by blending of some other lines in cooler A (but not for the hotter B), this line was discarded in calculating the mean C abundances, which were derived from the other three lines as    4).( 2   Eq. 1 in T19). 12C/ 13 C is the ratio of carbon isotopes.

Equivalent width analysis
As done in T08, we also carried out a differential analysis relative to the Sun for the other 19 elements (Al, Si, K, Ca, Sc, Ti, V, Cr, Mn, Co, Ni, Cu, Sr, Y, Zr, La, Ce, Pr, and Nd) based on the equivalent widths of usable spectral lines, which were measured directly from the OAO spectra by the Gaussian fitting method.The procedures of this analysis are detailed in Section 4.1 of Takeda et al. (2005).The solar equivalent widths used as the reference for this analysis were derived similarly by Gaussian-fitting technique on Kurucz et al.'s (1984) solar flux spectrum.The resulting [X/H] values (line-by-line abundances relative to the Sun) for γ Leo A and B are presented in "ewanalys A.dat" and "ewanalys B.dat" of the online material, respectively.
It is worth noting that all these abundance results derived from equivalent widths are based on the conventional assumption that the line opacity is represented by a symmetric Voigt profile.However, lines of specific groups (e.g., Fe-peak elements of odd atomic number) are known to split into a number of sub-components (hyper-fine splitting), though the nature of splitting and its significance widely differs from case to case.In any event, care should be taken in interpreting the results obtained from such lines based on the single-line approximation.This effect is separately discussed for the representative cases of Sc, V, Mn, Co, and Cu lines in the Appendix.

Final abundances
Combining what has been described in Sect.4.2-4.4,the final results of the differential abundances relative to the Sun for 26 elements (except for Li and Be, which are the special cases and thus separately treated in Sect.5.1.1)derived for γ Leo A and B are summarized in Table 7, where the differences between A and B (δ[X/H] A−B ) are also given.The discussions pre-sented in Sect.5.1 and 5.2 will be primarily based on these data.

Light element abundances in context of theoretical predictions
We first discuss the abundances of light elements, which are expected to have suffered more or less changes from the initial composition, because nuclear-processed products are dredged-up to the surface by evolutioninduced mixing of red giants.

Li and Be
Regarding lithium, our fitting analysis in the Li i 6708 region resulted in converged solutions at A Li = −0.81(A) and −0.36 (B).However, these abundances must not be seriously taken because they both should be regarded rather as upper limits, since the corresponding equivalent widths (1.6 and 0.9 m Å) are comparable to or lower than the detection-limit value of a few m Å (cf.Appendix 2 of T17, where it was remarked that A Li 0 is below the reliability limit).Actually, the Li i 6708 line feature is too weak to be recognizable by an eye(cf.Fig. 5b) What can be said about the surface lithium abundances of γ Leo A and B is that they have suffered considerable depletion due to an efficient envelope mixing in the past (cf.Fig. 19 in T17 for reference).
As to beryllium, the abundance results are unfortunately less reliable, because the Be ii 3131 feature is seriously blended with the neighboring Fe line (owing to the appreciably large macroturbulence in this UV region presumably due to its height-increasing nature) and the Fe abundance had to be fixed (i.e.simultaneous determination with Be was not possible).Given this in mind, the derived A Be values of −0.23 (A) and 0.08 (B) correspond to [Be/Fe] = −1.24(A) and −0.96 (B) (assuming A Be = 1.42 as in T14), which suggests that the Be deficiency is more or less compatible with the theoretical prediction expecting [Be/Fe] ∼ −1 to −2 (see the orange line corresponding to M = 1.5M in Fig. 6 of T14).

C, N, O, and Na
The key elements, the abundances of which may be affected by the dredge-up of H-burning products are C, N, O (CNO-cycle), and Na (NeNa-cycle).These trends are more or less (at least qualitatively) consistent with the theoretical expectations (cf. a few hundredths dex; cf.Fig. 11b) is attributed to the chemical evolution effect for a mildly lower metallicity of [Fe/H] ∼ −0.4.Accordingly, we may state that the abundance characteristics of these light elements are reasonably explained by the canonical theory of stellar evolution.
However, a few previous studies done in 1990s reported apparently contradicting results regarding the C and N abundances.That is, a slightly subsolar [N/Fe] of ∼ −0.1 and a somewhat supersolar [C/Fe] of ∼ +0.2 were derived for γ Leo A by Shavrina et al. (1996a) and Shavrina et al. (1996b) based on NH bands (around ∼ 3360 Å) and CH bands (at 4230-4270 Å), which are just the opposite trend to what was obtained by Lambert & Ries (1981) and in this paper.Then, an independent study (again based on the NH bands around ∼ 3360 Å) was soon after carried out by Yakovina & Pavlenko (1998), who concluded [N/Fe] = 0.0(±0.1)for γ Leo A (slightly higher by 0.1 dex than Shavrina et al.'s result).In any event, the C and N abundances of γ Leo A derived by these groups from the spectrumsynthesis analysis of CH and NH bands in the blue-UV region are in conflict with the standard stellar evolution theory, which predicts a C-deficiency as well as an Nenrichment by a few tenths dex.Although any definite argument can not be made, their conclusions seem to be questionable.Since absolute CNO abundances determined from the molecular bands of hydride molecules (CH, NH, and OH) in short wavelength regions tend to suffer systematic errors, these errors for the target Table 7 Elemental abundances of both components and their differences.2003).( 4) Method for deriving the abundance: "fit" • • • spectrum fitting analysis , "eqw" • • • use of measured equivalent widths.( 5) Number of available lines (or features) of each species for A. ( 6) Final [X/H] value (averaged differential abundance of element X relative to the Sun; in dex) for A. ( 7  In panels (a) and (b) are plotted the [X/H] values (logarithmic abundance of element X relative to the Sun) against the atomic number (Z) for γ Leo A and B, respectively.The differences between A and B (δ ) are also shown in the bottom panel (c).The results derived from the spectrum synthesis analysis are shown by triangles while those from the equivalent width analysis are by circles (the data points for Fe are depicted by double circles).Note that the results for Li and Be are not shown here.

Any abundance difference between A and B?
Searching for characteristic chemical signatures in stars specific to their planet-harboring nature (such as metalrich tendency, abundance differences between volatile and refractory species; etc.) is important, since they may serve as a key to clarifying the physical mechanism of planet formation.A number of spectroscopic investigations on the chemical abundances of planet-host stars (along with the comparison sample of non-planethost stars) have been done toward this aim over the past quarter century.Although solar-type stars (FGKtype dwarfs) have been primarily targeted in most of these studies, several recent papers have focused also on evolved red giants (retired A-type stars) reflecting the increasing number of planets discovered around giants; e.g., Maldonado, Villaver, & Eiroa (2013), da Silva et al. (2015), and Jofré et al. (2015), and Maldonado & Villaver (2016).While some possible characteristic trends specific to planet-host giants are reported compared to normal non-planet-host giants (e.g., possible metal-rich tendency in the higher-mass regime, small difference in [X/Fe] for some elements), they are generally subtle and indistinct.Moreover, it is not easy to discern the effect due to the existence of planets from the systematic problem caused by the difference between the samples.
In contrast, our approach is more straightforward and simple: To examine whether any difference exists in the elemental abundances between γ Leo A (with planet) and γ Leo B (without planet), both of which are considered to have formed from the gas with the same composition.Based on the results summarized in Table 7, the final abundances relative to the Sun for 26 elements from C to Nd ([X/H] A , [X/H] B , and their differences δ[X/H] A−B ) are plotted against the atomic number in Fig. 6a-c.As seen from Table 7 and Fig. 6c, |δ[X/H] A−B | 0.1 dex holds for almost all of the studied elements.
The abundance errors due to ambiguities in atmospheric parameters (T eff , log g, and v t ) can be estimated for C, N, O, Na, S, and Zn (fitting-based abundances) by consulting Table 3 in T15, Table 3 in T16, and Table 2 in T19.Adopting ±20 K, ±0.1 dex, and ±0.1 km s −1 for the uncertainties in T eff , log g, and v t (cf.Sect.3.1), we obtained the corresponding abundance errors (root-sum-square of three error components) as ±0.04 dex for C i 5380 (though this line was eventually discarded, it is typical for high-excitation C i lines such as C i 5052 and C i 8335), ±0.06 dex for [C i] 8727, ±0.04 dex for N (from CN 8003), ±0.06 dex for O i 7774, ±0.03 dex for Na i 6161, ±0.06 dex for S i 6757, and ±0.04 dex for Zn i 6362.Meanwhile, regarding the abundances for many other elements derived from directly measured equivalent widths, their mean errors ( ) given in Table 7 are mostly within 0.06-0.07dex (exceptionally as large as ∼ 0.1 dex for a few cases).We may thus regard that the errors involved in both [X/H] A and [X/H] B values are 0.1 dex, which means that the abundances of γ Leo A (with planet) and B (without planet) are practically the same (i.e., the |δ[X/H] A−B | values of 0.1 dex are within the uncertain range).This conclusion may imply that the existence of a planet around A does not have any appreciable impact on the current surface chemical composition.
Our result is in agreement with the available previous work (cf.Table 1).Lambert & Ries's (1981) CNO analysis for A and B resulted in almost the same similarity (cf.Sect.5.1.3).Likewise, the same consequence can be drawn from the abundances of γ Leo A and B derived by McWilliam (1990): Table 13 in his paper shows that the values of δA A−B (mean differential abundances between A and B averaged over available lines) are +0.14, 0.00, +0.02, −0.07, +0.05, −0.04, +0.04, +0.06, −0.06, +0.06, +0.03, and +0.05 dex for Si i, Ca i, Sc ii, Ti i, Ti ii, V i, Co i, Ni i, Y ii, La ii, Nd ii, and Eu ii, respectively.
Finally, the [X/Fe] vs. T c plots for A and B are also displayed in Fig. 7.Although this diagram is known to be useful in searching for any chemical signature of proto-planetary material accreted at the time of planet formation (i.e., abundance difference between volatile elements of low T c and refractory elements of high T c ), its interpretation is difficult in the present case of red giants, because CNO abundances (representative low-T c elements) tend to suffer changes due to an evolutioninduced mixing.Anyway, no apparent T c -dependent trend is observed in [X/Fe] for both A and B (Fig. 7a and Fig. 7b)..

Mass-related problems
As summarized in Table 2, the mass values were derived in Sect.3.2 as 1.66 M (A) and 1.55 M (B) from the positions on the HR diagram in comparison with theoretical evolutionary tracks.Since the corresponding log g M R (1.80 and 2.56; evaluated from M and R) are consistent with the spectroscopic log g (1.89 and 2.53) and the resulting ages for A and B are in agreement with each other at ∼ 2 Gyr within the error bars (cf.Fig. 3), we may regard that these masses are reasonable.
As mentioned in Sect 1, previously determined mass values of γ Leo A are considerably diversified from ∼ 1.2M to ∼ 1.8M (cf.Table 1).Especially, since the value of 1.23 M adopted by Han et al. (2010) is presumably too low, the mass of the planet discovered by them (m p sin i p = 8.78M Jupiter ) should be revised upward by a factor of (1.66/1.23) 2/3 as m p sin i p 10.7M Jupiter .This value has got closer to the critical demarcation mass (13M Jupiter ) between planet and brown dwarf, increasing a possibility that this substellar object orbiting around γ Leo A may rather fall in the category of brown dwarf (depending on the inclination angle i p ).
As already remarked in Sect. 1, the orbital elements of γ Leo system are still subject to large uncertainties because of its very long period over several centuries.For example, according to Burnham's Celestial Handbook (Burnham 1978), determinations of its orbital period in old literature are considerably diversified from ∼ 400 yr to ∼ 700 yr.The Sixth Catalog of Orbits of Visual Binary Stars 8 (WDS-ORB6; cf.Hartkopf et al. 2001) gives P = 554(±27) yr (period), a = 3.10(±0.10)arcsec (semimajor axis), i = 41(±5) • (inclination angle), and e = 0.93(±0.02)(ellipticity) for γ Leo, though a low grade '4 (preliminary)' is assigned to these data.Then, revised elements were published by Mason et al. (2006;cf. Table 7 therein), as P = 510.3yr, a = 4.24 arcsec, i = 76.0 • , and e = 0.845 (again with grade '4').Following Kepler's third law, the sum of the masses in a binary system (M A + M B in unit of M ) is expressed in terms a (in arcsec), π (parallax; in arcsec), and P (in yr) as M A + M B = a 3 π −3 P −2 .However, this relation (with π = 25.07 × 10 −3 arcsec) yields M A + M B = 6.2 M (in case of WDS-ORB6 elements) or 18.6M (in case of Mason et al.'s elements), which seriously disagree with our result of M A + M B = 3.21M obtained in this study.This discrepancy manifestly suggests that the published orbital elements of the γ Leo system (even 8 Available at https://crf.usno.navy.mil/wds-orb6. the latest ones) should be viewed with caution.Further long-running observations (at least over the next hundreds of years) would be required before this problem could be settled.

Summary and conclusion
γ Leo is a binary system comprising two similar red giants of A (with planet) and B (without planet).It is worthwhile to examine if any difference exists between the surface abundances between these two, which may provide some information on a possible impact of planet formation upon the chemistry of the host star.
Yet, spectroscopic studies intending to clarify the chemical properties for both A and B seem to have been barely conducted so far.This motivated the author to newly determine the abundances of many elements for both components based on the high-dispersion spectra covering wide wavelength ranges.
Besides, the stellar parameters and related characteristics (e.g., stellar activity, kinematic information, etc.) were also studied because they are not necessarily well established, where particular attention was paid to clarifying the stellar mass (for which published results are diversified).
In addition, the nature of internal mixing in these evolved stars could be checked based on the light element abundances, because conflicting arguments were made by different authors regarding the surface abundances of C and N in γ Leo A (i.e., whether or not they are well explained by the standard theory for the evolution-induced dredge-up of H-burning products).
The atmospheric parameters (T eff , log g, and v t ) were spectroscopically determined from Fe i and Fe ii lines.The resulting Fe abundances are [Fe/H] = −0.41(A) and −0.38 (B); i.e., almost the same at a mildly subsolar metallicity.The kinematic parameters suggest that this system belongs to the thin-disk population.
The masses were derived from the positions on the HR diagram in comparison with theoretical evolutionary tracks as 1.66 M (A) and 1.55 M (B).Both A and B are likely to be in the stage of red clump giants after He-ignition.According to the newly determined M A , the mass of the planet around A was also revised as m p sin i p 10.7M Jupiter (increased by ∼ 20% from the original value reported by Han et al.).
The chromospheric activity was estimated from the core emission strength of the Ca ii 3934 line, and the projected rotational velocity (v e sin i) was determined from the spectrum-fitting analysis.It turned out that both γ Leo A and B are typical red giant stars of low activity and low rotational velocities.
Chemical abundances of especially important elements (Li, Be, C, N, O, Na, S, and Zn; either being affected by evolution-induced mixing or volatile species) were determined by the spectrum-fitting technique.Meanwhile, those of the remaining elements (Al, Si, K, Ca, Sc, Ti, V, Cr, Mn, Co, Ni, Cu, Sr, Y, Zr, La, Ce, Pr, and Nd; mostly refractory species) were derived by the conventional method using the directly measured equivalent widths.
Regarding the mixing-affected light elements, although much can not be said about Li (very depleted; only upper limit) and Be (considerably deficient by ∼ −1 dex, though less reliable) , a moderate deficiency of C, a mild enrichment of N, and a slight overabundance of Na, and a low 12 C/ 13 C ratio were obtained for both A and B, which are quite consistent with the trend expected from the canonical theory of stellar evolution.Likewise, the slightly positive [O/Fe] is reasonable for these somewhat metal-poor stars (galactic chemical evolution effect).
The chemical abundances of A and B turned out to be practically the same within 0.1 dex for almost all elements, which implies that the surface chemistry is not appreciably affected by the existence of a planet in A. Likewise, any meaningful T c -dependent trend (or difference between volatile and refractory species) in [X/Fe] was not observed.
Accordingly, what can be concluded from this investigation is as follows.
• Based on the results summarized above, we may state that the visual binary system γ Leo A+B is not so spectroscopically unusual as suspected initially when this investigation was motivated.• The fact that no clear abundance difference was detected between A (with planet) and B (without planet) suggests that hosting a planet does not have an appreciable impact on the surface abundances of red giants, though this is an argument specific to γ Leo and may not simply be generalized.• The abundances of light elements are well consistent with those predicted from the canonical mixing theory of stellar evolution, which means that both γ Leo A and B are ordinary red giants (presumably of red clump) like many others.
• As seen from the different extent of hfs correction between the three cases (Sun < γ Leo B < γ Leo A), T 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 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 (δ[X/H] B ) for γ Leo B are apparently insignificant (only a few hundredths dex in any case), appreciable downward corrections ranging from ∼ 0.0 to ∼ 0.3 dex (considerably differing from line to line) are expected for γ Leo A as seen from the values of δ[X/H] A .Fortunately, even in the latter case of γ Leo A, since the lines of large corrections (by ∼ 0.2-0.3dex) 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 δ[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).

Fig. 1
Fig. 1 Upper panels (a) and (b): AFe (Fe abundance) vs. W λ (equivalent width) relations.Lower panels (c) and (d): AFe vs. χ low (lower excitation potential) relations.These Fe abundances correspond to the finally established atmospheric parameters of T eff , log g, and vt for γ Leo A (left panels) and γ Leo B (right panels).The filled and open symbols correspond to Fe i and Fe ii lines, respectively.The mean abundance ( AFe ) is indicated by the horizontal dashed line.

Fig. 2
Fig. 2 Positions of γ Leo A and B (plotted by large filled circles with error bars indicated in yellow crosses) on the log T eff -log L diagram, where Bressan et al.'s (2012) PARSEC tracks computed for z = 0.006 (moderately metal-deficient by −0.37 dex lower than the solar metallicity) and various M values (1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, and 2.3 M ; thick lines for the cases of integer masses, otherwise thin lines) are overplotted for comparison.These theoretical tracks are depicted in different colors corresponding to their evolutionary stages: Red • • • shell-H-burning phase before He ignition (Red Giant phase or RG). Green • • • M ≤ 1.8 M stars at the He-burning phase (1st Red Clump giant phase or RC1).Blue • • • M > 1.8 M stars at the He-burning phase (2nd Red Clump phase or RC2).

Fig. 3 Fig. 4
Fig. 3 PARAM results of age (t) and mass (M ) for γ Leo A and B plotted on the age-M diagram, where tHe * (time of He-ignition) vs. M relation (taken from PARSEC tracks) is also shown by the dashed line.

(
[X/H] A or ([X/H] B ) along with their mutual differences (δ[X/H] A−B ).Since they are derived by applying the differential analysis under the same condition (spectrum-fitting done in the same manner or differential line-by-line analysis based on equivalent widths) to the three spectra of A, B, and the Sun.uncertainties in atomic line parameters (especially those of oscillator strengths) are cancelled out and thus irrelevant.
Fig. 11 in T15 for C, O, and Na; Fig. 12 in T19 for N and 12 C/ 13 C).The slightly positive [O/Fe] (despite that O may suffer a very slight deficiency by ) Mean error of [X/H] ( ≡ σ/ √ N ) for A (in dex).(8) Number of available lines (or features) for B. (9) Final [X/H] value for B. (10) Mean error of [X/H] for B. (11) Differential abundance of A relative to B (≡ [X/H]A − [X/H]B; in dex).
Fig. 6In panels (a) and (b) are plotted the [X/H] values (logarithmic abundance of element X relative to the Sun) against the atomic number (Z) for γ Leo A and B, respectively.The differences between A and B (δ[X/H]A−B ≡ [X/H]A−[X/H]B) are also shown in the bottom panel (c).The results derived from the spectrum synthesis analysis are shown by triangles while those from the equivalent width analysis are by circles (the data points for Fe are depicted by double circles).Note that the results for Li and Be are not shown here.

Fig. 7
Fig.7The [X/Fe] values (≡ [X/H] − [Fe/H]; logarithmic X-to-Fe abundance ratios relative to the Sun) are plotted against Tc (condensation temperature).Panels (a) and (b) are for γ Leo A and B, respectively.Otherwise, the same as in Fig.6.
Fig. 8Corrections to the absolute (A) or relative ([X/H]) abundances due to the hyperfine-splitting effect (cf.Table8) 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 γ Leo A (green) and the Sun (red).(b) Hfs corrections to [X/H] for γ Leo A. (c) Hfs corrections to A for γ Leo B (blue) and the Sun (red).(d) Hfs corrections to [X/H] for γ Leo B.

Table 1
Stellar parameters of γ Leo A and B reported in past publications.

Table 2
Fundamental parameters of γ Leo A and B adopted/derived in this study.

Table 3
Spectrum fitting analysis done in this study.The abundances of other elements than these were fixed by assuming [X/H] = [Fe/H] in the fitting.
* † Corresponding panel of

Table 5
Abundance results derived from spectrum fitting.

Table 6
Results from the fitting analysis of CN molecular lines.