SAG: Stars and Galaxies Vol.2, id.1 , 2019 December 27
c 2019. Center for Astronomy, University of Hyogo.
⃝

Determination of Potassium Abundancesfor Giant and Dwarf Stars in the Galactic Disk
Yoichi Takeda 1,2
1

National Astronomical Observatory, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
takeda.yoichi@nao.ac.jp
2
SOKENDAI, The Graduate University for Advanced Studies, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan(Received 2019 October 16; Accepted 2019 December 4)

Abstract
An extensive study on the potassium abundances of late-type stars was carried out by applying thenon-LTE spectrum-fitting analysis to the K i resonance line at 7698.96 Å to a large sample of 160 FGK
dwarfs and 328 late-G /early-K giants (including 89 giants in the Kepler field with seismologically known<ages) belonging to the disk population (−1 <∼ [Fe/H] ∼ 0.5), which may provide important observational
constraint on the nucleosynthesis history of K in the galactic disk. Special attention was paid to clarifying
the observed behaviors of [K/Fe] in terms of [Fe/H] along with stellar age, and to checking whether giants
and dwarfs yield consistent results with each other. The following results were obtained. (1) A slightly
increasing tendency of [K/Fe] with a decrease in [Fe/H] (d[K/Fe]/d[Fe/H] ∼ −0.1 to −0.15; a shallower
slope than reported by previous studies) was confirmed for FGK dwarfs, though thick-disk stars tend toshow larger [K/Fe] deviating from this gradient. (2) Almost similar characteristics were observed also
for apparently bright field giants locating in the solar neighborhood (such as dwarfs). (3) However, the[K/Fe] vs. [Fe/H] relation for more distant Kepler giants shows larger scatter and is systematically higher(by <∼ 0.1 dex) than that of dwarfs, implying that chemical evolution of K is rather diversified dependingon the position in the Galaxy. (4) Regarding the age-dependence, a marginal trend of increasing [K/Fe]with age is recognized for dwarfs, while any systematic tendency is not observed for Kepler giants. These
consequences may suggest that evolution of [K/Fe] with time in the galactic disk does exist but proceeded
more gradually than previously thought, and its condition is appreciably location-dependent.
Key words: Galaxy: disk — Galaxy: evolution — stars: abundances — stars: atmospheres — stars:
late-type1.

Introduction

While our understanding on the nucleosynthesis history of various elements in the Galaxy has remarkably
grown thanks to accumulated observational data of stellar
abundances as well as progress in theoretical modeling ofchemical evolution, significant discrepancies between theory and observation still remain for several elements. As
one of such cases, it has been known that abundance behaviors of potassium (K) observed in old metal-poor stars
do not well match theoretical predictions (see, e.g., Fig. 13
in Prantzos et al. 2018 and the references therein).
For the sake of ameliorating this situation, collecting reliable K abundances for as many stars as possible
should be important. However, spectroscopically established abundance data published so far are not necessarily
suﬃcient as long as this element is concerned. This is presumably due to the fact only the strong K i 7698.96 Å lineof the doublet (hereinafter often referred to as “K i 7699”)
has to be invoked, since the paired line at 7664.90 Å (K i
7665) tends to be severely blended with telluric lines andother potassium lines are generally too weak to be measurable. In addition, because of its conspicuous strength,
special diﬃculties are involved with abundance determination from this line: one problem is the sensitivity to achoice of (often uncertain) damping parameters, but more
important is that it suﬀers a considerable non-LTE eﬀect.
Actually, pioneering studies of stellar K abundances
done under the assumption of LTE (e.g., Gratton &Sneden 1987a,b; Chen et al. 2000) are not regarded asreliable as viewed from present-day standard. Meanwhile,eﬀorts of investigating the non-LTE eﬀect on K i 7699
by non-LTE calculations with suﬃciently complex atomicmodel of K have been made by several investigators not
only for the Sun (de la Reza & Müller 1975; Bruls etal. 1992; Zhang et al. 2006a) but also for stars of othertypes (Takeda et al. 1996; Ivanova & Shimanskiı̆ 2000;
Takeda et al. 2002; Shimansky et al. 2003; Zhang et al.
2006b; Andrievsky et al. 2010; Reggiani et al. 2019).
Making use of these theoretical accomplishments, chemical evolution studies of potassium based on the non-LTE
abundances derived from K i 7699 have gradually emerged

2

Y. Takeda

since the beginning of this century, where the targets of
those investigations are roughly divided into two groups:(i) mildly metal-poor or metal-rich stars of disk popu<
lation (−1 <∼ [Fe/H] ∼ 0.5) (Takeda et al. 2002; Zhang
et al. 2006b; Wang et al. 2009; Zhao et al. 2016;
Reggiani et al. 2019) and (ii) very metal-poor stars of<
halo population(−4 <∼ [Fe/H] ∼ −2) (Cayrel et al. 2004;
Takeda et al. 2009; Andrievsky et al. 2010; Roederer et
al. 2014; Reggiani et al. 2019).
The focus of this study is placed on the former mildly
metal-poor or metal-rich stars belonging to the galactic
disk population. A problem regarding this group to beclarified is that the behaviors of [K/Fe]1 vs.[Fe/H] relation (an important diagram for investigating the nucleosynthesis evolution of K in the Galaxy) derived for diskstars by several previous studies are not necessarily consistent with each other in the quantitative sense. Takeda
et al.’s (2002) non-LTE reanalysis on Chen et al.’s (2000)
spectra of thin-disk stars resulted in a progressive increaseof [K/Fe] with a decrease in [Fe/H] from [K/Fe] ∼ −0.1 (at[Fe/H] ∼ 0) to [K/Fe] ∼ +0.3 (at [Fe/H] ∼ −1) (cf. Fig. 4atherein), suggesting d[K/Fe]/d[Fe/H] ∼ −0.4. Meanwhile,
Zhang et al.’s (2006b; cf. Fig. 5 therein) results for thin<disk stars (−0.8 <∼ [Fe/H] ∼ −0.2) as well as Wang etal.’s (2009; cf. Fig. 9c therein) analysis on thin-disk stars<(−0.5 <∼ [Fe/H] ∼ +0.4) showed a similar linear tendency
but appreciably steeper gradient (d[K/Fe]/d[Fe/H] ∼−0.6). In contrast, Zhao et al.’s (2016) Fig. 9 suggests
a shallower slope of d[K/Fe]/d[Fe/H] ∼ −0.2 to −0.3 for<thin-disk stars (−0.8 <∼ [Fe/H] ∼ +0.2). Which of these
represents the actual trend of disk stars at all?
Here, the following points may be worth consideration:— First, the number of stars analyzed by each of thesestudies is only around ∼ 20, which is not suﬃcient for elucidating statistically meaningful tendency. Considerablyincreasing the sample size (ca., up to the order of ∼ 102 )would undoubtedly improve the situation.
— Second, all these previous K abundance studies for
disk-population stars made use of late F–early G dwarfs,
but red giants (of disk metallicity)2 seem to have neverbeen employed for this purpose. Since potassium is not expected to suﬀer any change by evolution-induced dredgeup (unlike lighter elements such as CNO or Na), primordial K abundances should be retained at the surface ofgiants. Then, why not use red giants (which are intrinsically bright and available in large numbers) for investigating the chemical evolution of K in the disk of the Galaxy?
— Third, since [Fe/H] is roughly related to stellar age (i.e.,
older stars tend to have lower [Fe/H]), it is worthwhile toexamine age-dependence of [K/Fe] if possible, since pro1

2

As usual, [X/Y] is the logarithmic abundance ratio of element
X
X to element Y relative to the Sun; i.e., [X/Y] ≡ (AXstar − A⊙ ) −Y ), where AX is the logarithmic number abundance
(AY
−
A
star
⊙
of element X normalized with AH = 12 (the suﬃx ⊙ denotes thesolar value).
In contrast, studies of K abundances in very metal-poor halostars predominantly invoked evolved giants (e.g., Cayrel et al.
2004); thus the situation is markedly diﬀerent from the case ofgalactic disk stars.

Vol. 2

gressive increase with age may as well be detected if [K/Fe]
grows with a lowering of [Fe/H]. In this context, it is interesting that recent Spina et al.’s (2016) high-precision differential abundance study on the solar twins of widely different ages showed that [K/Fe] is almost age-independent(unlike other elements which revealed systematic trendwith age). The successsive non-LTE reanalysis of Spinaet al.’s (2016) data by Reggiani et al. (2019) again resulted in almost the same conclusion. As such, this pointshould be worth reinvestigation based on a large numberof stars with known ages.
Motivated by these notions, this study aims at determining the non-LTE K abundances from the K i 7699 line
for an extensive sample of 160 late F–early K dwarfs aswell as 328 late G–early K giants (239 nearby giants and89 giants in the Kepler field) belonging to the disk pop<
ulation (−1 <∼ [Fe/H] ∼ 0.5), for which the spectra areconveniently available to the author and the stellar parameters are already determined (especially, stellar ages
are known for FGK dwarfs and Kepler giants). The points
of interest to be checked upon are as follows:• How are the [K/Fe] vs. [Fe/H] relations derived
for each of the groups (dwarfs, nearby giants, andKepler giants) compared with each other? Are they
consistent, or any diﬀerence is seen?
• What about the slope (d[K/Fe]/d[Fe/H]) of the resulting [K/Fe] values in comparison with the diversified gradients reported by previous studies?
• Is any systematic trend observed in [K/Fe] with stellar age?
2.

Observational Data and Stellar Parameters

All the observational materials and stellar parameters
employed for this investigation are those already used anddetermined in the previous studies of the author’s group.
2.1.

FGK dwarfs

Regarding dwarfs (including subgiants), the spectra of
160 stars observed in 2000–2003 with the 1.9 m reflector (+HIDES spectrograph) at Okayama AstrophysicalObservatory (OAO) and published by Takeda et al.
(2005a) were used. Besides, the Moon spectrum (substitute for the reference solar spectrum) was also takenfrom this database. The atmospheric parameters [Teﬀ(eﬀective temperature), log g (surface gravity), vt (microturbulence), and [Fe/H] (Fe abundance relative to theSun)] of these 160 stars were determined from the equivalent widths measured for a number of selected Fe i andFe ii lines, while requiring that abundances do not depend upon χ (lower excitation potential) as well as W
(equivalent width) and that mean abundances derived
from Fe i and Fe ii lines are equal (cf. Takeda et al.
2005b). Regarding the atmospheric parameters of Sun,
Teﬀ,⊙ = 5780 K, log g⊙ = 4.44, vt,⊙ = 1.0 km s−1 , and[Fe/H]⊙ = 0.00 were employed (note that practically thesame values were empirically derived with this method
using Fe i/Fe ii lines applied the Moon spectrum; cf.

id. 1

Potassium Abundances of Galactic Disk Stars

Takeda et al. 2005b). Takeda (2007) evaluated the age(log age) and mass (M ) for each of these 160 stars bycomparing the position in the log L (L: bolometric luminosity) vs. log Teﬀ diagram with theoretical stellar evolutionary tracks. These stellar parameters are summarizedin tableE1.dat (online material).
2.2.

Nearby giants

As to giants, the spectra of 239 late G or early K giants
were used, which were observed in 2012–2013 with the
1.9 m telescope and HIDES spectrograph at OAO anddescribed in Takeda et al. (2015). These 239 stars (apparently bright with V < 6 mag and comparatively near to
us within several hundreds parsec) are the subset of 322
giants targeted by the Okayama Planet Search Program.
for which the atmospheric parameters (Teﬀ , log g, vt , and[Fe/H]) were already established by Takeda et al. (2008)
in the same way as done for 160 dwarfs mentioned above.
However, the mass values (closely related to stellar age) of
these giants estimated by Takeda et al. (2008) are likely to
be appreciably overestimated and unreliable for a numberof red clump stars (constituting the majority of these sample stars), because of the diﬃculty in discriminating theevolutionary status of each star by using such a coarse gridof theoretical stellar evolutionary tracks as applied in that
paper (cf. Takeda & Tajitsu 2015; Takeda et al. 2016 formore details). Accordingly, mass and age are treated asundetermined and not mentioned in this paper for these239 giants, for which only four atmospheric parameters
are presented in tableE2.dat (online material).
2.3.

Kepler giants

In addition, as another set of giant stars, the spectraof late G–early K giants in the Kepler field observed withthe 8.2 m Subaru Telescope (+ HDS spectrograph) on
2014 September 9 (42 stars) and 2015 July 3 (47 stars)3
were also employed. Their atmospheric parameters werealready determined spectroscopically by Takeda & Tajitsu(2015) and Takeda et al. (2016) in same manner as thecases of dwarfs and nearby giants described above. The
distinct merit of these Kepler field giants is that the stellar
mass (M ) as well as the evolutionary status of each star
are confidently established by making use of the seismological information, by which the stellar age can be reliably
determined with the help of stellar evolutionary tracks as
done by Takeda et al. (2016). In tableE3.dat (online material) are given the values of Teﬀ , log g, vt , [Fe/H], M ,and log age for these 89 giant stars.
2.4.

Comparison between the groups

The mutual comparisons of Teﬀ , logg, vt , and [Fe/H] aredepicted in Figures 1a–1d, in order to illustrate the dif3

Actually, 48 stars in the Kepler field were observed in this observing run. However, for the case of KIC 7341231 which is avery metal poor subgiant with especially large (negative) radial
velocity (Vrhel ≃ −270 km s−1 ), the K i 7699 line unfortunately
fell on the gap of the echelle format at 7687–7694 Å and could
not be used. Therefore, this star had to be excluded from thisstudy.

3

ference or similarity of these star groups. The discussions
regarding correlations between these parameters are presented in Takeda et al. (2005b) and Takeda et al. (2008)
for the case of dwarfs and giants, respectively.
Figures 1e and 1f also show the positional distributions of the program stars in the XY Z-space, whereX ≡ d cos b cos l, Y ≡ d cos b sin l, and Z ≡ d sin b (d: distance from the Sun, l: galactic longitude, and b: galactic
latitude). It can be seen from these figures that, while
160 dwarfs (within several tens parsec) as well as 239
nearby giants (within several hundreds parsec) are solar
neighborhood stars as viewed from the galactic scale, 89
Kepler giants widely distribute with diversified distancesfrom ∼ 102 pc up to ∼ 2 kpc in the confined direction
to Cygnus. Accordingly, from the viewpoint of locationin the Galaxy. the former two groups (dwarfs, nearby giants) are almost similar but the last group (Kepler giants)
is distinctly diﬀerent.
3.

Kinematic Properties

3.1.

Space velocities and orbital parameters

Examining the kinematic properties of stars is important for understanding to which stellar population they
belong. Takeda (2007) computed the orbital motions
within the galactic gravitational potential for the 160 FGK
stars (program stars of this study) by using the positional
data and the velocity data (proper motions and radial velocity), and derived Rm (mean galactocentric distance), e(orbital eccentricity), zmax (maximum separation from thegalactic plane). These orbital quantities along with thespace velocity components relative to the Local Standardof Rest (ULSR , VLSR , WLSR ) are presented in electronic
tableE2 (kinepara.dat) of that paper.
Likewise, Takeda et al. (2008) carried out similar
analysis of kinematic properties for 322 red giants (fromwhich 239 nearby giants for this study were selected), andthe resulting parameters are given in electronic tableE1(kinepara.dat) of that paper.
These kinematic parameters for 89 giants in the Kepler
field were newly computed for this investigation, following
the same way as done in Takeda (2007). Regarding theparallax and proper motion data, the Gaia DR2 database(Gaia Collaboration et al. 2016, 2018) was invoked,
while the values measured from our Subaru HDS spectra were used for radial velocities (they were confirmed tobe consistent with Gaia DR2 data). The resulting orbitalparameters and space velocity components are given intableE4.dat of the online material.
3.2.

Classification of stellar population

According to Ibukiyama & Arimoto (2002), the zmax vs.
VLSR (rotation velocity component) diagram can be used
for discriminating thin-disk, thick-disk, and halo populations, as already done by Takeda (2007) and Takeda et al.
(2008) to examine the stellar populations of FGK dwarfs
and nearby giants. Figure 2a (reproduction of Fig. 14din Takeda 2007), Figure 2b (similar to Fig. 9a in Takeda
et al. 2008), and Figure 2c illustrate this situation for

4

Y. Takeda

160 FGK dwarfs, 239 nearby giants, and 89 Kepler giants,
respectively. From these figures, 6 (out of 160) dwarfs,
5 (out of 239) nearby giants, and 13 (out of 89) Kepler
field giants were concluded to be of thick-disk population(indicated by open symbols in the figures; see ReadMe.txt
in online material for their specific IDs), while all others
are of thin-disk population.
3.3.

Relation to metallicity and age

Figures 2d–2l also depict√ the correlations between the222 ), metalspace velocity |vLSR | (≡ ULSR
+ VLSR+ WLSR
licity ([Fe/H]), and stellar age. It can be read from thesefigures that (1) thick-disk stars tend to be old, metalpoor, and moving faster as compared to thin-disk stars,(2) lower-metallicity stars as well as older stars are apt tohave higher space velocity, and (3) there is a tendency ofolder stars having lower metallicity; all these trends arenatural and reasonably understood.
4.

Determination of K abundances

4.1.

Spectrum-fitting analysis

Although most of the previous studies mentioned in
Section 1 determined the potassium abundances from theequivalent widths (W ) of K i 7699 line, precisely measuring W is not necessarily an easy task for such a strongline often showing appreciable damping wings. In thisinvestigation was instead adopted a spectrum-fitting approach for establishing the non-LTE K abundances of the
program stars.
The procedure is similar to the one adopted in Takeda etal. (1996), which accomplishes the best fit between theoretical and observed profiles by finding the most optimum
solutions of three parameters [A(K) (K abundance)4 ,vM (macrobroadening parameter),5 and ∆λ (wavelength
shift)], while applying the numerical algorithm describedin Takeda (1995).
That is, unbroadened non-LTE theoretical profile,which was calculated for the relevant model atmosphereand non-LTE departure coeﬃcients (specified by Teﬀ ,log g, and [Fe/H]) along with the given microturbulence(vt ), was broadened (by convolving the broadening function corresponding to vM ) and shifted (by ∆λ) in order
to be compared with the observed profile. The model
atmosphere of each star was generated by interpolating
Kurucz’s (1993) ATLAS9 model grid in terms of Teﬀ ,log g, and [Fe/H], as done in Takeda (2007) or Takeda
et al. (2008). Similarly, the depth-dependent non-LTE
departure coeﬃcients of the relevant levels (i.e., groundlevel and first excited level) were derived by interpolating
the extensive grid computed in Takeda et al. (2002; cf.
Appendix therein). Regarding the atomic parameters of
the K i 7699 line, the same values as used in Takeda et
45

As usual, A(X) is the logarithmic number abundance of element
X normalized as A(H) = 12: i.e., A(X) = log[N (X)/N (H)] + 12.
This vM is the e-folding half width of the Gaussian macrobroadening function fM (v) ∝ exp[−(v/vM )2 ], which is regarded as a
combination of (i) instrumental broadening, (ii) macroturbulence broadening, and (iii) rotational broadening.

Vol. 2al. (2002) were adopted (cf. Sect. 4 therein). Appendix
shows that Takeda et al.’s (2002) non-LTE calculations,
upon which ths study is based, are in reasonable agreement with the recent ones of Reggiani et al. (2019).
This method turned out successful and a satisfactory
fit could be accomplished for almost all cases, as demonstrated in Figure 3 (160 FGK dwarfs + Moon), Figure 4(239 nearby giants) and Figure 5 (89 Kepler giants). Note
that, since telluric lines (or spectrum defects) sometimes
invaded into the fitting range depending on the radial velocity, they had to be masked and neglected in judging
the goodness of fitting (as highlighted in green in thesefigures).
4.2.

Equivalent widths and non-LTE corrections

Although the non-LTE K abundance (A) of each star
could be established based on the spectrum-fitting technique as such, only this information would not suﬃce. In
order for understanding the behaviors of resulting abundances (e.g., sensitivity to stellar parameters) diﬀeringfrom star to star, abundance-related quantities such asequivalent width (W ) or non-LTE correction (∆) are quite
useful. Therefore, by using Kurucz’s (1993) WIDTH9
program which was considerably modified by the author(e.g., to enable inclusion of non-LTE eﬀect). the corresponding W of K i 7699 was evaluated by using the solution of A along with the same model atmosphere andvt . Furthermore, based on such calculated W , the nonLTE abundance (ANLTE ) and LTE abundance (ALTE )were inversely derived, from which the non-LTE abundance correction (∆) was obtained as ANLTE − ALTE .
The resulting W , ANLTE , and ∆ values are presented intableE1.dat (FGK dwarfs), tableE2.dat (nearby giants),
and tableE3.dat (Kepler giants) of the online material.
Figure 6 illustrates how W and ∆ depend on Teﬀ andlog g and how they correlate with each other. Roughly
speaking, W /|∆| tends to decrease/increase with higher
Teﬀ or lower log g (cf. Figures 6a–6d), as long as stars
belonging to the same group (e.g., ‘dwarfs’ group or ‘giants’ group) are concerned. According to Figure 6e, theextent of ∆ tends to diminish as W increases. This is dueto the fact that comparatively weaker lines (100 mÅ <∼W<∼ 200 mÅ) are most saturated (i.e., line-forming layer
is high) at the shoulder or the flat part of curve of growthand suﬀer an especially large non-LTE eﬀect, while those<stronger lines (200 mÅ <∼ W ∼ 300 mÅ) are already in thedamping part and comparatively less sensitive to a nonLTE eﬀect (because deep-forming damping wings appreciably contribute to the total strength of such a strongline). This situation is elucidated in Figure 6f, where
log W is plotted against ANLTE + (χion − χexc )5040/Teﬀ(χion = 4.34 eV, χexc = 0.00 eV), which may be regarded
as the abscissa of curve of growth (controlling the A- andTeﬀ -dependence of line strength).

id. 1

Potassium Abundances of Galactic Disk Stars

5.

Behaviors of Potassium Abundances

5.1.

[K/Fe] vs. [Fe/H] relation

so diversified [K/Fe] may be due to their widely scattered locations along the direction to Cygnus (cf.
Figures 1e and 1f).

The [K/Fe] ratios of the program stars were calculated
from the potassium abundances determined in Section 4
as[K/Fe] ≡ (ANLTE − ANLTE) − [Fe/H],
⊙

5

(1)

where ANLTE
is the solar potassium abundance of 4.96⊙
derived from the spectrum of Moon.
Takeda et al. (2002) discussed the ambiguities involved
with the potassium abundances they derived from K i
7699 caused by uncertainties in atmospheric parameters(see Sect. 5 therein). In this investigation, the adopted
values of Teﬀ , logg, vt , and [Fe/H] of all program stars arethose consistently determined by the same method using
Fe lines, and their statistical errors are typically several−1tens of K, <∼ 0.1 dex, ∼ 0.1 km s , and a few hundredthsof dex, respectively (cf. Takeda et al. 2005b, 2008). By
combining these uncertainties with the results of Takeda
et al. (2002), the typical errors in [K/Fe] may be estimatedas <∼ 0.1 dex.
The resulting [K/Fe] vs. [Fe/H] diagrams for each of thethree stellar groups are displayed in Figures 7a–7c, where
the corresponding non-LTE corrections are also shown.
The characteristic trends recognized from these figures are
summarized below:• Generally, a qualitative trend is seen that [K/Fe]
tends to increases with a decrease in [Fe/H], whichis commonly seen in each of the groups (though specific details are diﬀerent).
• Almost all thick-disk stars (indicated by open symbols in the figures) have supersolar [K/Fe] (> 0),
mainly because they tend to be appreciably metalpoor ([Fe/H] < 0).
• Regarding the group of dwarf stars, [K/Fe] vs.
[Fe/H] relation shows a tight tendency with small
dispersion (cf. Figure 7a). Only one exceptional
outlier is HD 50554, which exhibits a very large[K/Fe] of +0.74 despite its near-solar metallicity([Fe/H] = −0.03); but the reason for this anomaly
is unclear.
• Nearby giants reveal a rather similar trend to thecase of dwarfs, though the dispersion is apparently
larger and the slope appears to be slightly steeper,
while several outliers with appreciably large [K/Fe](> 0) exist even around the solar metallicity (cf.
Figure 7b).
• However, a diﬀerent feature is recognized for thecase of giants in the Kepler field (cf. Figure 7c).
Here, while the increasing trend of [K/Fe] towards
lowered metallicity is still roughly seen by the existence of thick-disk stars, [K/Fe] values are generally
enhanced (i.e., tending to be supersolar irrespectiveof the metallicity) with a considerable scatter. Thisimplies that the chemical evolution history of these
Kepler giants would have been dissimilar to that ofsolar neighborhood stars. The reason why they show

5.2.

Comparison between dwarfs and giants

It is not easy to evaluate the quantitative characteristics of [K/Fe] (e.g., gradient with respect to a change
in [Fe/H]) in Figures 7a–7c only by eye-inspection,
because the plotted points are densely overlapped.
Therefore, mean ⟨[K/Fe]⟩ (and the corresponding
standard deviation) were computed by averaging the[K/Fe] values6 included at each of the seven metallicity
bins (∆[Fe/H] = 0.1dex at −0.5 ≤ [Fe/H] ≤ +0.2)
for three star groups, and comparisons were madefor nearby giants vs. FGK stars as well as Kepler
giants vs. FGK dwarfs, as shown in Figures 8a and
8b.
The linear-regression analysis applied to these⟨[K/Fe]⟩ data yielded the following relations: ⟨[K/Fe]⟩ =−0.129(±0 .022 )×[Fe/H]−0.008(±0 .005 ) (FGK dwarfs),⟨[K/Fe]⟩ = −0.157(±0 .013 )×[Fe/H]+0.004(±0 .003 )(nearbygiants),and⟨[K/Fe]⟩=−0.100(±0 .063 )×[Fe/H]+0.049(±0 .016 ) (Kepler giants), where the values in parentheses (denoted in Italics)
are the standard errors. These lines are also drawn in the
figures.
Figure 8a suggests that the [K/Fe] trend of nearby
giants is not much diﬀerent from that of FGK dwarfs(though marginally higher [K/Fe] by a few hundredths
dex and slightly steeper slope), while Kepler giants anddwarfs (shown in Figure 8b) are in disagreement witheach other as already mentioned (the former show systematically larger [K/Fe] values at the same metallicity).
Consequently, it can be concluded that (1) nearly consistent [K/Fe] vs. [Fe/H] relations could be derived from thisinvestigation for both dwarfs and giants as long as stars
in the solar neighborhood are concerned, (2) but the giants in the Kepler field are diﬀerent presumably because
they are in diversified locations far from the Sun where
chemical evolution history would have been more or lessvariant.
According to Figure 8a, the d[K/Fe]/d[Fe/H] gradient corresponding to galactic disk dwarfs in the solar
neighborhood (within several tens parsecs) is concluded
to be ∼ −0.1 to −0.15, while that for nearby giants(within several hundreds parsec) is similar around ∼−0.15. Regarding the questions raised in Section 1 (i.e.,
which of the variously reported slopes are correct), the resulting d[K/Fe]/d[Fe/H] gradient for thin-disk population
derived from this investigation (from ∼ −0.1 to −0.15)
is shallower than any of the past studies, though the recent Zhao et al.’s (2016) consequence (∼ −0.2 to −0.3)
is reasonably the closest among these. That these previous authors obtained diversified results of comparatively
steeper slope (from ∼ −0.2 to −0.6) may have originatedfrom the paucity of their sample stars.
6

In the averaging process, the data showing appreciable deviations within each bin-group were discarded, which were judged
by Chauvenet’s criterion (Taylor 1997).

6
5.3.

Y. Takeda
Relation to stellar ages

Finally, how the resulting [K/Fe] depends on the stellar
age is examined, which is possible for FGK dwarfs and
Kepler giants (ages are not available for nearby giants; cf.
Section 2.2). An inspection of Figure 7d reveals that asystematic but subtle increase exists in [K/Fe] with age
for these dwarfs in the solar neighborhood, which meansthat [K/Fe] in the gas of the solar neighborhood gradually evolved from ∼ +0.1 (∼ 1010 yr ago) to [K/Fe] ∼ 0(∼ 5 × 109 yr ago when the Sun was born) and further
down to ∼ −0.1 (∼ 109 yr ago). In contrast, any clear
age-dependence is hardly observed in the [K/Fe] values of
Kepler giants (cf. Figure 7f), which is presumably becausestars having experienced diversified chemical enrichment
histories are mixed up in this sample.
As mentioned in Section 1, precisely determined [K/Fe]
values for solar analog stars (with various stellar ages from∼ 109 yr to ∼ 1010 yr) determined by Spina et al. (2016)
and Reggiani et al. (2019) (non-LTE reanalysis) did notshow any clear dependence upon age, although most of
their sample stars are in the solar neighborhood. It should
be noted, however, that all those solar twins have almost
the same metallicity as that of the Sun ([Fe/H] ≃ 0), despite that they have diversified ages (i.e., metallicity is
not dependent upon age at all). Accordingly, since thetarget stars used in these two recent studies are rather
specific, their results can not be directly compared withthat of the present investigation based on a large numberof nearby dwarfs showing a rough age–metallicity relation(cf. Figure 2j). As a possibility, it may be that the enrichment of K in the Galaxy significantly depends upon
the local condition (i.e., not necessarily a unique functionof time) and that [K/Fe] is more tightly bound to [Fe/H]
rather than age; this might explain the reason why they
could not detect any age-dependence in their sample solar
analogs of [Fe/H] ≃ 0.
6.

Summary and Conclusion

Our understanding on the galactic chemical evolution ofpotassium is still insuﬃcient, because the observed [K/Fe]
relation can not be well reproduced by theoretical predictions. On the observational side, an embarrassing prob<
lem regarding galactic disk stars (−1 <∼ [Fe/H] ∼ +0.5)
is that the slopes of [K/Fe] vs. [Fe/H] relations derived by several previous studies are diversified and notconsistent with each other, though the qualitative tendency (increasing [K/Fe] with a decrease in [Fe/H]) is thesame. Besides, recent precision abundance analysis on solar twins of widely diﬀerent ages reported that [K/Fe] isnearly constant around ∼ 0 without showing any systematic trend with stellar age, which is hard to understand incontext of expected evolution of [K/Fe] with time.
With an aim to shed light to clarifying these issues,
an extensive determination of potassium abundances was
carried out based on the non-LTE profile-fitting analysisof the K i 7699 line applied to a large sample of 488 stars(160 late F–early K dwarfs, 239 late G–early K nearby gi-

Vol. 2

ants, and 89 late G–early K giants in the Kepler field), all<belonging to the disk population (−1 <∼ [Fe/H] ∼ 0.5), forwhich the spectra are available and the stellar parameters
are already determined (stellar ages are known for FGK
dwarfs and Kepler giants).
The main point of interest was to elucidate the observed
behaviors of [K/Fe] in the galactic disk, where special attention was paid to (i) checking whether these diﬀerent
star groups (especially dwarfs vs. giants) yield consistent
results with each other, (ii) clarifying the d[K/Fe]/d[Fe/H]
gradient to compare with previous studies. and (iii) checking whether [K/Fe] shows any systematic trend with stellar age.
The qualitative trend turned out to be almost the sameirrespective of the star group that [K/Fe] tends to increases with a decrease in [Fe/H]; especially, thick-diskstars of comparatively lower metallicity tend to have supersolar [K/Fe] (> 0). However, quantitative features are
more or less diﬀerent from group to group.
The [K/Fe] vs. [Fe/H] relation of dwarf stars shows atight tendency with small dispersion, and nearby giants
also exhibit an almost similar trend to the case of dwarfs,
though the dispersion is somewhat larger with a slightly
steeper slope and a marginal oﬀset by a few hundredths
dex. The corresponding mean d[K/Fe]/d[Fe/H] gradientfor these two groups turned out rather shallow (∼ −0.1
to −0.15 for dwarfs and around ∼ −0.15 for giants). It
may be concluded from these results that modestly consistent [K/Fe] trends with metallicity were obtained forboth dwarfs and giants as long as those solar neighborhood stars are concerned.
As to the comparison with diversified [K/Fe] vs. [Fe/H]
trends reported so far, the d[K/Fe]/d[Fe/H] gradient (∼−0.1 to −0.15) resulting from this investigation turned
out to be shallower than any of the previous studies.
The [K/Fe] values of Kepler giants are generally enhanced by <∼ 0.1 dex (tending to be supersolar irrespectiveof the metallicity) with a considerable scatter (making thegradient of [K/Fe] with respect to [Fe/H] rather ambiguous). This implies that the chemical evolution history ofthese Kepler giants would have been diﬀerent from thatof solar neighborhood stars. The reason why they show
so diversified [K/Fe] may be due to their widely scatteredlocations.
Regarding the age-dependence of potassium abundance,a marginal trend of increasing [K/Fe] with stellar age isrecognized for dwarfs, while any systematic tendency is
not observed for Kepler giants. The reason why Spina etal. (2016) and Reggiani et al. (2019) could not detect any
dependence upon age in the [K/Fe] values of nearby solar
twins may be due to their specific samples (same metallicity stars of widely diﬀerent ages). It may be possiblethat the galactic chemical evolution of K is not necessarily a monotonic function of time but more significantly
depends upon the local condition, by which [K/Fe] would
be more tightly bound to [Fe/H] rather than age.
This investigation is based in part on the data collected
at Subaru Telescope, which is operated by the National

id. 1

Potassium Abundances of Galactic Disk Stars

Astronomical Observatory of Japan.
This research has made use of the data fromthe European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by theGaia Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium).
Funding for the DPAC has been provided by national
institutions, in particular the institutions participating in
the Gaia Multilateral Agreement.
Appendix. Comparison with Reggiani et et.’s(2019) Non-LTE Calculations

7

and 9b, respectively. We can see from these figuresthat both are in reasonable consistency, though W NLTE(Reggiani) tends to be somewhat lower than W NLTE(Takeda) when the line is very strong (W >∼ 500 mÅ) and∆NLTE (Reggiani) begins to deviate from ∆NLTE (Takeda)
near to ∆NLTE ∼ −1 (around the largest |∆NLTE |).
Accordingly, it can be stated that Takeda et al.’s (2002)
results based on their somewhat outdated calculations(upon which this study is based) are not significantly different from those of Reggiani et al.’s (2019) new non-LTE
calculations using up-to-date atomic data.
References

Takeda et al. (2002; cf. Appendix therein) publishedthe non-LTE equivalent widths and non-LTE corrections
for both the K i 7699 and 7665 lines calculated on an extensive grid of 300 models resulting from combinations offive Teﬀ (4500, 5000, 5500, 6000, 6500), five log g (1.0, 2.0,
3.0, 4.0, 5.0), four [Fe/H] (0, −1, −2, −3), and three vt (1,2, 3) values. The adopted atomic data for the calculations
were the same as used in Takeda et al. (1996). For example, regarding collisions with neutral hydrogen atoms(generally important in non-LTE calculations for late-typestars), the rates computed by the conventionally used classical formula were drastically reduced by multiplying by
an empirically determined factor of k(= 10h ) = 10−3 ; andas to van der Waals damping width (which plays a significant role in calculating profiles or equivalent widths ofstrong lines), the classically evaluated damping constantC6classic (so-called Unsöld approximation) was increased byan empirically established correction of ∆ log C6 = +1.0
(corresponding to multiplying the classical van der waals
damping width Γclassic
by a factor of 2.5); see Takeda et6al. (1996) for more details.
Very recently, Reggiani et al. (2019) conducted new
non-LTE calculations for neutral potassium by using therealistic atomic data achieved by modern physics without invoking any classical formula or empirical corrections. They also published non-LTE equivalent widths
and non-LTE corrections of K i 7699 and 7665 lines computed for a large number of models in the parameter
range of 4000 K ≤ Teﬀ ≤ 8000 K, 0.5 ≤ log g ≤ 5.0,
−5.0 ≤ [Fe/H] ≤ +0.5, and three vt of 1, 2, and 5 km s−1 .
It is interesting to check how Takeda et al.’s (2002) gridsof non-LTE line strengths and abundance corrections arecompared with those Reggiani et al.’s (2019) new calculations. Regarding the input K abundance, Takeda et al.
(2002) adopted [K/Fe] = −0.3, 0.0, +0.3 for [Fe/H] = 0
models, while +0.2, +0.5,+0.8 for metal-poor [Fe/H] (< 0)models. In contrast, Reggiani et al. (2019) varied the Kabundance 11 times as [K/Fe] = −1.25, −1.00, −0.75, · · ·,+1.00, and +1.25) irrespective of [Fe/H]. Therefore, in order to enable a direct comparison at the same set of input
parameters, comparisons are made only on the cases ofK i 7699 line with [Fe/H] = [K/Fe] = 0, vt = 2 km s−1 ,and combinations of (Teﬀ = 4500, 5000, 5500, 6000, 6500)
and (log g = 2, 3, 4, 5).
The mutual comparisons of the non-LTE equivalent
widths and non-LTE corrections are depicted in Figures 9aAndrievsky, S. M., Spite, M., Korotin, S. A., Spite, F.,
Bonifacio, P., Cayrel, R., Françis, P., Hill, V. 2010, A&A,
509, A88
Bruls, J. H. M. J., Rutten, R. J., Schchukina, N. G. 1992,
A&A, 265, 237
Cayrel, R., et al. 2004, A&A, 416, 1117
Chen, Y.-Q., Nissen, P. E., Zhao, G., Zhang, H. W., Benoni,
T. 2000, A&AS, 141, 491
de la Reza, R., Müller, E. 1975, Sol. Phys., 43, 15
Gaia Collaboration et al. 2016, A&A, 595, A1
Gaia Collaboration et al. 2018, A&A, 616, A1
Gratton, R. G., Sneden, C. 1987a, A&A, 178, 179
Gratton, R. G., Sneden, C. 1987b, A&AS, 68, 193
Ibukiyama, A., Arimoto, N. 2002, A&A, 394, 927
Ivanova, D. V., Shimanskiı̆, V. V. 2000, Astron. Rep, 44, 376
Kurucz, R. L. 1993, Kurucz CD-ROM, No. 13 (HarvardSmithsonian Center for Astrophysics)
Prantzos, N., Abia, C., Limongi, M., Chieﬃ, A., Cristallo, S.
2018, MNRAS, 476, 3432
Reggiani, H., et al. 2019, A&A, 627, A177
Roederer, I. U., Preston, G. W., Thompson, I. B., Shectman,
S. A., Sneden, C., Burley, G. S., Kelson, D. D. 2014, AJ,
147, 136
Shimansky, V. V., Bikmaev, I. F., Galeev, A. I., Shimanskaya,
N. N., Ivanova, D. V., Sakhibullin, N. A., Musaev, F. A.,
Galazutdinov, G. A. 2003, Astron. Rep., 47, 750
Spina, L., Meléndez, J., Karakas, A. I., Ramı́rez, I., Monroe,
T. R., Asplund, M., Yong, D. 2016, A&A, 593, A125
Takeda, Y. 1995, PASJ, 47, 287
Takeda, Y. 2007, PASJ, 59, 335
Takeda, Y., et al. 2005a, PASJ, 57, 13
Takeda, Y., Kaneko, H., Matsumoto, N., Oshino, S., Ito, H.,
Shibuya, T. 2009, PASJ, 61, 563
Takeda, Y., Kato, K., Watanabe, Y., Sadakane, K. 1996,
PASJ, 48, 511
Takeda, Y., Ohkubo, M., Sato, B., Kambe, E., Sadakane, K.
2005b, PASJ, 57, 27 [Erratum: PASJ, 57, 415]
Takeda, Y., Sato, B., Murata, D. 2008, PASJ, 60, 781
Takeda, Y., Sato, B., Omiya, M., Harakawa, H. 2015, PASJ,67, 24
Takeda, Y., Tajitsu, A. 2015, MNRAS, 450, 397
Takeda, Y., Tajitsu, A., Sato, B., Liu, Y.-J., Chen, Y.-Q.,
Zhao, G. 2016, MNRAS, 457, 4454
Takeda, Y., Zhao, G., Chen, Y.-Q., Qiu, H.-M., Takada-Hidai,
M. 2002, PASJ, 54, 275
Taylor, J. R. 1997, An Introduction to Error Analysis, The
Study of Uncertainties in Physical Measurements, 2nd ed.
(Herndon, V.A.: University Science Books)
Wang, X. M., Shi, J. R., Zhao, G. 2009, MNRAS, 399, 1264

8

Y. Takeda

Zhang, H. W., Butler, K., Gehren, T., Shi, J. R., Zhao, G.
2006a, A&A, 453, 723
Zhang, H. W., Gehren, T., Butler, K., Shi, J. R., Zhao, G.
2006b, A&A, 457, 645
Zhao, G., et al. 2016, ApJ, 833, 225

Vol. 2

id. 1

Potassium Abundances of Galactic Disk Stars

1

1
(b)
nearby giants

2

-2

2

log g (cm s )-2

log g (cm s )(a)3

FGK dwarfs
Keplergiants

4
5
7000
4

6000
5000
Teff (K)3454000 -1
4

(c)

0.5

4
3
2
-2
log g (cm s )1-1

vt (km s )3-1

vt (km s )-0.5
0[Fe/H] (dex)
(d)

3
2
1

2
1

0
7000
2

6000
5000
Teff (K)

4000

0
5
2

(e)

(f)
1

0

Z (kpc)1
Y (kpc)9

Galactic
Center-1(horizontal projection)

-2
-2

-1

0
X (kpc)

1

0
-1

2

-2
-2

Galactic
Center(vertical projection)-1

0
1
X (kpc)2

Fig. 1. Panels (a)–(d) show the mutual correlations of adopted atmospheric parameters: (a) log g vs. Teﬀ , (b) log g vs. [Fe/H], (c)vt vs. Teﬀ , and (d) vt vs. log g. The lower two panels (e) and (d) are the cross sectional diagrams projected onto the Z = 0 plane(galactic plane passing the Sun) and the Y = 0 plane (plane perpendicular to the galactic plane, passing the Sun and the galactic
center), respectively, which illustrate the locations of the program stars in the Galaxy (Sun at the origin of X = Y = Z = 0). Threegroups of program stars are distinguished by diﬀerent symbols: green circles — 160 FGK dwarfs, blue crosses — 239 nearby giants,
and pink triangles — 89 Kepler giants. The Sun is indicated by the red double circle.

10

Y. Takeda

1.5

1.5

1.5

zmax (kpc)

FGK dwarfs

thick
disk

0.5

|vLSR| (km s-1)
|vLSR| (km s-1)

Kepler giants

11

thin 0.5
disk

0.5

(a)

0

-200 -100 0
VLSR (km s-1)(b)0-200 -100 0
VLSR (km s-1)

300

300

300

200

200

200

100

100

100

0

(d)
-1

-0.5 0[Fe/H]

0.5

0

300

300

200

200

100

100

0

[Fe/H]

nearby giants

1 halo0Vol. 2(g)
9 9.5 10log age (yr)

0

(e)
-1

-0.5 0[Fe/H]

0.5

0

N/A
(h)
9 9.5 10log age (yr)

0

0

0

0

-0.5

-0.5

9 9.5 10log age (yr)-1-0.5 0[Fe/H]

0.5

100

0.5

-1

(f)

200

0.5

(j)

-200 -100 0
VLSR (km s-1)

300

0.5

-1

(c)

N/A

9 9.5 10log age (yr)

9 9.5 10log age (yr)

-0.5
-1

(k)

(i)

(l)
9 9.5 10log age (yr)Fig. 2. In the top (1st) row are shown the correlation diagrams between the maximum separation from the galactic plane(zmax ) and the rotation velocity component relative to LSR (VLSR ), which may be used for classifying the stellar population(the boundaries are indicated by the dashed lines; cf. Ibukiyama & Arimoto 2002). The extents of space velocities relative to222
LSR [|vLSR | ≡ (ULSR+ VLSR+ WLSR)1/2 ] are plotted against [Fe/H] and age in the 2nd and 3rd rows, respectively. The age vs.
metallicity ([Fe/H]) relations are depicted in the bottom (4th) panels. The left, middle, and right panels correspond to FGK dwarfs,
nearby giants, and Kepler giants, respectively. Stars of thin-disk and thick-disk populations are indicated by (blue) filled and(red) open symbols, respectively. Note that, in panel (c), one star (KIC 2714397) of thick-disk population (VLSR = −181 km s−1 ,zmax = 3.17 kpc) is outside of the plot range.

id. 1

Potassium Abundances of Galactic Disk Stars

11

HD
000123

HD039587

HD103095000400000693004307043042043318104304HD
161797163989107213165341

049933004614109358050554004628004813052265052711110897111395165908168009055575114642114710168443005015006582006920007439059984114946061421067228115383115617173667178428179949007476067767117176009562009826069830120136069897070110121370122742

182488010307010476075732010697010700076151076932124570124850185144186408125184

186427010780079028081809127334

187013128167082328131156131511

187691190406013555014214168151
169830181096181655182572015335015798082885082943016141084737133640134987016673016895086728136064087141088737088986137052137108137510207978019994020630089125089744141004142373210277210855021019091752091889142860143761215648095128144585030562095241145675217014217107030743032923098991

149661150706218470219623033636099747101501151769220117153597156826222368017925018803022049022484099491034411035296102634102870038529

0.5

7698

0.5

7699

7698

193664
195019196755197076
199960200790216385224930225239Moon

157214

0.5

7699
7698
Wavelength (Å)

0.5

7699

7698

7699

Fig. 3. Synthetic spectrum fitting for 160 FGK dwarfs/subgiants (and the Sun/Moon) in the region comprising the K i 7699 line.
The best-fit theoretical spectra are shown by blue solid lines, and the observed data are plotted by pink open circles (while thosemasked/disregarded in the fitting are highlighted in green). A vertical oﬀset of 0.5 (in terms of the normalized flux with respect tothe continuum) is applied to each spectrum relative to the adjacent ones. Each of the spectra are arranged in the increasing orderof star number (indicated on the left to each spectrum). The wavelength scale of each spectrum is adjusted to the laboratory frame.

12

Y. Takeda

HD
000087000360000448000587000645001239002114002952003421003546003817003856004188004440004627004732005395005608005722006186007087009057009408009774010348010761010975011037011949012139012339012583013468013692013994014129014770015779015920016400016901017656017824018474018953018970019476019845020618020791022409022675022796026409027348027371027697027971028100028305HD0283070305570308140320080345380345590353690354100360790371600386560390040390190393640415970430390454100454150484320505220510000533290541310548100557300577270583670609860623450625090653450657140711150713690747390749180762190762940768130779120782350794520804990822100827410835060844410854440911900916120921250932910988390996481006151006961009201014841049791049850.57698 7699

Vol. 2

HD
106057106714
107383107950108225109317109379113226115659119126120420125454
127243129312129336129972130952133208133392134190136512138716138905139641141680142091142198144608145001
146791147677147700148387148786150030150997152815154084156874156891
158974
159181159353
162076163532
163917165760168656168723170474171391
174980176598177241
177249180540180711
181276
182694
1827620.5

HD183491
184010185194185351
185758185958186675
188310188650188947189127
192787
192944
192947
194013
194577
1996652000392013812032222033872043812047712054352064532093962103542104342107022108072113912114342115542122712123202124302124962137892139302139862145672148782150302153732157212159432161312172642177032185272191392196152199452213452220932223872225742232522245330.57698 7699
7698 7699
Wavelength (Å)

0.5

7698 7699

Fig. 4. Synthetic spectrum fitting for 239 nearby red giants. Otherwise, the same as in Figure 3.

id. 1

Potassium Abundances of Galactic Disk Stars

KIC
01726211

KIC
04770846

KIC
07799349

02013502

04902641

08378462

02303367

04952717

08475025

02424934

0500030708493735

02448225

05033245

08702606

02573092

05088362

08718745

02696732

0512817108751420

02714397

05266416

09145955

02988638

05283798

09173371

03098045

05307747

09349632

03217051

05514974

09583430

03323943

05530598

09812421

03425476

05598645

10382615

03455760

05611192

10474071

03531478

05723165

10600926

03730953

05737655

10604460

03744043

05806522

10709799

03758458

05858034

10866415

04036007

05866737

11177749

04039306

05990753

04044238

06117517

11352756

04056266

06144777

11401156

04243623

06276948

1161810304243796

06531928

1171712004350501

06579495

11721438

04351319

06665058

11802968

04445711

07205067

11819760

04448777

07581399

12008680

0457012007584122

12070114

04726049

07734065

0.57698 7699

0.57698 7699
Wavelength (Å)

11251115

0.57698 7699

Fig. 5. Synthetic spectrum fitting for 89 giants in the Kepler field. Otherwise, the same as in Figure 3.

13

14

Y. Takeda

400

400

(a)

200
100

6000
5000
Teff (K)

1

4
3
2
-2
log g (cm s )

1

-0.2

-0.4

-0.4

-0.6

-0.6

-0.8

-0.8

7000

6000
5000
Teff (K)

4000

5
2.8

(e)

2.6
log W (mÅ)

-0.2
-0.4
-0.6

(f)

2.4
2.2
2

-0.8
0

4
3
2
-2
log g (cm s )

0 (d)

(c)
∆ (dex)∆ (dex)

0
5

4000

-0.2

∆ (dex)

200
100

filled circles: FGK dwarfs
crosses: nearby giants
open triangles: Kepler giants

0
7000

0

(b)

300
W (mÅ)W (mÅ)

300

0Vol. 2

100

200 300
W (mÅ)

400

1.8
A

8

NLTE

9
10
+ (χion - χexc) 5040/Teff

Fig. 6. Equivalent widths (W ) of the K i 7699 line are plotted against Teﬀ and log g in panels (a) and (b), while the dependencesof non-LTE corrections (∆) upon Teﬀ , log g, and W are shown in panels (c), (d), and (e), respectively. In panel (f) are plotted thelog W values against ANLTE + (χion − χexc )5040/Teﬀ (abscissa of curve of growth), where ANLTE is the non-LTE abundance derived
for each star and χion /χexc is the ionization/excitation potential (in eV). The same meanings of the symbols as in Figure 1.

id. 1

Potassium Abundances of Galactic Disk Stars

1[K/Fe]

0.5

1(a)

HD 50554

0

0.5

1
(b)

-0.5

-0.5

∆

nearby giants

Kepler giants

0

0

0

-0.5

-0.5

-0.5

-1

-1

-0.5 0[Fe/H]

1[K/Fe]

0.5

0.5

0

-0.5

-1

0
FGK dwarfs

-0.5

0

0

-0.5

-0.5

-1

-1

-0.5 0[Fe/H]

1(d)

9 9.5 10log age (yr)(c)

0FGK dwafs

∆

0.5

0

-0.5

15

-1

-1

-1

-0.5 0[Fe/H]

1
(e)

0.5
N/A
nearby giants

(f)

0
-0.5

Kepler giants

0
N/A
9 9.5 10log age (yr)

-0.5
-1

9 9.5 10log age (yr)Fig. 7. The values of [K/Fe] (non-LTE K-to-Fe abundance ratio) and ∆ (non-LTE correction) derived for each star are plottedagainst [Fe/H] (upper panels) and log age (lower panels), respectively. As in Figure 2, the left, middle, and right panels correspondto FGK dwarfs, nearby giants, and Kepler giants, respectively. Likewise, the same meanings of the symbols hold as in Figure 2.

16

Y. Takeda<[K/Fe]>, δ[K/Fe]

0.2

Vol. 2(a)open symbols: nearby giants

0.1
0
-0.1

filled symbols FGK dwarfs

-0.2
-0.6

<[K/Fe]>, δ[K/Fe]

0.2

-0.4

-0.2
0
[Fe/H]

open symbols: Kepler giants

0.2

(b)

0.1
0
-0.1
filled symbols FGK dwarfs

-0.2
-0.6

-0.4

-0.2
0
[Fe/H]

0.2

Fig. 8. The mean ⟨[K/Fe]⟩ values calculated at each metallicity group (0.1 dex bin within −0.5 ≤ [Fe/H] ≤ +0.2) are illustrated bysymbols (attached error bars denote standard deviations), where filled and open circles correspond to dwarfs and giants, respectively.
The bar graphs represent the giants−dwarfs diﬀerences (⟨[K/Fe]⟩giants − ⟨[K/Fe]⟩dwarfs ). The upper panel (a) shows the comparisonof nearby giants vs. FGK dwarfs while the lower panel (b) is for Kepler giants vs. FGK dwarfs. The linear regression lines determinedfrom these ⟨[K/Fe]⟩ values (cf. Section 5.2) are also drawn by solid, dashed, and dotted lines for FGK dwarfs, nearby giants, andKepler giants, respectively.

id. 1

Potassium Abundances of Galactic Disk Stars

1000(Reggiani)

400

W

600

NLTE

800

Teff = 4500, 5000, 5500, 6000, 6500 K
log g = 2, 3, 4, 5
[K/Fe] = [Fe/H] = 0.0
vt = 2 km s-1

200
(a)
0
0

200

400
600
800
NLTE
W
(Takeda)

1000

0

-0.5

∆

NLTE

(Reggiani)

0.5

-1

-1.5
-1.5

(b)
-1

-0.5
∆

NLTE

0

0.5

(Takeda)Fig. 9. Comparison of the non-LTE equivalent widths (W NLTE : upper panel) and non-LTE corrections (∆NLTE : lower panel). In
the ordinate are the values taken from Reggiani et al.’s (2019) non-LTE grid computed for the K i 7698.974 line by using the recent
up-to-date atomic data, while those published by Takeda et al. (2002) are in the abscissa. Shown here are the cases of [K/Fe] =[Fe/H] = 0 and vt = 2 km s−1 with the combinations of (Teﬀ = 4500, 5000, 5500, 6000, 6500 K) and (log g = 2, 3, 4, and 5), forwhich direct comparisons are possible.

17