On the iron ionization balance of cool stars
M. Tsantaki, N. C. Santos, S. G. Sousa, E. Delgado-Mena, V. Adibekyan, D. T. Andreasen
MMNRAS , 1–11 (2018) Preprint 20 February 2019 Compiled using MNRAS L A TEX style file v3.0
On the iron ionization balance of cool stars
M. Tsantaki, (cid:63) N. C. Santos, S. G. Sousa, E. Delgado-Mena, V. Adibekyan, D. T. Andreasen Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, Porto, 4150-762, Portugal
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
High-resolution spectroscopic studies of solar-type stars have revealed higher iron abundancesderived from singly ionized species compared to neutral, violating the ionization equilibriumunder the assumption of local thermodynamic equilibrium. In this work, we investigate theoverabundances of Fe ii lines reported in our previous work for a sample of 451 solar-typeHARPS stars in the solar neighborhood. The spectroscopic surface gravities of this samplewhich emerge from the ionization balance, appear underestimated for the K-type stars. In or-der to understand this behavior, we search our Fe ii line list for unresolved blends and outliers.First, we use the VALD to identify possible unresolved blends around our lines and calculatewhich ones are strong enough to cause overestimations in the equivalent width measurements.Second, for our sample we use reference parameters (e ff ective temperature and metallicity)and the Gaia
DR2 parallaxes to derive surface gravities (trigonometric gravities) and calcu-late the Fe i and Fe ii abundances from di ff erent line lists. We exclude the Fe ii lines whichproduce overabundances above 0.10 dex. The derived surface gravities from the clean line listare now in agreement with the trigonometric. Moreover, the di ff erence between Fe i and Fe ii abundance does not show now a correlation with the e ff ective temperature. Finally, we showthat the ionization balance of Ti can provide better estimates of surface gravities than iron.With this analysis, we provide a solution to the ionization balance problem observed in theatmospheres of cool dwarfs. Key words: techniques: spectroscopic, surveys, stars: fundamental parameters, abundances
A standard method to determine the atmospheric parameters viaspectroscopy is to measure the equivalent widths (EW) of severalspectral lines of a metallic species and calculate their abundances.Then, we derive the e ff ective temperature ( T e ff ) and surface gravity(log g ) of a star when excitation and ionization balances are satis-fied simultaneously under the assumption of local thermodynamicequilibrium (LTE). In most cases, we use neutral and singly ionizediron lines because they are numerous and well studied in terms oftheir atomic data in the optical wavelength region. This methodhas been successfully applied to a plethora of studies for FGK-type stars from the characterization of Galactic stellar populations(e.g. Adibekyan et al. 2012) to the characterization of planet-hoststars (e.g. Santos et al. 2013) mainly with high resolution spec-troscopy. Even though the above methods provide high enough pre-cision and accuracy for T e ff and metallicity , the determination ofsurface gravity shows some caveats (see Morel & Miglio 2012; (cid:63) E-mail: [email protected] We note that in this study we use iron as a proxy for the overall metallicitywhich is defined as: [ Fe / H ] ≡ log N Fe N H (cid:63) – log N Fe N H (cid:12) , where N is the number Mortier et al. 2014, for surface gravity comparisons between dif-ferent methods) and is di ffi cult to constrain from the ionization bal-ance of iron lines because the neutral-to-singly-ionized ratio is notvery sensitive to gravity changes compared to other ionization lev-els (see Gray 2005). Moreover, the number of ionized lines is verylimited compared to neutral lines in the optical.Several works in high resolution report discrepancies betweenneutral and singly ionized iron abundances for dwarf stars in sev-eral open clusters (Hyades, Pleiades, and M34) and the Ursa Ma-jor moving group without considering non-LTE e ff ects (Yong et al.2004; Schuler et al. 2006; Chen et al. 2008; Schuler et al. 2010;Aleo et al. 2017). The discrepancies are stronger for the cooler stars( T e ff (cid:46) ii abundance over Fe i .The enhanced Fe ii abundances over Fe i can be quite significant,for example in the high resolution study of Pleiades the di ff erencereaches up to 0.8 dex (Schuler et al. 2010). The deviation from theionization balance for the cooler dwarfs is also present in field starsin the solar neighborhood (Allende Prieto et al. 2004; Ramírez et al.2007; Bensby et al. 2014). In this work, we refer as the ionization of atoms per unit volume. Iron abundance is defined as: log A ( Fe ) ≡ log N Fe N H (cid:63) + (cid:13) a r X i v : . [ a s t r o - ph . S R ] F e b M. Tsantaki balance problem , the observed di ff erences between Fe i and Fe ii abundances in LTE and not to the LTE departures when the meanintensity, J ν , is larger than the Planck function, B ν , for species intheir minority ionization stage in the ultraviolet wavelengths (e.g.Asplund 2005).Departures from the LTE were suggested as responsible forthe Fe i –Fe ii discrepancy a ff ecting the correct log g determinationfor very metal-poor stars (Korn et al. 2003; Ruchti et al. 2013)but they are not expected to occur around solar metallicity K-typedwarfs (Lind et al. 2012). In addition, other model uncertainties re-lated to granulation and activity of K-type stars have been proposedto explain these di ff erences in the case of HIP 86400 (Ramirez2008) but to be fully understood 3D non-LTE investigations shouldbe carried out (Amarsi et al. 2016).Alternatively, if the adopted stellar parameters are not correct,the iron abundances will not be correct either. For example, if weincrease the T e ff of a K-type star by 100 K which is a typical error,this leads to a reduction of the Fe ii abundance by ∼ i abundance almost unchanged.The ionization imbalance a ff ects directly the determination ofsurface gravity when it is derived from the Fe i –Fe ii tuning. Thecomparison of surface gravity from spectroscopy and estimatedfrom more direct methods such as using astrometry (trigonometriclog g ), shows spurious correlations with T e ff with higher deviationsfor the cooler stars (Tsantaki et al. 2013; Tabernero et al. 2017; Del-gado Mena et al. 2017). In the Gaia era, we have precise parallaxesfor a huge number of stars, and therefore, trigonometric gravitiescan be used as reference, assuming well constrained T e ff , to test theaccuracy of spectroscopic log g .This spectroscopic method relies significantly on the qualityof the iron line list and has to be carefully selected. In previouswork, we showed that blended iron lines can produce overestima-tions in the spectroscopic e ff ective temperature scale compared tothe photometric one (Tsantaki et al. 2013, hereafter TS13). Also,Aleo et al. (2017) recently showed that a careful selection of theirFe ii lines can decrease the Fe i –Fe ii di ff erences for K-type stars inthe Hyades cluster but not eliminate them.In this work, we use high resolution spectra of a well-studiedsample of solar-type dwarfs to investigate if the observed overabun-dances of Fe ii in the literature arise from the quality of the iron linelist. If this is the case for the Fe i –Fe ii discrepancy, other mecha-nisms are not necessary, at least in first order, to explain the ioniza-tion balance problem. Under this assumption, a selection of optimaliron lines to solve the ionization balance problem will also elimi-nate the di ff erences between the spectroscopic and trigonometricgravities and their trends with T e ff . The compilation of the iron line list is very important for the abun-dance analysis, especially for the cooler stars because their spectraare highly line crowded and the EW of these spectral lines cannotbe measured accurately. Our line list is taken from TS13 which wasvisually checked to discard blended lines in the cooler stars. The ef-fective temperature and metallicity derived with the TS13 line listhave been compared with other literature sources and have beenvalidated for their accuracy. For example, the comparison of the T e ff from TS13 with more model independent methods, such as theinfrared flux method (IRFM) and interferometry showed very goodagreement, and the metallicity is in agreement with Sousa et al.(2008). We note that the metallicity in TS13 is derived only from Fe i lines and the T e ff from the excitation balance of the Fe i lines.Therefore, the Fe i lines of this list are reliable enough to estimatee ff ective temperatures and metallicities. However, the TS13 linelist failed to provide accurate surface gravities in particular for thecooler stars ( T e ff < i and Fe ii abundances to beequal. We suggest that the Fe ii lines must mostly contribute to thewrong surface gravity estimates we observe. Therefore, we searchfor unresolved blends around the Fe ii lines in the TS13 line listwhich contains 120 Fe i and 18 Fe ii lines. The Fe i lines are morenumerous than Fe ii and the latter are more di ffi cult to be foundisolated. Also, because of their small number their dispersion inabundances is high and usually a 3 σ clipping of outliers which isa commonly used does not work.In the following Sections, we perform two separate tests toselect the optimal Fe ii lines for our abundance analysis. With this test we want to discover unresolved blends which cannotbe detected neither by visual inspection nor by our automated tools.In this case, these lines will be fitted by a single Gaussian instead oftwo (or more), leading to an overestimation of their true EW. In ourworks, we use
ARES (Sousa et al. 2015) for the automatic EW mea-surements which has been extensively used in the literature for highresolution studies (e.g. for the Gaia -ESO survey, Smiljanic et al.2014; Jofré et al. 2014). The suggested distance of two consecu-tive lines to be resolved as separate with
ARES is more than 0.07 Åfor high resolution spectra and specifically, this value has been setfor the analysis of the HARPS GTO planet search sample (Sousaet al. 2008, 2011). Ideally, this value should be set depending onspectral type, instrumental resolution, and signal-to-noise ratio butsince it is di ffi cult to evaluate this value per spectrum, we use thedefault value provided for ARES in this work. This test is based onthe idea that since
ARES cannot resolve two lines in shorter distancethan 0.07 Å, the unresolved blends will be inside the intervals of0.14 Å wide. To be conservative, we select wider intervals, 0.20 Åwide, and we query around our Fe ii lines within these intervals forall possible lines from the Vienna Atomic Line Database (VALD;Piskunov et al. 1995; Kupka et al. 1999; Ryabchikova et al. 2015).VALD includes dozens of lines in our regions to be potentialblends. However, not all lines that appear inside the intervals leadto overestimation of the iron EW because their strengths dependon the physical conditions in the atmospheres they are formed. Forexample, ionic metallic lines are stronger in the atmospheres of thehotter stars.We calculate the theoretical EW for all the VALD lines tofind which ones are strong enough relative to the EW of the Fe ii line in each interval. For this analysis, we use the atomic data (os-cillator strengths, log g f ) from VALD, the spectral analysis code, MOOG ( ewfind driver, Sneden 1973; Sneden et al. 2012), and aKurucz (1993) Atlas 9 model atmosphere of a cool star (HD 21749: T e ff = g = Fe / H ] = ii line similarlyto Boeche & Grebel (2016). We define the Fe ii lines as blended ifthe EW of each potential blend relative to the sum of the EW of the ARES 2.0 : http: // / sousasag / ares VALD: http: // vald.inasan.ru / vald3 / php / vald.php MOOG 2017 : http: // verdi.as.utexas.edu / moog.htmlMNRAS , 1–11 (2018) n the iron ionization balance of cool stars Table 1.
The blended Fe ii lines based on VALD data are marked with a (cid:88) for each isolation threshold. The median and median absolute deviations(MAD) are calculated for each Fe ii line shown in Fig. 3 for the two di ff er-ent damping options. N is the number of stars with T e ff < † are considered ’bad’ lines based on thecriteria of Sect. 2.2. lines (Å) Isolation threshold Blackwell damping Barklem damping N10% 20% 50% median MAD median MAD(dex) (dex) (dex) (dex)4508.28 (cid:88) (cid:88) † (cid:88) (cid:88) † (cid:88) † (cid:88) (cid:88) (cid:88) † (cid:88) (cid:88) –0.04 0.22 0.01 0.23 1295197.57 † (cid:88) † (cid:88) (cid:88) (cid:88) † (cid:88) (cid:88) † (cid:88) (cid:88) † (cid:88) (cid:88) (cid:88) † † (cid:88) (cid:88) iron line plus the EW of the potential blend is higher than a thresh-old value. The higher the threshold value, the less lines will beconsidered blended. We selected three indicative threshold valuesof 10%, 20%, and 50%. The results are shown in Table 1. With thisanalysis, we find that using a 10% threshold, 11 lines appear to beblended: 4508.28, 4520.22, 4576.33, 4731.45, 4923.93, 5197.57,5337.72, 5991.37, 6149.25, 6442.97, and 6516.08 Å.In Fig. 1, we use
MOOG ( synth driver) to synthesize the ironlines which appear blended, and their blends for the same modelatmosphere. The lines which pass the 50% blending threshold are4731.45, 5337.72, and 6442.97 Å. The first appears visually mostblended in Fig. 1 and the latter two are too weak (EW ≈ g f value is calculated from the EW of the total blend. If the blendhas similar behavior as Fe ii , the calibrated log g f can mitigate thee ff ects of blending and probably will deliver a reliable abundance.Therefore, we need to combine other tests along with this analysisto confidently exclude the bad lines. We use a sample of 451 FGK-type dwarfs to estimate empiricallywhich iron lines give outlying abundances that are too high to rec-oncile with the majority for each spectrum. The sample is part ofthe HARPS GTO planet search program (Mayor et al. 2003) withvery high spectral quality, resolution of 110 000, and 90% of their The expression of the blend threshold we use is:threshold = blend / (blend + iron line) spectra have signal-to-noise ratio higher than 200. The stellar pa-rameters of this sample were derived by imposing excitation andionization equilibria on weak iron lines with MOOG , using the Ku-rucz (1993) Atlas 9, plane parallel, 1D static models in LTE. Thesame model atmospheres are used throughout this paper unlessspecified. These stars were firstly analyzed in terms of their pa-rameters by Sousa et al. (2008) and secondly by Tsantaki et al.(2013) with the same method but a shorter line list to correct foroverestimations in the e ff ective temperature for the cooler stars. Asmentioned before, their e ff ective temperatures and metallicities arein very good agreement with various spectroscopic and photomet-ric works and thus, we consider these parameters very reliable tobe used as reference.Even though the e ff ective temperatures agree very well withmore model-independent methods, such as the IRFM, surface grav-ities on the other hand, appear flat in the Hertzsprung-Russell (HR)diagram for the cooler stars (Fig. 2). More reliable surface gravitiesare obtained from methods with less model dependence, such as as-teroseismology or from dynamic mass and radius measurements ineclipsing binary systems. However, these measurements for dwarfstars are limited to a relatively small number. With the Gaia mis-sion (Gaia Collaboration et al. 2018), we have access to parallaxeswith unprecedented precision for millions of stars. In lack of theother direct log g estimates, trigonometric gravities are very usefulto test our spectroscopic determinations. Trigonometric gravitiesare derived from the following expression:log gg (cid:12) = log MM (cid:12) + T e ff T e ff (cid:12) + . V + BC ) + π + .
104 (1)where M is the stellar mass, V the visual magnitude, BC the bolo-metric correction, and π the parallax in mas. From the above ex-pression, we derived the trigonometric log g for the 451 HARPSstars with the Gaia
DR2 parallaxes (Luri et al. 2018), V magnitudesfrom the Hipparcos catalog (Perryman et al. 1997), bolometric cor-rection based on Flower (1996) and Torres (2010), solar magni-tudes from Bessell et al. (1998), and the T e ff of TS13. No correctionfor interstellar reddening is needed since all stars are less than 56 pcin distance. Because of systematics in the Gaia
DR2 parallaxes, weadd a conservative value of 0.03 mas proposed by the
Gaia collab-oration (Lindegren et al. 2018). Moreover, we increase the errorsin parallaxes to consider the ∼
30% underestimation in uncertain-ties for bright stars (Luri et al. 2018; Arenou et al. 2018). Stellarmasses are derived from the
PARAM 1.3 tool using the PARSECtheoretical isochrones from Bressan et al. (2012) and a Bayesianestimation method (da Silva et al. 2006). The trigonometric log g are also depicted in Fig. 2 which follow the expected isochronesfor the solar neighborhood.First, we measure the EW of the complete TS13 line list forall spectra with ARES . Then, we use our reference spectroscopic T e ff , [ Fe / H ], and microturbulence from TS13, and the trigonomet-ric gravities to derive the individual Fe i and Fe ii abundances foreach star with MOOG ( abfind driver) using a curve-of-growth ap-proach. As mentioned before, the log g f values of the line list arecalibrated to match the solar abundances (log A ( Fe ) (cid:12) = PARAM 1.3 tool: http: // stev.oapd.inaf.it / cgi-bin / param_1.3MNRAS000
PARAM 1.3 tool using the PARSECtheoretical isochrones from Bressan et al. (2012) and a Bayesianestimation method (da Silva et al. 2006). The trigonometric log g are also depicted in Fig. 2 which follow the expected isochronesfor the solar neighborhood.First, we measure the EW of the complete TS13 line list forall spectra with ARES . Then, we use our reference spectroscopic T e ff , [ Fe / H ], and microturbulence from TS13, and the trigonomet-ric gravities to derive the individual Fe i and Fe ii abundances foreach star with MOOG ( abfind driver) using a curve-of-growth ap-proach. As mentioned before, the log g f values of the line list arecalibrated to match the solar abundances (log A ( Fe ) (cid:12) = PARAM 1.3 tool: http: // stev.oapd.inaf.it / cgi-bin / param_1.3MNRAS000 , 1–11 (2018) M. Tsantaki
Figure 1.
Synthetic Fe ii lines in blue and the synthetic Fe ii plus the blends in red. The HARPS spectrum of a K-type star (HD 21749) is depicted (blackdotted) for comparison. The center of the Fe ii line and the blends within the range of 0.20Å are shown with the black solid vertical lines. Figure 2.
The HR diagram for the 451 stars for the two set of parameters:the spectroscopic parameters of TS13 (red points), and spectroscopic T e ff and log g from Gaia parallaxes (blue points). The dotted line correspondsto 12.7 Gyr isochrone of 0.035 metallicity, and the dashed line to 1 Gyrisochrone of 0.0001 metallicity. The solid lines correspond to isochronesbetween 1–12.7 Gyr of solar metallicity. hancement factor recommended by the Blackwell group (dampingoption 2 within MOOG for the 2017 version).Even though the strength of a weak line is dominated by theDoppler core rather than the Lorentzian wings, large uncertaintiesin the damping parameters a ff ect the derived abundances even forweak lines (see e.g. Ryan 1998). A di ff erent approach to determinedamping parameters is described by the ABO theory (Anstee &O’Mara 1991; Barklem et al. 1998, 2000) which uses cross sectionsto determine the individual damping values. The TS13 line list con-tains 115 out of 137 lines with damping based on the ABO theoryfrom Barklem et al. (2000). All of the Fe ii lines have Barklem et al.(2000) damping data. We evaluate how the two di ff erent dampingapproaches a ff ect the abundances of the Fe ii lines. Before we dothat, we recalibrate the log g f values for the damping of Barklemet al. (2000) using the Sun as reference with a solar spectrum fromHARPS. The recalibration is essential because the initial TS13 linelist was calibrated with the Blackwell damping.In Fig. 3, we plot the di ff erence between Fe ii – Fe i for the451 stars using the di ff erent damping parameters. In the traditionalLTE approach, the di ff erences should be zero but in our case theyare enhanced for the cooler stars ( ∼ The enhancement factor, E, is given by the relation: E = + · EP,where EP is the excitation potential of the specific line.MNRAS , 1–11 (2018) n the iron ionization balance of cool stars Figure 3. Di ff erences in iron abundances (Fe ii – Fe i ) as a function of T e ff for the 451 stars for the two di ff erent damping options. Red points representthe di ff erences with Barklem damping values and the blue points the di ff er-ences with Blackwell. The abundances are derived with the T e ff , [ Fe / H ],and microturbulence from TS13, and the trigonometric log g . proach performs better as in both cases the di ff erences in the ironabundances are equally large.Our goal is to select the Fe ii lines which produce the sameabundance as Fe i (which is equal to the total iron abundance sinceit is measured only from Fe i lines). In Fig. 4, we present the di ff er-ences of the overall iron abundance minus the abundance of eachFe ii line for the cooler stars (134 stars) since the Fe ii overabun-dances are more evident for T e ff < ff erentdamping approaches. The results of all Fe ii lines are also presentedin Table 1. We exclude lines with median di ff erence higher than0.10 dex and at the same time their mean absolute deviation isabove 3 σ following a similar analysis as in Sousa et al. (2014). Fora cool star, a di ff erence of 0.10 dex in the Fe ii – Fe i abundance canbe produced by an underestimation of 0.15 dex in log g which corre-sponds to the di ff erences we roughly observe in Fig. 2 between thespectroscopic and trigonometric log g and therefore can be a validlimit to exclude Fe ii lines. Both damping approaches give similardi ff erences, within 0.02 dex, but the highest reaches 0.06 dex forthe 5197.57 Å. In both cases the same lines are excluded.The remaining good lines are: 4508.28, 4620.51, 4656.98,5234.63, 5264.81, 5414.07, 6247.56 Å. The line 6442.97 Å is tooweak to appear in stars with T e ff < ff erences smaller than 0.10 dex for thesame analysis but for the rest of the sample). We note that for starswith T e ff > ff erences below 0.10 dex, exceptfor 5337.72 Å. We confirm that 10 out of 11 lines from the previousanalysis in Sect. 2.1 are also classified as bad in this test, suggest-ing they are in fact blended. The reasons for the rest of the lineswhich give overabundances in this test could be related to bad EWmeasurements either because they are in regions di ffi cult to normal-ize correctly or their atomic data are not accurate. To include thesereasons, we adopt this Fe ii line list as more robust compared to theone in Sect. 2.1.We also performed the same analysis but this time we usedthe MARCS (Gustafsson et al. 2008) model atmospheres to checkwhether the iron abundances di ff er significantly depending on thechoice of model atmospheres. To have meaningful results, we re- Figure 4. Di ff erence in abundance (Fe ii – Fe) produced by each Fe ii line forthe cool stars of our sample. The dotted lines show the ± ff erent colors represent di ff erent damping options. The lines in squaresare the ones selected by our criteria. calibrate the atomic data of our line list with a MARCS solar modelatmosphere and derive the Fe ii – Fe i abundances. We discover thatthe di ff erences are almost identical to the ones derived with Kuruczmodels and subsequently the same lines were excluded.Summarizing, we exclude 55% of the lines (10 out of 18)showing the di ffi culty to find good Fe ii lines in the optical. There are numerous iron line lists in the literature used for highresolution studies. In this Section, we check how two line lists per-form in order to extend our number of good Fe ii lines or obtainimproved atomic data by comparing lines in common. The two linelists are: 12 Fe ii lines from the Gaia -ESO ’golden’ list (Jofré et al.2014), and 120 Fe ii lines from Meléndez & Barbuy (2009). Wenote that the line list of Aleo et al. (2017) which was used to reducethe Fe ii – Fe i di ff erences for the Hyades cluster, contains 12 Fe ii lines which are all selected from Meléndez & Barbuy (2009). Thelines from the Gaia -ESO ’golden’ list were obtained by calculat-ing the mean and standard deviation of all abundances for a sampleof 34 FGKM stars and selected those lines that agreed within 2 σ with the average abundance and had to be analyzed by at least threedi ff erent research groups.We performed the analysis of Sect. 2.2 for both line lists toshow how many of these lines produce good abundance determi-nations. For this analysis, we used the two di ff erent damping op- MNRAS , 1–11 (2018)
M. Tsantaki
Table 2.
The final Fe ii lines from the analysis of all line lists with the exci-tation potential (EP) and the optimal atomic data taken from the reference.lines (Å) EP (ev) log g f Reference4369.41 2.78 –3.650 Meléndez & Barbuy (2009)4508.28 2.86 –2.405 TS134522.63 2.84 –2.250 Meléndez & Barbuy (2009)4576.34 2.84 –2.950 Meléndez & Barbuy (2009)4582.84 2.84 –3.180 Meléndez & Barbuy (2009)4620.51 2.83 –3.236 TS134656.98 2.89 –3.679 TS134666.76 2.83 –3.280 Meléndez & Barbuy (2009)5234.63 3.22 –2.237 TS135264.81 3.23 –3.093 TS135414.07 3.22 –3.571 TS136239.95 3.89 –3.410 Meléndez & Barbuy (2009)6247.56 3.89 –2.300 Meléndez & Barbuy (2009)6442.97 5.55 –2.400 TS13 tions (when Barklem data were available), and we also did not findsignificant di ff erences on the derived abundances. Therefore, forsimplicity, we use only the Blackwell damping parameters for therest of the paper since this option was used for the derivation ofthe initial parameters of the HARPS sample we compare in the fol-lowing sections, and more importantly, since we showed that thedamping does not a ff ect significantly the results of this analysis.We select the lines which fulfill the criteria of Sect. 2.2 resulting inonly two good lines from Jofré et al. (2014) and 15 from Melén-dez & Barbuy (2009). The two lines from the Gaia -ESO line list(5264.81, 5414.07 Å) are in common with the good lines of Melén-dez & Barbuy (2009) and show the same median abundances butwith the atomic data of TS13, their median values are smaller, andtherefore, we keep the latter atomic data. There are six lines fromMeléndez & Barbuy (2009) which are not in the TS13 list and arenow included as new good lines.From the lines in common between TS13 and Meléndez &Barbuy (2009), we select the atomic data of those which presentthe lowest median and dispersion values. For example, the line4576.34 Å with the solar calibrated log g f from TS13 gives dif-ference in the abundances of 0.13 dex, yet with the atomic data ofMeléndez & Barbuy (2009) the di ff erence is reduced to 0.07 dex.Inversely, the 4508.29 Å which was excluded by Aleo et al. (2017)as blended according to their criteria, does not give overabundanceswith the atomic data of TS13. This test demonstrates that the atomicdata play an important role, as important as the correct EW mea-surement itself, on the abundance analysis. The final line list con-tains 14 lines from both Meléndez & Barbuy (2009) and TS13 andis described in Table 2. We remind the reader that the atomic datafor the TS13 line list are derived after solar calibration with thedamping Blackwell approximation. Now, we perform the inverse exercise to show that in fact the cleanFe ii list we compiled previously provides more reliable surfacegravities. We derive the atmospheric parameters for the sampleusing the spectral analysis tool FASMA (Andreasen et al. 2017). FASMA tool: http: // / fasma Figure 5. Di ff erences in e ff ective temperature (upper plot), surface gravity(middle plot) and metallicity (bottom plot) between this work and TS13.The average error bars are plotted as black points. FASMA is wrapped around
ARES and
MOOG , and includes the modelinterpolation and minimization processes. The parameters are de-rived based on the same principles as in TS13, i.e. imposing exci-tation balance (the slope of iron abundance and excitation potentialshould be lower than 0.001) and ionization balance (the di ff erencebetween the average abundances of Fe i and Fe ii should be lessthan 0.01 dex) in a fully automatic way. These convergence criteriaare defined in Andreasen et al. (2017). We apply a 3 σ clipping toremove outliers.In Fig. 5, we show our derived parameters compared withTS13. The mean di ff erence and standard deviation between FASMA and TS13 for T e ff is –11 and 34 K, for log g is 0.08 and 0.13 dexand for [ Fe / H ] is 0.00 and 0.02 dex. We show that the scale of thee ff ective temperature and metallicity of this work is in very goodagreement with TS13 which we expect because the Fe i lines didnot change.In Fig. 6 (middle plot), we plot the comparison between ourspectroscopic surface gravities and the trigonometric. The meandi ff erences and standard deviations between the log g of this workand the trigonometric is 0.02 and 0.10 dex, and between the log g of TS13 and trigonometric is –0.06 and 0.13 dex. Even though theagreement of our spectroscopic log g with the trigonometric is verygood, we notice an overestimation of our log g for values higherthan ∼ ∆ log g – T e ff relation in this work (upper plot of Fig. 6) and our MNRAS , 1–11 (2018) n the iron ionization balance of cool stars Figure 6. Di ff erences in log g of this work with trigonometric (greenpoints), and of TS13 with trigonometric (red points), for the di ff erent at-mospheric parameters: ∆ log g – T e ff (upper plot), ∆ log g – trigonometriclog g (middle plot), ∆ log g – [ Fe / H ] (bottom plot). The colored lines in theupper plot represent a linear fit of the two samples and the black point inthe middle plot the average error. dispersion values are smaller. These results indicate that the crite-ria of the line selection were e ffi cient enough because that lineardependence between ∆ log g and T e ff has diminished significantlywith a slope of practically zero (9.7 · − dex K − ). Finally, there isno general correlation between ∆ log g and [ Fe / H ] (bottom plot ofFig. 6) but there is an overestimation of spectroscopic log g for themost metal-poor stars of this sample ([ Fe / H ] < –0.4 dex). Theseare the same stars which produce the overestimations in the middleplot with log g > ffi cult to explain why metal-poorstars do not still have well constrained gravities. These di ff erencescannot be attributed to non-LTE e ff ects since these e ff ects wouldcause an underestimation of log g and not an overestimation we ob-serve here (see discussion below).Using the spectroscopic T e ff and [ Fe / H ], and the trigonomet-ric gravity, we calculate the new Fe ii and Fe i abundances for oursample similarly as in Sect. 2.2. In Fig. 7, we plot the di ff erence inFe ii – Fe i with T e ff for the whole sample of 451 stars.This plot shows that ionization balance is on average fulfilledfor the lines we consider clean after the blending analysis. The Fe ii – Fe i mean di ff erence is –0.01 dex and the standard deviation is0.04 dex, and thus, we can say that the ionization balance is muchbetter satisfied. The highest dispersion appears for the cooler stars. Figure 7. Di ff erence between Fe ii – Fe i abundances for the stars of oursample with the clean Fe ii list T e ff . The remaining di ff erences can be attributed to the e ff ects we didnot consider in this work. For instance, Lind et al. (2012) show thatthe Fe i abundances are underestimated under the LTE assumptionand the amount of non-LTE corrections depends on stellar param-eters. The highest correction for non-LTE e ff ects in Fe i abundanceis expected for hot, metal-poor giants and for the parameters ofour sample it should be less than ∼ T e ff = g = / H] = g > T e ff < ii abundancesover Fe i and non-LTE e ff ects could not explain the large di ff er-ences between spectroscopic and trigonometric gravities. However,they provide empirical calibrations for the coolest stars to correctfor the discrepancies in the log g determinations.Jofré et al. (2014) also find discrepancies between Fe ii andFe i abundances for their sample which are higher for the K-dwarfs(their table 3). The authors also quantified the departures from LTEfor their sample to be usually less than 0.03 dex for the FGK dwarfsand concluded that non-LTE e ff ects are too small to justify the ion-ization balance problem.The di ff erences of Fig. 7 are small enough to be caused byother e ff ects, such as activity, but also inaccuracies at this level ofour reference stellar parameters should not be excluded. In the previous Section, we showed that a careful selection Fe ii lines can improve the trends of iron abundances with e ff ective tem-perature and provide log g in agreement with astrometry. However,other species could be more suitable for the surface gravity deter-minations. We search for species with enough neutral and ionizedlines in the optical in two line lists: i) from Neves et al. (2009), and ii) from the joint list of Lawler et al. (2013) and Wood et al. (2013),hereafter LW13. MNRAS000
MOOG , and includes the modelinterpolation and minimization processes. The parameters are de-rived based on the same principles as in TS13, i.e. imposing exci-tation balance (the slope of iron abundance and excitation potentialshould be lower than 0.001) and ionization balance (the di ff erencebetween the average abundances of Fe i and Fe ii should be lessthan 0.01 dex) in a fully automatic way. These convergence criteriaare defined in Andreasen et al. (2017). We apply a 3 σ clipping toremove outliers.In Fig. 5, we show our derived parameters compared withTS13. The mean di ff erence and standard deviation between FASMA and TS13 for T e ff is –11 and 34 K, for log g is 0.08 and 0.13 dexand for [ Fe / H ] is 0.00 and 0.02 dex. We show that the scale of thee ff ective temperature and metallicity of this work is in very goodagreement with TS13 which we expect because the Fe i lines didnot change.In Fig. 6 (middle plot), we plot the comparison between ourspectroscopic surface gravities and the trigonometric. The meandi ff erences and standard deviations between the log g of this workand the trigonometric is 0.02 and 0.10 dex, and between the log g of TS13 and trigonometric is –0.06 and 0.13 dex. Even though theagreement of our spectroscopic log g with the trigonometric is verygood, we notice an overestimation of our log g for values higherthan ∼ ∆ log g – T e ff relation in this work (upper plot of Fig. 6) and our MNRAS , 1–11 (2018) n the iron ionization balance of cool stars Figure 6. Di ff erences in log g of this work with trigonometric (greenpoints), and of TS13 with trigonometric (red points), for the di ff erent at-mospheric parameters: ∆ log g – T e ff (upper plot), ∆ log g – trigonometriclog g (middle plot), ∆ log g – [ Fe / H ] (bottom plot). The colored lines in theupper plot represent a linear fit of the two samples and the black point inthe middle plot the average error. dispersion values are smaller. These results indicate that the crite-ria of the line selection were e ffi cient enough because that lineardependence between ∆ log g and T e ff has diminished significantlywith a slope of practically zero (9.7 · − dex K − ). Finally, there isno general correlation between ∆ log g and [ Fe / H ] (bottom plot ofFig. 6) but there is an overestimation of spectroscopic log g for themost metal-poor stars of this sample ([ Fe / H ] < –0.4 dex). Theseare the same stars which produce the overestimations in the middleplot with log g > ffi cult to explain why metal-poorstars do not still have well constrained gravities. These di ff erencescannot be attributed to non-LTE e ff ects since these e ff ects wouldcause an underestimation of log g and not an overestimation we ob-serve here (see discussion below).Using the spectroscopic T e ff and [ Fe / H ], and the trigonomet-ric gravity, we calculate the new Fe ii and Fe i abundances for oursample similarly as in Sect. 2.2. In Fig. 7, we plot the di ff erence inFe ii – Fe i with T e ff for the whole sample of 451 stars.This plot shows that ionization balance is on average fulfilledfor the lines we consider clean after the blending analysis. The Fe ii – Fe i mean di ff erence is –0.01 dex and the standard deviation is0.04 dex, and thus, we can say that the ionization balance is muchbetter satisfied. The highest dispersion appears for the cooler stars. Figure 7. Di ff erence between Fe ii – Fe i abundances for the stars of oursample with the clean Fe ii list T e ff . The remaining di ff erences can be attributed to the e ff ects we didnot consider in this work. For instance, Lind et al. (2012) show thatthe Fe i abundances are underestimated under the LTE assumptionand the amount of non-LTE corrections depends on stellar param-eters. The highest correction for non-LTE e ff ects in Fe i abundanceis expected for hot, metal-poor giants and for the parameters ofour sample it should be less than ∼ T e ff = g = / H] = g > T e ff < ii abundancesover Fe i and non-LTE e ff ects could not explain the large di ff er-ences between spectroscopic and trigonometric gravities. However,they provide empirical calibrations for the coolest stars to correctfor the discrepancies in the log g determinations.Jofré et al. (2014) also find discrepancies between Fe ii andFe i abundances for their sample which are higher for the K-dwarfs(their table 3). The authors also quantified the departures from LTEfor their sample to be usually less than 0.03 dex for the FGK dwarfsand concluded that non-LTE e ff ects are too small to justify the ion-ization balance problem.The di ff erences of Fig. 7 are small enough to be caused byother e ff ects, such as activity, but also inaccuracies at this level ofour reference stellar parameters should not be excluded. In the previous Section, we showed that a careful selection Fe ii lines can improve the trends of iron abundances with e ff ective tem-perature and provide log g in agreement with astrometry. However,other species could be more suitable for the surface gravity deter-minations. We search for species with enough neutral and ionizedlines in the optical in two line lists: i) from Neves et al. (2009), and ii) from the joint list of Lawler et al. (2013) and Wood et al. (2013),hereafter LW13. MNRAS000 , 1–11 (2018)
M. Tsantaki
Figure 8. Di ff erences in log g of the TS13 (red points) with the trigonomet-ric and from Ti of this work with the line list of Neves et al. (2009) (greenpoints) with the trigonometric as a function of log g (upper plot) and T e ff (bottom plot). The colored lines in the bottom plot represent the linear fitsof the two samples. The slope of the Ti (green) line is 2.4 · − dex K − . The element with most numerous ionized lines after iron is Ti inthis line list (Sc and Cr follow after) and contains 30 Ti i and 8 Ti ii lines. Our goal is to check whether the surface gravities derivedfrom the ionization equilibrium of Ti are more precise and accuratethan from Fe.The atomic data of this list were also derived after solar cali-bration and the damping parameters used for their analysis is basedon the Blackwell approximation which we also used in this Sec-tion. The EW of Ti i and Ti ii lines are measured with ARES forthe whole sample of Sect. 2.2. We modify
FASMA to obtain surfacegravities from the ionization equilibrium of Ti having the other stel-lar parameters fixed to the values of TS13. The mean di ff erence andstandard deviation between log g derived from Ti and the trigono-metric is 0.00 and 0.09 dex and are smaller than the derived fromthe Fe ionization equilibrium (upper plot of Fig. 8). Additionally,the slope of ∆ log g and T e ff is ∼ T e ff > The line list of LW13 provides logg f data from the measurementsof the branching fractions in solar FTS and echelle spectra. Fromthe 948 Ti i lines of Lawler et al. (2013) and the 364 Ti ii lines ofWood et al. (2013), the authors defined 128 and 31 lines respec-tively in the optical suitable for the solar abundance determination.However, it is not guaranteed this line list will work for cooler at-mospheres because severe blending occurs in lower temperatures.In fact, we used the complete ’solar’ LW13 line list to derive sur-face gravities but with unrealistic results. A fast and e ffi cient wayto select the best lines is to perform a similar test as in Sect. 2.2 forthe HARPS sample, by measuring the EW of Ti i and Ti ii lines with ARES and deriving their abundances. We select the lines with Ti ii – Ti i di ff erence less than 0.10 dex and dispersion lower than 3 σ .The clean line list of LW13 now contains 59 Ti i and 11 Ti ii . Thedamping parameters for this line list are based on the Blackwellapproximation.We obtain surface gravities from the ionization equilibrium ofTi with FASMA . The results are depicted in Fig. 9 where the meandi ff erence and standard deviation between log g derived from Ti andthe trigonometric is 0.02 and 0.08 dex respectively, and the slopeof ∆ log g and T e ff is also ∼
0. There is a small overestimation ofspectroscopic log g in this case for the cooler stars and not for thehottest ones as in Fig. 8. The di ff erences in these figures are onthe opposite direction with T e ff and suggest that non-LTE e ff ectsshould not be cause because they would a ff ect the abundances thesame way but probably we can attribute them on errors on the lineselection. However, since these over-, under-estimations are smallwith both line lists, we consider already the results reliable enough.Both Ti line lists in this Section give smaller standard devia-tions than Fe and flattest slopes with T e ff . Therefore, Ti is a betterindicator to probe surface gravity than Fe, once the other stellarparameters are defined. Bergemann (2011) studied the non-LTE ef-fects of Ti in the atmospheres of very metal-poor stars ([ Fe / H ] < –1.28 dex) and suggested that they should not be ignored in the caseof giant stars at low metallicities. Even though these parameters areoutside our parameter space, one should be careful when applyingthis method without the necessary corrections to these stars. The ionization balance problem has troubled astronomers in sev-eral works in the literature. Several hypotheses have been proposedto explain the di ff erences between Fe ii and Fe i abundances butwith no fully satisfactory answer yet. In this work, we propose lineblending as the main reason for the overabundances of Fe ii . We in-vestigate the quality of our Fe ii line list for unresolved blends thatwere missed by visual inspection from previous work. We querythe VALD for lines very close to our Fe ii lines and calculate howstrong the blend is compared to our lines. We remove the onesthat have significant EW contribution by setting di ff erent isolationthresholds.We also perform an empirical test to remove Fe ii lines usinghigh resolution spectra of 451 solar-type stars with reference stellarparameters ( T e ff , [ Fe / H ], and microturbulence) from our previouswork. Additionally, we combined two iron line lists from the lit-erature to enhance the number of lines or improve the atomic data MNRAS , 1–11 (2018) n the iron ionization balance of cool stars Table 3.
The final Ti lines we extracted from the LW13 line list.lines (Å) EP (eV) log g f
Element4512.73 0.84 –0.40 Ti i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i Figure 9. Di ff erences in log g of the TS13 (red points) with the trigonomet-ric and from Ti of this work with the clean line list of LW13 (green points)with the trigonometric as a function of log g (upper plot) and T e ff (bottomplot). The colored lines in the bottom plot represent the linear fits of the twosamples. The slope of the Ti (green) line is –2.2 · − dex K − . Table 3 – continued lines (Å) EP (eV) log g f Element4330.24 2.05 –1.64 Ti ii ii ii ii ii ii ii ii ii ii ii MNRAS000
Element4512.73 0.84 –0.40 Ti i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i Figure 9. Di ff erences in log g of the TS13 (red points) with the trigonomet-ric and from Ti of this work with the clean line list of LW13 (green points)with the trigonometric as a function of log g (upper plot) and T e ff (bottomplot). The colored lines in the bottom plot represent the linear fits of the twosamples. The slope of the Ti (green) line is –2.2 · − dex K − . Table 3 – continued lines (Å) EP (eV) log g f Element4330.24 2.05 –1.64 Ti ii ii ii ii ii ii ii ii ii ii ii MNRAS000 , 1–11 (2018) M. Tsantaki of the existing. More accurate gravities are derived based on the
Gaia parallaxes in conjunction with precise spectroscopic e ff ectivetemperatures. Using these parameters, we exclude the Fe ii lineswhich give abundances higher than 0.10 dex and dispersion lowerthan 3 σ . The clean Fe ii line list contains 14 lines and is a combi-nation of the TS13 and Meléndez & Barbuy (2009) line list. Theatmospheric parameters for our stellar sample with the new line listshow significant improvement in the derivation of surface gravities,whereas the e ff ective temperature and metallicity are in very goodagreement with TS13. Moreover, the di ff erences between Fe ii –Fe i abundances do not show trends with the e ff ective temperature.Finally, we show that the ionization equilibrium of Ti providesmore accurate surface gravities than iron using for the Ti line listsof Neves et al. (2009) and LW13. Even though surface gravity stillremains the parameter most di ffi cult to constrain via spectroscopy,there are significant improvements presented in this work and inlack of parallax measurements, we can now provide more accuratesurface gravities even for the lower main sequence stars. In thiswork, we propose for the optimal determination of stellar parame-ters, to use the TS13 line list to obtain T e ff and [ Fe / H ], and the Tiline lists for a better determinations of log g . This procedure will beimplemented for public use in FASMA via the webpage.The high quality spectra and reference atmospheric parame-ters of this sample can function very well to test the quality of aline list. With this data, we present an empirical solution to the ion-ization balance problem in cool stars. The bad lines excluded fromthis test can be attributed not only to blending e ff ects but to otherprocesses such as bad normalization, wrong atomic data, and wecannot easily distinguish which of them is responsible. We note thatin this work we did not test the a ff ects of other phenomena, such asthe impact of 3D model atmospheres, non-LTE e ff ects, and stellaractivity to explain the di ff erences between the Fe ii and Fe i abun-dances but from our analysis we expect them to have secondarye ff ects on the results. ACKNOWLEDGMENTS
The authors thank the anonymous referee for the useful comments.M. T., E. D. M., V. Zh. A., N. C. S., and S. G. S. acknowledgethe support from Fundação para a Ciência e a Tecnologia (FCT)through national funds and from FEDER through COMPETE2020by the following grants UID / FIS / / / FIS-AST / / / FIS-AST / / / BPD / / / / / CP1273 / CT0003and in the form of an exploratory project with the same ref-erence. V. Zh. A., N. C. S., and S. G. S. also acknowl-edge the support from FCT through Investigador FCT contractsIF / / / CP1273 / CT0001, IF / / / CP0150 / CT0002,and IF / / / CP1215 / CT0002 funded by FCT (Portugal)and POPH / FSE (EC).This research made use of the Vienna Atomic Line Databaseoperated at Uppsala University, the Institute of Astronomy RAS inMoscow, and the University of Vienna. We thank the PyAstronomyand Astropy communities.This work has made use of data from the European SpaceAgency (ESA) mission
Gaia (https: // / gaia),processed by the Gaia
Data Processing and Analysis Consortium(DPAC, https: // / web / gaia / dpac / consortium). Funding for the DPAC has been provided by national institutions,in particular the institutions participating in the Gaia
MultilateralAgreement.
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