A new spectroscopic calibration to determine T e ff and [ Fe / H ] of FGK dwarfs and giants

We present a new spectroscopic calibration for a fast estimate of Teff and [Fe/H] for FGK dwarfs and GK giant stars. We used spectra from a joint sample of 708 stars, composed by 451 FGK dwarfs and 257 GK-giant stars with homogeneously determined spectroscopic stellar parameters. We have derived 322 EW line-ratios and 100 FeI lines that can be used to compute Teff and [Fe/H], respectively. We show that these calibrations are effective for FGK dwarfs and GK-giant stars in the following ranges: 4500 K < Teff < 6500 K, 2.5 < log g < 4.9 dex, and −0.8 < [Fe/H] < 0.5 dex. The new calibration has a standard deviation of 74 K for Teff and 0.07 dex for [Fe/H]. We use four independent samples of stars to test and verify the new calibration, a sample of giant stars, a sample composed of Gaia FGK benchmark stars, a sample of GK-giant stars from the DR1 of the Gaia-ESO survey, and a sample of FGK-dwarf stars. We present a new computer code, GeTCal, for automatically producing new calibration files based on any new sample of stars.


Introduction
Deriving accurate and precise stellar parameters is a fundamental aspect of astrophysical studies.In order to determine the mass, radius, and age of stars it is necessary to measure stellar atmospheric parameters, such as effective temperature (T eff ), surface gravity (log g), metallicity ([Fe/H]), and microturbulence(v mic ), obtained mainly by spectroscopic or photometric methods (e.g.Casagrande et al. [3], Sousa et al. [12], Tsantaki et al. [20]).
The volume of data being produced by large-survey observational programs [2,4] requires the existence of quick methods to obtain stellar parameters for a diverse range of stellar spectral types.
Methods such as line-strength ratios can be used to obtain T eff [5,6,9], and equivalent widths (EWs) of FeI can be used to derive [Fe/H] [15].The success of these methods is tied to the quality of the empirical calibrations.
One of the spectroscopic methods that can be used to determine spectral parameters is the ARES+MOOG method.This method makes use of the ARES code (to measure the EWs of a spectrum [11,17]), and the MOOG code (to measure individual line abundances) combined with a minimization algorithm in order to derive the parameters of the stellar atmosphere [18].For a more detailed description of this method see Sousa [16].
e-mail: guilherme.teixeira@astro.up.ptAn automated tool, TMCalc, can be used to obtain T eff and [Fe/H] using measurements of EWs of spectral lines [15].It relies on EW line-ratios and on the EWs of FeI lines.The accuracy and precision of this TMCalc are mainly limited by the T eff and [Fe/H] calibrations [15].TMCalc is less accurate than the ARES+MOOG method but it is computationally more efficient.
The main body of this work was presented in detail in Teixeira et al. [19].

Stellar samples
We used six distinct stellar samples: two samples were used for calibration and four other samples were used for independent testing of the new calibration.A summary of each sample can be found in Table 1.
The parameters for each sample have been consistently determined homogeneously with ARES+MOOG.The samples used were: • 451 FGK-dwarf stars described in Sousa et al. [12] that was revised in Tsantaki et al. [20], hereafter the So08 sample.
• 36 GK-giant stars from the Gaia-ESO survey DR1 1 with log g < 3.9, hereafter the GES sample.
For calibration, we used a combination of the So08 and Al15 samples, hereafter the joint sample.The other sample were used to test our new calibration.

Calibration
This work aimed to build new T eff and [Fe/H] spectroscopic calibrations for both FGK dwarfs and GK giants improving upon the work of Sousa et al. [15], hereafter the So12 calibration.The rationale for each step of the calibration procedure can be found in Teixeira et al. [19].

T eff calibration
In order to obtain the T eff calibration we used the established relations between EW line-ratios, R_EW [13].This technique is based on the different sensitivity that metal lines have to T eff .EW line-ratios are more precise than the use of EWs of individual lines [5,6,9,13].
To compute the T eff calibration we: • Selected lines with a difference in excitation potential greater than 3 eV.
• Fitted a linear and a third-degree polynomial function to the distributions of T eff as a function of: a) R_EW; b) 1/R_EW; and c) log R_EW.
• Used a 2-σ cut on the distributions, reffited the functions and selected the fit with the smaller standard deviation.
• Only accepted a function that could fit 2/3 of the calibration sample.

Metallicity calibration
We calibrated the metallicity using only iron absorption lines, as iron abundance is a proxy for stellar metallicity [15].We discarded ionized iron lines given their dependence on log g.We obtained the metallicity calibration by: • Considering only lines with EW < 70 mÅ.
• Solved equation: • Applied the IQR and a 2-σ to a linear fit made with the inversion of the previous equation.
• Made sure that the slope of the comparison between the calibrated and spectroscopic [Fe/H] was within 3% of the identity line.
• Only considered lines if the function had σ < 0.06dex.

GeTCal
As a by-product of our work we created a Python code: GeTCal.This code is a pratical implementation of the methods described in Sects.

Results
Figure 1 compares the computed T eff with the spectroscopic T eff using the different calibrations.The top panel of Fig. 1 shows the previous calibration, the middle panel shows the new calibration and the bottom panel shows the difference between the new calibration and the spectroscopic values.The Te16 calibration improves in the low T eff and low log g regimes, i.e., the giants.
Figure 2 shows the same type of analysis but now for the computed [Fe/H].The bottom panel shows most stars well within 0.2 dex from the zero value.
As shown in Table 3, for the joint sample, the T eff standard deviation is 74 K, and the standard deviation of [Fe/H] is 0.07 dex for the Te16 calibrations.
The limits of the Te16 calibration reflect the parameters of the calibration sample and are presented in Table 2.  Higher uncertainties will result from using the Te16 calibration outside the applicability limits [19].
After obtaining the Te16 calibration for T eff and [Fe/H], we applied it to the four independent samples.Figure 3 shows the comparison of T eff results between the Te16 calibration and the values from spectroscopy for the validation samples.Stars outside the limits of the Te16 calibration (log g < 2.5) are not plotted.
The results for the [Fe/H] computation of the independent samples are shown in Fig. 4. The outliers are stars with low-log g values and T eff and, therefore, very close to our applicability limits (see Table 2).
A summary of the application of the Te16 calibration to the various validation samples is provided in Table 3.

Conclusions
We presented new calibrations to obtain T eff and [Fe/H] from the EWs of stellar spectra.These calibrations cover both FGK dwarfs and GK giants simultaneously [19].The Te16 calibration is effective within the range of 4500K < T eff < 6500K, 2.5 < log g < 4.9 dex, and −0.8 < [Fe/H] < 0.5 dex.
We built a Python code, GeTCal, capable of computing T eff and [Fe/H] calibrations for any given sample of calibration stars.This program produces calibration files compatible with the existing TMCalc code.
This work provides a fast way to determine stellar atmospheric parameters from spectrographic observations of FGK-dwarf and GK-giant stars.

Figure 1 :
Figure 1: Comparison between the T eff computed in this work and the spectroscopic values with the So12 calibration (top panel) and the Te16 calibration (middle panel) for the joint sample.The line in the two plots represents the identity line, the standard deviation is plotted as the cross in both panels.In the bottom panel we show the difference between the Te16 calibration and the spectroscopic T eff as a function of T eff , the error bars represent the errors in our computation.The plots are colourcoded for log g.Figure from [19].

Figure 2 :
Figure 2: Comparison between the [Fe/H] computed in this work and the spectroscopic values for the So12 calibration (top panel) and the Te16 calibration (middle panel) for the joint sample.The black line represents the identity line, the standard deviation is shown as the cross.The bottom panel shows the difference between [Fe/H] from spectroscopy and the one in this work as a function of [Fe/H], the error bars are the errors resulting from this work.The plots are colour-coded for log g.Figure from [19].

Figure 3 :
Figure 3: Comparison between the T eff computed with TMCalc and the spectroscopic values with the Te16 calibration for the Gaia (closed triangles), Sa09 (circles), GES (open diamonds), and So11 (closed squares) sample.The colour-code represents the log g values and the black line represents the identity line.Only stars within the limits of applicability are plotted.

Figure 4 :
Figure 4: Comparison between the [Fe/H] computed with TM-Calc and the spectroscopic values with the Te16 calibration for Gaia closed triangles), Sa09 (circles), GES (open diamonds), and So11 (closed squares) sample.The colour-code represents the log g values and the black line represents the identity line.Only stars within the limits of applicability are plotted.

Table 1 :
Summary of the stellar samples.

Table 2 :
Limits of applicability of the Te16 calibration.

Table 3 :
Application of the Te16 calibration to the samples.This code is freely distributed and available for use by the community 2 .