Fluorine Abundances in the Galactic Disk

No useful atomic fluorine lines are available in the visible region of the spectrum, and detectable atomic F i lines lie in the far-UV at λ ∼ 950 Å. However, in cool stars, fluorine abundances can be derived using the HF molecule, which has transitions in the infrared that provide detectable lines from its fundamental vibrational mode.

In order to study the HF rotational-vibrational transitions near 2.358 μm in the spectra of red giants, high-resolution spectra were obtained with combinations of spectrographs and telescopes; some instrumental setups allowed only for the observation of the HF (1−0) R9 line, while in others secondary HF lines could be observed. The observed red giants and corresponding spectrograph/telescope combinations used are listed in Table 1.

Observations with the NOAO Phoenix Spectrograph (Hinkle et al. 2003) were obtained on two different telescopes: the Kitt Peak National Observatory (KPNO) 2.1 m and the Gemini South 8.1 m Telescope. In addition, the 3.0 m NASA Infrared Telescope Facility (IRTF) was used with the iSHELL spectrograph (Rayner et al. 2016). The spectra obtained with iSHELL on the IRTF were geared toward observations of low-metallicity stars based on SDSS/APOGEE (Majewski et al. 2017) DR14 stellar parameters, while the Phoenix observations were aimed primarily at red giants having intermediate metallicities, as determined from Washington photometry in the GGSS (Kundu et al. 2002).

The Phoenix spectra were centered at ∼23360 Å and have a resolution R ≡ λ/Δλ = 50,000. The Phoenix spectra have a limited spectral coverage of ∼100 Å; although small, the selected region contains molecular lines of CO, the HF (1−0) R9 transition, and, in particular for the Gemini-S spectra, an isolated atomic Fe i line at 23308.477 Å that can (in the absence of spectra with larger spectral coverage) be used to estimate the stellar metallicity. It should be noted, however, that the Phoenix spectra obtained with the KPNO 2.1 m have a slightly different wavelength coverage (from 23315 to 23430 Å) and do not contain the Fe i line. The reduction of all the obtained Phoenix spectra to one dimension followed standard procedures; see the discussion in Cunha et al. (2003).

The iSHELL spectra analyzed here have higher resolution than the Phoenix spectra (R ≡ λ/Δλ = 75,000) and much larger spectral coverage, between ∼22850 and 23750 Å. The available Spextool v5.0.2 (SPectral EXtraction TOOL; Cushing et al. 2004) was used to perform the reduction of the iSHELL spectra to one dimension. The reduction steps include the following: normalized flat-field images and wavelength calibration files were created; a nonlinearity correction was applied to the raw data and flat fields; aperture positions were identified and extracted; the raw data were divided by the flat fields; telluric corrections and flux calibrations were performed on combined multiorder spectra; telluric-corrected spectra were merged into a single continuous spectrum for each star; and finally, the continuous spectra were corrected by removing bad pixels.

In addition to the Phoenix and iSHELL spectra, we collected IR spectra from the Fourier Transform Spectrometer (FTS) archive (Pilachowski et al. 2017;  https://sparc.sca.iu.edu), for a sample of disk red giants observed with the FTS on the KPNO 4 m telescope (Hall et al. 1979). The FTS spectra analyzed have R ≡ λ/Δλ = 45,000 and cover the spectral region between 19500 and 24000 Å. Most of the selected FTS targets are bright, nearby red giants analyzed previously for chemical abundances by Smith & Lambert (1985, 1986, 1990) and Jorissen et al. (1992). We also analyzed the higher-resolution (R = 100,000) FTS spectrum obtained with the 4 m telescope of the "standard" red giant Arcturus (Hinkle et al. 1995; ftp://ftp.noao.edu/catalogs/arcturusatlas/ir/). All spectral data sets included observations of hot standard stars observed on the same nights (except for two stars with observations from the FTS archive) whenever possible over a range of air masses. These were used to map the telluric lines in this spectral region (consisting of a mixture of CH₄ and H₂O lines), which were then removed by dividing the program stars by the hot star, taking into account air-mass differences. The task "telluric" within the software package IRAF was used, except for the iSHELL spectra, where telluric division was included as part of the reduction pipeline. In addition, all stellar and telluric spectra were inspected visually in the regions of the HF lines to ascertain the significance of telluric contamination to each line.

Figure 1 shows sample reduced spectra for each one of the three different infrared spectrographs used in the observations: FTS (top panel), Phoenix (middle panel), and IRTF (bottom panel). The spectra are shown in the region between ∼23300 and 23400 Å, most of which is available for all targets.

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Four of our target stars (HD 19697, HD 20305, HD 28085, and HD 90862) were also observed with the high-resolution optical Sandiford Cassegrain Echelle Spectrometer (SES) on the 2.1 m Struve Telescope at McDonald Observatory; the SES spectra analyzed have a resolution R = 60,000 and cover wavelength range between 6030 and 7980 Å. The optical spectra of these four targets were used to derive the metallicities for the stars given that their Phoenix spectra (obtained on the KPNO 2.1 m telescope) had limited wavelength coverage, not reaching the Fe i line at 23308.477 Å. The reduction of the SES spectra to one dimension (described in Bizyaev et al. 2006) used the IRAF package and standard steps for bias subtraction, division by flat-field, scattered light subtraction, as well as wavelength calibration using a Th–Ar lamp.

The optical spectrum of the "standard" red giant Arcturus (Hinkle et al. 2000) was also analyzed here with the goal of comparing the metallicity scales obtained from the analysis of the optical and infrared spectra and evaluating possible systematic offsets between the derived metallicities. The results from this comparison will be presented in Section 5.

The effective temperatures for the studied stars were obtained from a photometric calibration, from optical lines of Fe i, or from the H-band APOGEE spectra, depending on the availability of spectra, reliability of photometric magnitudes, and degree of extinction.

For those target stars not having optical or APOGEE spectra, we derived photometric T_eff values from the V − K colors (Table 1), using the calibration in Bessell et al. (1998) (T_eff = 9102.523–3030.654(V − K) + 633.3732(V − K)² − 60.73879(V − K)³ + 2.135847(V − K)⁴). For two stars in the sample (2MASS 06232713−3342412 and 2MASS 07313775−2818395) V magnitudes were not available and we used the 2MASS J − K magnitudes, transformations from Carpenter (2001), and the same calibration (Bessell et al. 1998) to estimate the effective temperatures. For the nearby stars in our sample interstellar extinction was not considered; for stars with distances larger than 150 pc and less than 1 kpc, we determined A_V using the Chen et al. (1998a) extinction law with the reddening correction E(B − V) and extinction A_K determined using R_V = 3.070 and R_K = 0.342 from McCall (2004). For more distant stars (having distances larger than ∼1 kpc; Table 1), we relied on Green et al. (2018), who provide E(B − V) using 3D Dust Mapping with Pan-STARRS 1 and Two Micron All Sky Survey (2MASS) data.

For the target stars taken from the SDSS IV—APOGEE survey (observed with the iSHELL spectrograph), we adopted the APOGEE DR14 calibrated effective temperatures derived from the APOGEE spectra automatically by the ASPCAP pipeline (García Pérez et al. 2016). ASPCAP derives stellar parameters and metallicities from synthetic spectra and global 7D fits to the APOGEE spectra via χ-squared minimization.

The effective temperatures for those stars having SES spectra (HD 19697, HD 20305, HD 28085, and HD 90862; Table 1) were determined using a sample of Fe i lines between 6050 and 6860 Å and their measured equivalent widths. The methodology adopted in the determination of the stellar parameters derives at the same time the stellar metallicities and will be discussed in Section 4.2.

The surface gravities for the stars were derived using the PARAM 1.3 code (http://stev.oapd.inaf.it/cgi-bin/param_1.3) with parallaxes, V magnitudes (Table 1), effective temperatures, initial values for the metallicities as inputs (Table 2), and the PARSEC isochrones from Bressan et al. (2012) for scaled-solar composition, with the Y = 0.2485+1.78Z relation and Z_⊙ = 0.0152. The PARAM 1.3 code is a web interface for the Bayesian estimation of stellar parameters (see Rodrigues et al. 2014 and da Silva et al. 2006). The parallaxes for the stars were taken from Gaia DR2. In a few cases, however, parallaxes were not available in Gaia DR2, and Hipparcos parallaxes (van Leeuwen 2007) were used instead (distances for those stars with parallaxes only in Hipparcos were determined by simply the inverse of the parallax).

For those targets with results available in APOGEE DR14, we can compare our derived log g values obtained using the PARAM 1.3 code, with those obtained by the APOGEE team using APOGEE spectra and the APOGEE stellar parameter abundance pipeline (ASPCAP; García Pérez et al. 2016). It should be noted, however, that the ASPCAP surface gravities for red giants have systematic offsets. These are, however, well calibrated using log values from seismic studies; the APOGEE team also releases calibrated values of log g (see the discussion in Holtzman et al. 2018). The mean difference between the log g values adopted in this study (from PARAM 1.3) and the calibrated log g values from APOGEE DR14 is $\langle \delta \,\mathrm{log}\,g\rangle$ = −0.01 ± 0.11.

Synthetic spectra were calculated in local thermal equilibrium (LTE) with the code Turbospectrum (TS; Alvarez & Plez 1998; Plez 2012), noting that TS is compatible with the adopted spherical model atmospheres given its spherical radiative transfer treatment. Best fits between synthetic and observed spectra were obtained, and the synthetic spectra were manipulated using the plotting and broadening routines from the MOOG code (Sneden 1973). The model spectra were broadened by convolution with a Gaussian profile, which represents the combination of the instrumental profile, macroturbulent velocity, and projected rotational velocity (v sin i; it is expected that the v sin i values for red giants should be small).

4.1.1. Fluorine Abundances

Fluorine abundances were derived from a sample of up to five vibrational–rotational HF (1−0) transitions: R9, R13, R14, R15, and R16, depending on the spectral coverage for each target star. Table 3 presents the HF lines used in the abundance analyses, along with the excitation potential (χ; from Jönsson et al. 2014b and Decin 2000), log gf (from Jönsson et al. 2014b), and dissociation energy (D_◦ = 5.869 eV; from Sauval & Tatum 1984) of the transitions. We note that there remains some uncertainty in the value of D_◦ for HF, as Luo (2007) has reported a value of D_◦ = 573.398 ± 0.011 kJ mol⁻¹, or 5.943 eV mol⁻¹. This difference of 0.074 eV would lead to a slightly lower absolute F abundance of ∼0.04 dex for a typical red giant from this sample. To our knowledge no non-LTE calculations have been made for the HF transitions for stellar atmosphere conditions. However, vibrational–rotational transitions in molecules in the ground electronic state should, in general, be in LTE (Hinkle & Lambert 1975). Sample synthetic profiles and best-fit syntheses for the studied HF lines are presented in Figure 3.

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Table 3.  Infrared Fluorine and Iron Lines

Species/	λair		χ		Γ6	D◦
Molecule	(Å)	Line ID	(eV)	log gf		(eV)
H19F	23358.329	(1–0)R9	0.227 (a), (b)	−3.962(a)	⋯	5.869 (c)
	22957.938	(1–0)R13	0.455 (a)	−3.941(a)	⋯	5.869 (c)
	22886.733	(1–0)R14	0.524 (a)	−3.947(a)	⋯	5.869 (c)
	22826.862	(1–0)R15	0.597 (a)	−3.956(a)	⋯	5.869 (c)
	22778.249	(1–0)R16	0.674 (a)	−3.969(a)	⋯	5.869 (c)
Fe i	19923.343	⋯	5.020	−1.530	−7.16	⋯
	20349.718	⋯	4.186	−2.625	−7.54	⋯
	20840.808	⋯	6.027	0.075	−6.94	⋯
	20991.042	⋯	4.143	−3.150	−7.73	⋯
	21238.467	⋯	4.956	−1.300	−7.00	⋯
	21284.344	⋯	5.669	−3.320	−7.87	⋯
	21284.348	⋯	3.071	−4.470	−7.27	⋯
	21735.462	⋯	6.175	−0.700	−6.87	⋯
	22257.107	⋯	5.064	−0.745	−7.00	⋯
	22260.180	⋯	5.086	−0.941	−7.54	⋯
	22380.797	⋯	5.033	−0.600	−6.99	⋯
	22385.102	⋯	5.320	−1.550	−7.00	⋯
	22392.879	⋯	5.100	−1.270	−7.10	⋯
	22419.982	⋯	6.218	−0.234	−6.85	⋯
	22419.990	⋯	6.283	−4.568	−8.10	⋯
	22473.268	⋯	6.119	0.381	−6.88	⋯
	23308.477	⋯	4.076	−2.645	−7.18	⋯
	23566.666	⋯	6.144	0.197	−7.09	⋯
	23683.741	⋯	5.305	−1.152	−7.50	⋯

Note. (a) Jönsson et al. (2014a); (b) Decin (2010); (c) Sauval & Tatum (1984).

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4.1.2. Iron Abundances

Iron abundances were determined using a sample of 19 Fe i lines in the wavelength range between ∼19900 and 23700 Å, with Fe i lines in the full wavelength range used for the stars observed with iSHELL. Table 3 presents the Fe i line list selected for the abundance analysis and the relevant atomic data. The log gf values of these Fe i transitions were determined astrophysically, using the solar spectrum as a reference. The solar spectrum analyzed was the very high resolution (R = 40,000) center-of-disk intensity spectrum obtained from http://www.eso.org/sci/facilities/paranal/decommissioned/isaac/tools/spectroscopic_standards.html. A canonical solar MARCS model atmosphere with T_eff = 5770 K, log g = 4.44, and ξ = 1.0 km s⁻¹ was adopted in the calculations, and solar gf values were obtained assuming a solar abundance of A(Fe) = 7.45 (Asplund et al. 2005).

In addition to the astrophysical gf values, the van der Waals damping constants, Γ₆, were adjusted using both the TS code (consistent with the abundance analysis in this study) and the MOOG code. The reason behind using two codes for the calculations of LTE synthetic spectra was to evaluate possible differences in the solar syntheses, given that the current version of TS does not consider Stark broadening in the computation of synthetic spectra. The gf values derived using the two codes were similar, with mean differences in the log gf values of $\langle {\rm{\Delta }}(\mathrm{log}\,{gf})\rangle$ = −0.02 ± 0.07. Most of the studied Fe i transitions have log gf values larger than −1.5 dex. As shown in Figure 4, our solar log gf values are in good agreement with another set of solar gf values obtained independently by Thorsbro (2016) using the LTE synthesis code Spectroscopy Made Easy (SME; Valenti & Piskunov 1996): the mean difference "This Work—Throsbro" $\langle \delta (\mathrm{log}\,{gf})\rangle$ = −0.05 ± 0.06, with rms = 0.08. The agreement with the values found in the Kurucz (1994) line list is also good, in particular for the stronger lines, while some of the weaker lines show larger discrepancies.

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The individual Fe i line abundances obtained in this study are presented in Table 4. Given the nonhomogeneous set of observed spectra in this study, the number of Fe i lines analyzed to obtain the stellar metallicities was varied and depended on the spectral coverage available in each case. For a few stars only one Fe i line at 23308 Å could be measured, and we verified that the Fe abundances from this Fe i line in particular were not systematically offset when compared to the abundances from the other Fe i lines.

Table 4.  Individual Fe i Line Abundances from Infrared Spectra

Star	A(Fe)	A(Fe)	A(Fe)	A(Fe)	A(Fe)	A(Fe)	A(Fe)	A(Fe)	A(Fe)	A(Fe)	A(Fe)	A(Fe)	A(Fe)	A(Fe)	A(Fe)	A(Fe)	A(Fe)
	λ1	λ2	λ3	λ4	λ5	λ6	λ7	λ8	λ9	λ10	λ11	λ12	λ13	λ14	λ15	λ16	λ17
Arcturus	6.97	6.93	6.91	7.00	6.92	6.82	6.92	6.84	6.94	6.86	7.01	6.88	6.95	6.82	7.02	⋯	⋯
10 Dra	⋯	⋯	⋯	7.37	⋯	⋯	7.42	⋯	⋯	7.37	⋯	⋯	7.48	7.34	7.34	⋯	⋯
41 Com	⋯	⋯	⋯	7.42	⋯	7.38	7.43	7.28	⋯	7.32	⋯	7.32	7.43	7.44	7.27	⋯	⋯
β And	7.48	⋯	7.38	⋯	7.37	⋯	7.44	⋯	7.37	7.34	7.35	⋯	⋯	7.34	7.39	⋯	⋯
β Peg	⋯	⋯	⋯	7.27	⋯	⋯	⋯	7.03	⋯	7.14	7.23	⋯	7.18	7.28	7.17	⋯	⋯
β UMi	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	7.42	⋯	7.37	7.48	7.34	7.45	⋯	⋯
γ Dra	7.40	⋯	7.40	7.49	7.36	7.35	⋯	7.33	7.35	7.32	⋯	⋯	⋯	7.34	7.43	⋯	⋯
μ Leo	7.75	⋯	⋯	⋯	⋯	7.65	⋯	7.58	⋯	⋯	⋯	⋯	7.83	⋯	7.94	⋯	⋯
ω Vir	⋯	7.46	⋯	7.54	⋯	⋯	7.45	7.35	⋯	7.44	⋯	⋯	7.50	7.48	7.34	⋯	⋯
BD +06◦2063	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	7.28	7.32	⋯	7.22	⋯	7.39	7.49	⋯	⋯
BD +16◦3426	⋯	⋯	⋯	7.49	⋯	⋯	7.48	7.31	⋯	⋯	⋯	⋯	7.56	7.44	7.34	⋯	⋯
HD 96360	⋯	7.31	⋯	⋯	7.36	⋯	⋯	⋯	⋯	7.27	⋯	7.22	7.50	7.29	7.27	⋯	⋯
HD 189581	⋯	⋯	⋯	7.17	7.06	⋯	⋯	7.13	7.15	⋯	⋯	⋯	⋯	7.27	6.94	⋯	⋯
TYC 5880-423-1	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	6.64	⋯	⋯
UCAC2 22625431	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	6.82	⋯	⋯
2MASS 06232713−3342412	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	6.98	⋯	⋯
2MASS 07313775−2818395	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	7.02	⋯	⋯
2MASS 01051470+4958078	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	6.42	6.39	6.47
2MASS 02431985+5227501	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	6.59	⋯	⋯
2MASS 04224371+1729196	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	6.61	6.67	⋯
2MASS 20410375+0001223	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	6.56	⋯	6.66
2MASS 22341156+4425220	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	6.23	6.19

Note. Iron lines: λ₁ = 19923 Å, λ₂ = 20349 Å, λ₃ = 20840 Å, λ₄ = 20991 Å, λ₅ = 21238 Å, λ₆ = 21284 Å, λ₇ = 21735 Å, λ₈ = 22257 Å, λ₉ = 22260 Å, λ₁₀ = 22380 Å, λ₁₁ = 22385 Å, λ₁₂ = 22392 Å, λ₁₃ = 22419 Å, λ₁₄ = 22473 Å, λ₁₅ = 23308 Å, λ₁₆ = 23566 Å, and λ₁₇ = 23683 Å.

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4.2.1. Iron Abundances

For the four stars in this sample with infrared spectra not having spectral coverage that includes any Fe i lines, their iron abundances were derived from measured equivalent widths of optical Fe i lines using the same LTE code TS. Fe i lines in the spectral region covered by the SES spectra were selected from the master line list presented in the recent study by Ghezzi et al. (2018); the gf values in that study are solar gf values obtained for an assumed solar reference abundance A(Fe)_Sun = 7.50 (Asplund et al. 2009). The selected line list containing 53 Fe i lines and the atomic data adopted are presented in Table 5.

Table 5.  Optical Iron Lines and Equivalent Widths

λair	χ			HD 19697		HD 20305		HD 28085		HD 90862
( Å)	(eV)	log gf	Γ6	EW (mÅ)	A(Fe)	EW (mÅ)	A(Fe)	EW (mÅ)	A(Fe)	EW (mÅ)	A(Fe)
6056.005	4.73	−0.556	−7.130	78.2	7.07	92.2	7.11	102.0	7.45	85.3	6.92
6078.491	4.80	−0.292	−7.410	77.0	6.88	94.6	7.00	106.0	7.37	91.2	6.87
6079.009	4.65	−1.064	−7.177	52.6	6.98	68.7	7.10	73.6	7.37	50.7	6.71
6082.710	2.22	−3.622	−7.654	118.0	7.36	117.0	7.18	96.6	7.36	127.0	7.20
6093.642	4.61	−1.402	−7.202	41.2	7.02	45.8	6.97	58.3	7.40	41.1	6.81
6096.664	3.98	−1.861	−7.152	60.8	6.98	61.4	6.85	70.1	7.32	61.6	6.75
6098.243	4.56	−1.825	−7.238	39.5	7.34	38.3	7.19	38.7	7.44	37.3	7.13
6127.906	4.14	−1.503	−7.790	74.5	7.09	83.9	7.08	91.4	7.49	66.9	6.70
6136.993	2.20	−3.037	−7.691	144.0	7.19	150.0	7.12	143.0	7.65	162.0	7.06
6151.618	2.18	−3.357	−7.696	129.0	7.19	130.0	7.06	111.0	7.27	137.0	6.95
6157.728	4.08	−1.257	−7.790	109.0	7.45	32.7	7.23	120.0	7.75	114.0	7.23
6159.378	4.61	−1.910	−7.216	⋯	⋯	⋯	⋯	34.3	7.50	44.8	7.39
6165.360	4.14	−1.487	−7.780	69.1	6.97	77.1	6.95	80.1	7.28	75.8	6.83
6173.336	2.22	−2.938	−7.690	147.0	7.16	152.0	7.07	137.0	7.48	158.0	6.92
6187.990	3.94	−1.724	−7.179	86.6	7.26	83.7	7.03	82.2	7.32	81.1	6.88
6200.312	2.61	−2.457	−7.589	121.0	6.78	140.0	6.99	134.0	7.45	142.0	6.82
6213.429	2.22	−2.650	−7.691	160.0	7.05	171.0	7.01	157.0	7.50	180.0	6.87
6219.280	2.20	−2.549	−7.694	178.0	7.11	187.0	7.03	166.0	7.49	199.0	6.93
6220.779	3.88	−2.390	−7.208	63.7	7.41	61.5	7.24	45.8	7.34	33.7	6.64
6226.734	3.88	−2.143	−7.208	76.4	7.40	62.8	7.02	66.5	7.42	58.3	6.83
6232.640	3.65	−1.232	−7.540	112.0	6.88	126.0	6.94	129.0	7.38	122.0	6.75
6240.646	2.22	−3.337	−7.661	132.0	7.52	115.0	6.83	108.0	7.29	140.0	7.14
6265.132	2.18	−2.633	−7.700	190.0	7.25	186.0	7.06	171.0	7.58	202.0	6.99
6335.329	2.20	−2.423	−7.698	189.0	7.04	⋯	⋯	165.	7.30	199.	6.77
6380.743	4.19	−1.312	−7.790	84.0	7.14	86.6	7.00	89.7	7.31	90.2	6.98
6385.718	4.73	−1.887	−7.187	18.8	7.11	20.6	7.08	29.2	7.51	19.7	6.99
6392.537	2.28	−4.007	−7.643	79.2	6.91	78.5	6.86	62.2	7.27	84.2	6.74
6574.226	0.99	−5.019	−7.830	157.0	7.74	144.0	7.20	104.0	7.26	164.0	7.20
6591.312	4.59	−2.065	−7.697	35.7	7.54	25.6	7.20	28.4	7.50	26.1	7.13
6593.871	2.43	−2.469	−7.629	154.0	7.13	174.0	7.11	⋯	⋯	174.	6.91
6597.561	4.80	−0.984	−7.190	57.1	7.18	54.3	6.95	72.2	7.41	57.9	6.96
6608.025	2.28	−4.017	−7.648	85.4	7.01	88.0	7.00	66.9	7.33	91.6	6.85
6609.110	2.56	−2.708	−7.610	136.0	7.28	143.0	7.13	144.	7.71	149.	6.99
6627.543	4.55	−1.542	−7.250	43.5	7.11	50.2	7.10	61.6	7.49	54.3	7.09
6646.930	2.61	−3.988	−7.604	66.5	7.16	61.9	7.05	55.5	7.54	71.2	7.00
6653.851	4.15	−2.475	−7.153	32.7	7.25	23.9	6.98	28.2	7.39	30.6	7.03
6699.141	4.59	−2.167	−7.667	31.8	7.55	22.3	7.22	23.3	7.48	20.8	7.10
6703.565	2.76	−3.078	−7.633	101.0	7.14	105.0	7.08	94.1	7.38	109.0	6.97
6710.318	1.49	−4.876	−7.733	108.0	7.12	106.0	7.01	87.6	7.49	120.0	7.04
6713.742	4.80	−1.485	−7.207	38.4	7.29	29.0	6.96	41.6	7.39	34.3	7.01
6725.355	4.10	−2.257	−7.181	28.0	6.85	40.1	7.02	42.9	7.38	35.4	6.84
6726.666	4.61	−1.062	−7.500	56.9	6.98	67.6	7.00	71.9	7.24	58.5	6.77
6732.064	4.58	−2.208	−7.700	40.5	7.77	⋯	⋯	25.0	7.55	25.9	7.26
6733.151	4.64	−1.490	−7.247	49.4	7.31	44.6	7.07	58.6	7.50	47.6	7.05
6739.520	1.56	−4.955	−7.726	97.5	7.08	85.0	6.84	57.5	7.24	90.5	6.68
6745.100	4.58	−2.164	−7.726	29.5	7.47	16.9	7.04	19.7	7.37	17.7	6.99
6745.955	4.08	−2.709	−7.820	19.8	7.05	15.1	6.85	18.0	7.28	13.4	6.69
6750.151	2.42	−2.672	−7.609	153.0	7.42	158.0	7.13	154.	7.67	165.	7.00
6806.842	2.73	−3.153	−7.643	106.0	7.28	101.0	7.02	95.4	7.35	111.	7.02
6839.830	2.60	−3.433	−7.617	95.5	7.11	102.0	7.13	86.6	7.41	106.	7.00
6842.685	4.64	−1.245	−7.189	58.8	7.24	65.7	7.18	67.9	7.39	52.6	6.89
6857.249	4.08	−2.125	−7.820	49.1	7.13	46.9	6.97	⋯	⋯	50.0	6.93

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The equivalent widths for the Fe i lines were measured with the IRAF splot package (Tody 1993) and assuming Gaussian profiles. Equivalent widths for a subset of the sample Fe i lines had been previously measured by V. Smith. A comparison of the equivalent width measured by these two coauthors is shown in Figure 5; the agreement is good without obvious offsets. The average of the differences between the equivalent width measurements in this study and those measured by V. Smith is 0.6 ± 3 mÅ with rms = 3.4 mÅ.

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The adopted methodology for analyzing the optical spectra derives, simultaneously, the effective temperature, the mean iron abundance, and the microturbulent velocity for each star. The effective temperature is defined when reaching an absence of trend (zero slope) in the diagram of the excitation potential (χ) of the Fe i lines versus their individual iron abundances, while the microturbulent velocity parameter is defined from the requirement of finding zero slope in the equivalent width versus iron abundance diagram. The log g values were derived with the code PARAM 1.3. Each calculation was started with an estimated log g value for the star and iterated until the results for the effective temperature, metallicity, microturbulent velocity, and log g (obtained with the code PARAM 1.3; Section 3.2) were all consistent. Figure 6 shows an example of the solution obtained for the star HD 20305: the top panel of the figure displays the effective temperature diagram and the bottom panel the microturbulent velocity diagram.

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Uncertainties in the derived abundances can be estimated from the sensitivities of the Fe i and HF measured abundances to changes in the stellar parameters corresponding to typical errors in T_eff (±100 K), log g (±0.25 dex), metallicity (±0.1 dex), and microturbulent velocity (±0.3 km s⁻¹). Table 6 has the estimated uncertainties, ΔA (the square root of the sum in quadrature of the corresponding abundance changes δT_eff, δlog g, δ[Fe/H], and δξ), for baseline model atmospheres representative of the studied sample: one more metal-rich (T_eff = 3917 K, log g = 1.30, [Fe/H] = −0.08 dex, ξ = 1.75 km s⁻¹) and another more metal-poor (T_eff = 3725 K, log g = 0.30, [Fe/H] = −1.10 dex, ξ = 1.70 km s⁻¹). We also present the sensitivity of the optical Fe i lines for a baseline model with T_eff = 4075 K, log g = 1.45, [Fe/H] = −0.40 dex, ξ = 1.67 km s⁻¹. As discussed in Guerço et al. (2019), errors in the effective temperatures account for most of the uncertainties in the fluorine abundances. In addition, we estimate an uncertainty of 0.05 dex (or in many cases less) for the abundance uncertainty due to uncertainties in placement of the continuum. While the fluorine abundances are most sensitive to T_eff, the derived iron abundances show more sensitivity to log g and ξ. The standard deviations of the mean derived fluorine and iron abundances (corresponding to line-to-line abundance scatter) are presented in Table 2; these are typically less than 0.1 dex.

While Section 2 pointed out that HF is best studied in the cooler red giants (T_eff ≤ 4000 K), due to the rapidly decreasing HF line strength with increasing temperatures, the task of finding suitably cool red giants at low metallicity is a challenge, due to the shift in the RGB toward higher T_eff, at a given luminosity, with decreasing metallicity. Nonetheless, the abundance results presented in Table 7 show that HF has been detected, with F abundances derived, in red giants spanning a range of Fe abundances from roughly solar down to values of [Fe/H] ∼ −1.2. Over this interval in the Fe abundance, the F abundances vary by about a factor of 25; these are the first F abundance measurements that span such a large range of metallicity and provide the most detailed view to date of how F abundances change with changing Fe abundances.

6.1.1. The Observed Behavior of Fluorine

Figure 9 plots F versus Fe abundances for the red giants studied here; included is one low-metallicity red giant from Li et al. (2013) where HF was detected and analyzed. (Li et al. detected HF in a second low-metallicity red giant, which is a CH star and thus has likely had its primoridal F abundance increased by He burning and neutron captures [e.g., Jorissen et al. 1992], and in a third star exhibiting abundance patterns of dwarf spheroidals.) The cloud of points surrounding the solar abundances are the bright, nearby late K and M giants that were observed with the KPNO 4 m FTS, and these abundances cluster around the solar value or slightly below, with the size of the cloud roughly corresponding to the uncertainties in our derived abundances. As A(Fe) decreases below about 7.2, the fluorine abundance is found to rapidly decrease by about ∼0.5 dex over a very narrow range in Fe (less than ∼0.1 dex). At lower Fe abundances, the majority of red giants have F abundances that decrease linearly in the logarithmic A(F)–A(Fe) plane, with a slope of very nearly 1.0. This type of chemical evolution demonstrates that F behaves as a primary product of nucleosynthesis relative to Fe; the long-dashed line in Figure 9 has a slope of 1.0 and is set to pass approximately through the low-metallicity points to demonstrate primary chemical evolution of F with Fe (we note that this is not a fit to the points). The dotted line that originates at the solar abundance with decreasing F and Fe abundances has a slope of 2.0 and is plotted to demonstrate how secondary chemical evolution with Fe would behave. Although at the higher metallicities the chemical evolution of F may be complex, its behavior at Fe abundances below about −0.5 dex solar displays a clear primary behavior with Fe.

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One further item to note in Figure 9 is the position of two metal-poor red giants that fall well above the A(F)–A(Fe) line that defines most of the metal-poor stars; these two red giants have been identified, based on their Galactic positions, space motion, and peculiar chemistry, to be probable members of the Monoceros overdensity, which is a feature in the outer Galaxy and is probably an overdensity structure in the outer disk, or, as initially proposed by Newberg et al. (2002), related to an accreted dwarf galaxy. The stellar members of this structure display peculiar chemical abundance distributions (Chou et al. 2010) and, thus, may not display the same F–Fe abundance patterns as more nearby Galactic populations. Alternatively, this abundance pattern could be representative of the outer thin disk, if Monoceros is a structure of the flared thin disk.

Figure 10 is similar to Figure 9 but uses two panels to compare the derived values of [F/Fe] versus [Fe/H] (including results from Jönsson et al. 2014a, 2017; Pilachowski & Pace 2015 and Li et al. 2013) to predictions from a variety of models. The top panel shows only the derived stellar values of [F/Fe], while the bottom panel overlays the various chemical evolution models over the observed abundances. In the near-solar-metallicity regime, all of the various abundance results roughly overlap, although they exhibit scatter that can be at least partially explained by the internal errors and possible systematic in the different studies, or, it is also possible that part of the scatter may be real. At values of [Fe/H] < −0.4, [F/Fe] displays a roughly constant value, within the uncertainties, which is the signature of F behaving as a primary product relative to Fe (as noted in Figure 9). The flat dashed line in the top panel of Figure 10 is the average value of [F/Fe] for the red giants from this study having Fe abundances of less than [Fe/H] ∼ −0.3 and values of [F/Fe] < −0.2: this mean value is [F/Fe] = −0.36 ± 0.10. The dashed line connecting the solar value to the plateau line has a slope of 1.0, illustrating secondary F production with respect to Fe. Note that the results from Jönsson et al. (2017) for the slightly metal-poor stars in their sample scatter about this secondary line. The observationally derived behavior of [F/Fe] as a function of [Fe/H] suggests a primary production of F at low metallicities with a near-constant subsolar value of [F/Fe] ∼ −0.36, with a secondary source possibly driving a significant increase in the F abundance over a small interval in the Fe abundance.

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6.1.2. Comparisons with Chemical Evolution Models

Metallicity gradients are a common feature in galaxies, and our own Galaxy is no exception; it is well known that metallicities in galaxy disks decrease with increasing distance from the galactic center. In the Milky Way, radial metallicity gradients are observed in several stellar populations, such as H ii regions (e.g., Esteban & García-Rojas 2018), B stars (e.g., Daflon & Cunha 2004; Bragança et al. 2019), Cepheids (e.g., Lemasle et al. 2008; Genovali et al. 2014), open clusters (e.g., Yong et al. 2012; Magrini et al. 2017; Donor et al. 2018; Carrera et al. 2019), and planetary nebulae (e.g., Stanghellini & Haywood 2018). In addition, results from recent spectroscopic surveys confirm the existence of chemical abundance gradients for field low-mass stars, indicating that gradients also vary with distance from the galactic plane (e.g., Cheng et al. 2012; Hayden et al. 2015) and age of the population (e.g., Bergemann et al. 2014; Anders et al. 2017), while radial mixing, via heating and/or migration, affects the radial abundance gradients (Schönrich & Binney 2009; Minchev et al. 2013; Kubryk et al. 2015). There is a vast literature on radial gradients for several elements in the Milky Way, but the fluorine abundance gradient has not yet been probed.

In this study we have the opportunity to investigate the variation of the fluorine abundance (along with iron) as a function of galactocentric distance (see also Puls 2018). Our sample contains stars between roughly R_g ∼ 8.7 and 13 kpc, with one star in the inner Galactic region at R_g ∼ 6 kpc. A significant fraction of our targets are in the solar neighborhood, having galactocentric distances close to the solar value (${R}_{{g}_{\odot }}$ = 8.33 ± 0.35 kpc; Gillessen et al. 2009). Given the goal of probing fluorine at low metallicities, roughly half of the targets were selected to be both cool and metal-poor, possibly being from the thick disk or halo, from known overdensities, or stellar substructures. In fact, two of the targeted stars (2MASS 01051470+4958078 and 2MASS 22341156+4425220) lie at $| Z|$ ∼ 1.2 kpc from the Galactic plane and appear to be members of the halo, with rotational velocities V_ϕ ∼ 0 km s⁻¹ (calculated using Gaia DR2 combined with APOGEE DR14 radial velocities), but are relatively metal-rich for the halo with [Fe/H] ∼ −1, suggesting that they may be members of the Gaia-Enceladus or Gaia-Sausage accretion event (Belokurov et al. 2018; Helmi et al. 2018). Examining the APOGEE DR14 (Holtzman et al. 2018) chemical abundances for these stars, they have low [X/Fe] for (C+N), Mg, Al, and Ni, consistent with the chemical abundance profile of this accreted population in the Milky Way halo (Hayes et al. 2018).

Two other stars in our sample (2MASS 02431985+5227501 and 2MASS 04224371+1729196) are notable owing to their high [F/Fe] for their relatively low metallicities of [Fe/H] ∼ −0.8 (see Figures 9 and 10). These two stars lie below the Milky Way plane by 1–2 kpc at galactocentric radii R_GC ≳ 11 kpc but are rotating in the same direction as the disk, with rotational velocities around V_ϕ ∼ 230 km s⁻¹. This suggests that these stars are perhaps members of the Monoceros overdensity, which has been reported as a metal-poor overdensity moving with velocities similar to the disk, but lying below the nominal disk midplane by 1–3 kpc at these galactocentric radii (Crane et al. 2003; Ibata et al. 2003; Rocha-Pinto et al. 2003; Morganson et al. 2016). Additionally, these stars have nearly solar α-element abundances consistent with the chemistry of the Monoceros Ring (Chou et al. 2010).

The [F/Fe] ratio versus R_g for the studied sample is shown in Figure 11. Most of the targets have Gaia DR2 distances with estimated errors of the order of 0.3–0.4 kpc (Bailer-Jones et al. 2018; 1). Here again we segregate the targets based on a purely geometric definition of the thin/thick disk: stars having $| Z| \gt 300$ pc taken as probable thick-disk/halo population (filled blue circles) and $| Z|$ < 300 pc as probable thin-disk stars (filled red circles). Although having $| Z|$ < 300 pc, Arcturus was not included in the thin-disk sample given that it is known to be a thick-disk star (Ramirez et al. 2007). It is clear that the sample of thin-disk stars in our study does not cover a range in galactocentric distances large enough to define a gradient. For the solar neighborhood stars the [F/Fe] abundances cluster around the solar [F/Fe] value with a mean $\langle [{\rm{F}}/\mathrm{Fe}]\rangle$ = 0.01 ± 0.15. Only one probable thin-disk star (2MASS 07313775−2818395) is located ∼2 kpc beyond the solar vicinity and has an elevated [F/Fe] ratio when compared to the solar average for the solar neighborhood.

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Focusing on the sample of probable thick-disk/halo stars, the gradient of [F/Fe] for this population has a shallow slope of 0.02 ± 0.03 dex kpc⁻¹, and given its error, this is consistent with a flat behavior for [F/Fe] with galactocentric distance between ∼6 and 13 kpc. The [F/Fe] ratio for these stars, all having $| Z|$ > 300 pc above the Galactic plane, is subsolar, indicating a quasi-plateau corresponding to ∼−0.3 dex. As discussed in the previous section, such a floor in [F/Fe] likely corresponds to the production of fluorine in SNe II via neutrino nucleosynthesis (Figure 10), while the thin-disk stars between ∼8 and 10 kpc would potentially follow a sequence with a steeper positive slope with R_g, having [F/Fe] from roughly solar to ∼+0.3 dex, although this is based on the abundances obtained for one single more distant thin-disk star in our sample and is a pure speculation at this point.

A relatively flat abundance gradient for the thick disk is in general agreement with other results from the literature (e.g., Cheng et al. 2012; Boeche et al. 2013; Mikolaitis et al. 2014; Hayden et al. 2015; Weinberg et al. 2019). We note, however, the very discrepant positions in the plane [F/Fe]–R_g of those targets tagged as being possible members of the Monoceros overdensity. These two stars have significantly higher fluorine abundances for their metallicities, among the highest [F/Fe] in our sample, with a mean [F/Fe] = +0.38 dex (see also their location in Figures 9 and 10). Compared with the other stars in the outer disk sample, their F/Fe abundances are roughly 1 dex higher than those for stars at similar R_g. Such discrepancy is well beyond the expected uncertainties in the abundance determinations that have been done homogeneously. Given the clear inconsistent abundances obtained for these two Monoceros targets, these stars were not included in the derivation of the radial gradients discussed above. The very distinct fluorine abundance behavior for the two possible Monoceros targets when compared with the radial gradient obtained for other target stars away from the midplane ($| Z|$ > 300 pc) adds to the ongoing debate about the origin of the Monoceros overdensity. Given their high fluorine content and the fact that in the outer galaxy the chemical thin disk flares (Minchev et al. 2015, 2017; Bovy et al. 2016; Mackereth et al. 2017), it would be tempting to speculate (just based on their abundances) that the abundance pattern in these stars could represent an extension of the fluorine gradient in the thin disk. However, given the small number of stars analyzed and the lack of outer thin-disk stars in our sample, this speculation should be viewed with extreme caution. It is clear, however, that the fluorine abundances for these two Monoceros stars do not match those of the thick-disk/halo stars.