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Appendix A: Nodes and methods

The UVES data of late-type stars are analyzed in parallel by 13 different Nodes. The details of each analysis methodology and the codes employed are described in the subsections below. Table 2 summarizes some characteristics of the methodology employed by each Node.

Appendix A.1: Bologna

The Bologna Node employs the classical EW method for determining atmospheric parameters and abundances. The atmospheric parameters are determined by erasing any trend of the abundances of the iron lines with excitation potential and with EW, and by minimizing the difference between the abundances given by ionized and neutral iron lines. A final health check of the method is provided by verifying that no significant trend of iron abundances with wavelength is present. Abundances are derived for each absorption line of the species of interest.

To measure EWs, the automated FORTRAN code DAOSPEC (Stetson & Pancino 2008, 2010) is used. DAOSPEC is designed to measure EWs in high-resolution (R ≥ 15 000) high-S/N stellar spectra (≥30). Upon request, the code normalizes the spectrum by adjusting, iteratively, polynomials to the residuals spectrum (i.e., a spectrum obtained by removing all measured lines from the original spectrum). DAOSPEC provides a global uncertainty of the fit in the form of an average root mean square (rms) of the residuals spectrum, a radial velocity measurement (with its 1σ spread and the number of lines on which it is based), and the EWs with their uncertainty and quality parameters.

DAOSPEC can be somewhat difficult to configure, especially when many spectra with different properties, i.e., S/N, line crowding, full width half maximum (FWHM) and exact spectral coverage, need to be measured in a short time, as is the case for Gaia-ESO. Therefore, the code is executed through a wrapper that automatically configures many of its parameters, providing all the statistics and graphical tools to explore the results and correct the deviant cases. This wrapper program is called DOOp (DAOSPEC Option Optimizer Pipeline, Cantat-Gaudin et al. 2014a).

Finally, to derive the atmospheric parameters and elemental abundances automatically, the code GALA²⁰ is used (Mucciarelli et al. 2013). GALA is based on the Kurucz suite of abundance calculation codes (Kurucz 2005; Sbordone et al. 2004). GALA can run starting from a random first guess of the atmospheric parameters and converges rapidly to meaningful solutions for spectra with the resolution, S/N, and wavelength coverage of the UVES spectra analyzed here. GALA performs a rejection of too weak or too strong absorption lines (the limits are set around the log  (EW/λ) ≃−4.7 and −5.9, depending on the star), selects only lines having a certain measurement error (cutting above 5−20%, depending on the spectrum), and performs a sigma-clipping rejection in abundance (set to 2.5σ). GALA provides uncertainties on the atmospheric parameters and on the derived abundances, both in the form of a 1σ spread of the abundances of each line (together with the number of lines used for each species) and in the form of errors on the abundances induced by the uncertainties on the atmospheric parameters (using the prescription of Cayrel et al. 2004, in the case of the present analysis).

Appendix A.2: Catania (OACT)

The Catania Node uses the code ROTFIT, developed by Frasca et al. (2003, 2006) in IDL²¹ software environment. The code originally performed only an automatic MK spectral classification and vsini measurement minimizing the χ² of the residual (observed − reference) spectra. The reference spectra come from an adopted spectrum library and are artificially broadened by convolution with rotational profiles of increasing vsini. The code was later updated for evaluating the atmospheric parameters T_eff, log g, and [ Fe / H ] with the adoption of a list of reference stars with well-known parameters (e.g., Guillout et al. 2009).

Unlike codes based on the measurements of EWs and curves of growth, ROTFIT can be applied to the spectra of FGK-type stars with relatively high rotational velocity (vsini≥ 20 km s^-1), where the severe blending of individual lines either hampers or absolutely prevents the use of the above methods. Nevertheless, the analysis was limited to stars with vsini≤ 300 km s^-1.

A reference library composed of 270 high-resolution (R = 42 000) spectra of slowly-rotating FGKM-type stars available in the ELODIE archive (Prugniel & Soubiran 2001) was used. For most of these reference stars, basically those with spectral type in the range from mid-F to late-K, the atmospheric parameters have been redetermined by L. Spina using the EPInArBo methodology (see Sect. A.5). For the remaining few stars, either the recent values tabulated in the PASTEL catalog (Soubiran et al. 2010) or derived in the works of Rojas-Ayala et al. (2012) and Boyajian et al. (2012) for M-type dwarfs, were used. Although the parameter space is not regularly sampled, the reference stars cover all regions relevant for analysis of FGK-type stars with [Fe/H] ≥ − 2.0.

Segments of the spectra with 100 Å each are analyzed independently. Spectral regions heavily affected by telluric lines and the cores of Balmer lines, that can be contaminated by chromospheric emission, are excluded. The final stellar parameters T_eff, log g, [ Fe / H ], and vsini, are the averages of the results of each i-th spectral segment weighted according to the of the fit and to the amount of information contained in the segment, which is expressed by the total line absorption f_i = ^∫(F_λ/F_C − 1)dλ. The uncertainties of T_eff, log g, [ Fe / H ], and vsini are the standard errors of the weighted means added in quadrature to the average uncertainties of the stellar parameters of the reference stars evaluated as ±50 K, ±0.1 dex, ±0.1 dex, and ±0.5 km s^-1 for T_eff, log g, [ Fe / H ], and vsini, respectively. Moreover, the MK spectral type and luminosity class of the star is also provided. They are defined as those of the reference star that more frequently matches the target spectrum in different spectral regions.

Appendix A.3: CAUP

The CAUP Node determines the stellar atmospheric parameters (T_eff, log g, ξ) and the metallicity automatically, with a method used in previous works now adapted to the Gaia-ESO Survey (e.g., Sousa et al. 2008, 2011). The method is based on the excitation and ionization balance of iron lines using [Fe/H] as a proxy for the metallicity. The list for the iron lines used to constrain the parameters was selected from the Gaia-ESO line list using a new procedure described in detail in Sousa et al. (2014).

The EW of the lines are automatically determined using the ARES²² code (Sousa et al. 2007), following the approach of Sousa et al. (2008, 2011) to adjust ARES according to the S/N of each spectrum.

The stellar parameters are computed assuming LTE using the 2002 version of MOOG (Sneden 1973) and the MARCS grid of models. For that purpose, the interpolation code provided with the MARCS grid was modified to produce an output model readable by MOOG. Moreover, a wrapper program was implemented on the interpolation code to automatize the method.

As damping prescription, the Unsld approximation multiplied by a factor recommended by the Blackwell group (option 2 within MOOG) was used. The atmospheric parameters are inferred from the previously selected Fe i-Fe ii line list. A minimization algorithm, the Downhill Simplex Method (Press et al. 1992), is used to find the best parameters. In order to identify outliers caused by incorrect EW values, a 3σ clipping of the Fe i and Fe ii lines is performed after a first determination of the stellar parameters. After this clipping, the procedure is repeated without the rejected lines. The uncertainties in the stellar parameters are determined as in previous works (Sousa et al. 2008, 2011).

Individual abundances are derived using the same tools and methodology as described above, but using the 2010 version of MOOG (see Neves et al. 2009; Adibekyan et al. 2012, for details). The line list for elements other than Fe was selected through the cross-matching between the line list used by Adibekyan et al. (2012) and the line list provided by Gaia-ESO. The atomic data from the Gaia-ESO Survey was adopted. The errors for the abundances represent the line-to-line scatter.

Appendix A.4: Concepcion

The Concepcion Node uses the abundances from Fe i and Fe ii lines to obtain atmospheric parameters using the classical EW method. The atmospheric parameters are determined by satisfying the excitation and ionization equilibrium, and by minimizing trends of abundance with EW. The spectroscopic optimization of all the atmospheric parameters is achieved simultaneously.

The EWs are determined with the automatic code DAOSPEC (see description in Sect. A.1). The code adopts a saturated Gaussian function to fit the line profile and a unique value for the FWHM for all the lines. The input values of FWHM are derived manually using the IRAF²³ task splot, leaving DAOSPEC free to readjust the values according to the global residual of the fitting procedure. The measurement of EWs is repeated by using the optimized FWHM value as a new input value until convergence is reached at a level of 5%. The EWs are measured after a renormalization of the continuum, to remove any residual trends introduced during the data reduction.

GALA is used to determine the atmospheric parameters and elemental abundances (see description of GALA in Sect. A.1). Starting from an initial guess of atmospheric parameters, GALA converges rapidly to a meaningful solution. Finally, it computes accurate internal errors for each atmospheric parameter and abundance. When the initial set of parameters are poorly known or in cases of large uncertainties, the guess working-block of GALA is used. This working-block verifies the initial parameters quickly by exploring the parameters space in a coarse grid, saving a large amount of time. In addition, the errors in the EW measurement obtained from DAOSPEC are provided as an input, so the best model atmosphere is computed taking the abundance uncertainties of the individual lines into account.

Appendix A.5: EPInArBo

The EPInArBo (ESO-Padova-Indiana-Arcetri-Bologna) Node performs the spectral analysis with the codes DOOp and FAMA (Fast Automatic Moog Analysis, Magrini et al. 2013)²⁴. The former (described in Sect. A.1) makes it more convenient to measure EWs in hundreds of spectra in a single batch. The latter is an automation of the 1D-LTE code MOOG and allows the determination of stellar parameters and individual element abundances.

The EWs are measured after a renormalization of the continuum. Each line is measured using a Gaussian fit. Equivalent widths between 20−120 mÅ were used for Fe i and Fe ii lines and between 5−120 mÅ for lines of other elements.

FAMA uses the EWs of Fe i and Fe ii to derive stellar parameters (T_eff, log g, [Fe/H], and ξ). A set of first-guess parameters are first produced using the available photometric data and information from the target selection, using the following steps:

• 1.

  A first guess estimation of T_eff is given by the Alonso et al. (1999) and Casagrande et al. (2010) relations for both cluster and field stars.

• 2.

  The cluster parameters, such as distance, age, and reddening, available in the reports prepared by Gaia-ESO WG 4 (cluster stars target selection, see Bragaglia et al., in prep.) are used to fix the surface gravity.

• 3.

  For the field stars, the information available from target selection is used (i.e., whether the star was a turn-off dwarf or bulge/inner-disk giant) to set a first guess gravity.

The stellar parameters are obtained by searching iteratively for the three equilibria, excitation, ionization, and the trend between log n(Fe I) and log  (EW/λ), i.e., with a series of recursive steps starting from a set of initial atmospheric parameters and arriving at a final set of atmospheric parameters that fulfills the three equilibrium conditions.

The convergence criterion is set using information on the quality of the EW measurements, i.e., the minimum reachable slopes are linked to the quality of the spectra, as expressed by the dispersion σ_FeI around the average value ⟨log n(FeI)⟩. This is correct in the approximation that the main contribution to the dispersion is due to the error in the EW measurement rather than to inaccuracy in atomic parameters, e.g., the oscillator strengths (log gf).

Appendix A.6: IAC-AIP

The IAC-AIP Node employs the optimization code FERRE to identify the combination of atmospheric parameters of a synthetic model that best matches each observed spectrum. FERRE searches for the best solution in a χ² sense using the Nelder-Mead algorithm (Nelder & Mead 1965), and the model evaluation is sped up by holding a precomputed grid in memory and interpolating within it. The algorithm is the same as described by Allende Prieto et al. (2006) for the analysis of SDSS/SEGUE data and by Ahn et al. (2014) for the analysis of SDSS/APOGEE spectra. Model interpolations are carried out with cubic Bezier splines, whose accuracy has been studied in detail by Mészáros & Allende Prieto (2013). For each spectrum, five searches initialized at randomly chosen points on the parameter space are performed and the best solution is retained.

The adopted grid of model spectra was not the one described in Sect. 5.3. It was calculated using the code Turbospectrum (Alvarez & Plez 1998; Plez 2012) based on MARCS model atmospheres with the VALD3 line list (Kupka et al. 2011), with updates on log gf values according to the Gaia-ESO line list version 3.0. The parameter range covered by the grid is: T_eff = 3000−7000 K, log g = 0.0−5.0, [Fe/H] = −2.5−+1.0, vsini = 1−128 km s^-1, ξ = 0.5−4 km s^-1, and [α/Fe] = −0.4−+0.4. The model spectra were smoothed by Gaussian convolution to the resolving power of the observations (R = 47 000). To speed up the analysis, the [α/Fe] is tied to the overall metallicity of each star, i.e., with enhanced [α/Fe] ratios at low metallicity, while ξ is tied to both T_eff and log g according to the Gaia-ESO microturbulence relation for the iDR1 analysis.

We use all of the individual UVES orders before they are merged, excluding only regions with many telluric lines and the core of the Hα line. The continuum for both the observations and the models is set by cutting the spectra into 2 Å wide chunks, dividing each chunk by its mean value, and all spectra are weighted according to their variance. All observations are shifted to rest wavelength. When only one value of v_rad is available in the header, this value was used. If two values were present (one for each CCD), the average value was used. In case no velocity was available, a cross correlation using a hot template star (T_eff = 7000 K, log g = 2) spun up to 50 km s^-1 was used to derive the radial velocity. If this failed, a value of 0.0 km s^-1 was used.

Appendix A.7: Liège

The Liège Node performs the analysis using the GAUFRE tool (Valentini et al. 2013). GAUFRE is a C++ code that performs the determination of atmospheric parameters and abundances in an automatic way. The tool is made up of several subprograms with specific tasks (see Valentini et al. 2013, for details). For the Gaia-ESO Survey UVES spectra, GAUFRE-EW is used. This subprogram determines T_eff, log g, [M/H], and ξ, in an iterative way using the EWs of Fe lines.

The starting point is the normalization of the spectrum and the measurement of the EWs of every line present in the input line list (when detectable). The program selects a spectral range of 3−4 Å around the line center and the spectrum is then fitted with a polynomial function in order to determine the continuum and the line position. At this stage several parameters, such as the degree of the function and the amplitude of the spectral range to fit, can be defined by the user.

The program then feeds MOOG with the measured EWs and an appropriate MARCS model atmosphere. Within the errors, the MOOG results must satisfy four conditions: fulfill the Fe ionization and excitation equilibria, show no dependence between the Fe i abundances and log  (EW/λ), and, finally, yield a mean metallicity identical to that of the adopted model atmosphere. The appropriate MARCS model atmosphere is derived by interpolating within the MARCS grid.

The program iterates until the four conditions are fulfilled. The Downhill Simplex Method (Nelder & Mead 1965; Press et al. 2002) is adopted for estimating the new set of atmospheric parameters at each iteration. The starting point of the process can be determined by the user. Photometric temperatures using Ramírez & Meléndez (2005) and, when available, log g from asteroseismology were adopted. When no information from photometry or asteroseismology is available, the starting point is set to T_eff = 5000 K, log g = 4.0 dex, [M/H] = 0.0 dex, and ξ = 1.0 km s^-1.

The uncertainty in T_eff is derived from the standard deviation of the least-squares fit of the Fe i abundance vs. excitation potential. The uncertainty in log g is determined by propagating the uncertainty in T_eff. The uncertainty in ξ is calculated based on the standard deviation of the least-squares fit of the Fe i abundance vs. log  (EW/λ). The uncertainty in [Fe/H] takes into account the uncertainties in T_eff, log g, ξ, and the line-to-line scatter of the Fe i abundances.

Appendix A.8: LUMBA

The LUMBA (Lund-Uppsala-MPA-Bordeaux-ANU) Node uses a stellar parameter and abundance pipeline (hereafter referred to as SGU) that is based upon the SME (Spectroscopy Made Easy) spectrum synthesis program (Valenti & Piskunov 1996)²⁵. SME is a suite of IDL and C++ routines developed to compute theoretical spectra and perform a χ² fit to observed spectra. The code assumes LTE and plane-parallel geometry. Chemical equilibrium for molecules is determined as described in Valenti et al. (1998).

A detailed description of the SGU pipeline will be published elsewhere (Bergemann et al. 2014c, in prep.). Briefly, in the SGU pipeline, synthetic spectra are computed in predefined wavelength segments, which are 5 to 20 Å wide. The selected line list is a reduced version of the Gaia-ESO version 3.0 line list and includes the atomic and molecular blends relevant for the analysis of FGKM-type stars. Basic stellar parameters are determined iteratively, exploring the full parameter space in T_eff,log g, [Fe/H], micro- and macro-turbulence. The number of iterations varies, depending on the stellar parameters, value of the goodness-of-fit test (χ²), and convergence. The main purpose of SGU is to control the sequence of steps that defines the parameters to solve for in the current iteration, and specify the wavelength regions to include in the test statistics. Usually, three to four steps for dwarfs and subgiants, and two steps for giants are used. The wavelength regions (referred to as “masks”) to be included in the χ² fit also vary, depending on the step. The masks cover the lines of H i (H_β and H_α), Mg i triplet at 5170 Å, and a carefully selected set of Fe lines. In total, about 60 diagnostic Fe i and Fe ii transitions are used. The merged not normalized Gaia-ESO spectra are used with a runtime continuum normalization. For the abundance analysis, special masks were developed, which cover the lines of selected elements. For iDR1, atmospheric parameters were computed assuming LTE. For iDR2, the pipeline was modified to include NLTE corrections in Fe (Bergemann et al., in prep.). That resulted in improved stellar parameters (especially log  g) for low-metallicity stars. Further, the effects were quite small for more metal-rich stars. Abundances are determined in the last step using stellar parameters from the previous runs.

Errors in the other stellar parameters are estimated from internal SME errors based on S/N and Fe line-to-line scatter (but in many cases, lines of different elements were used to derive stellar parameters, including H and Mg), combined with the spread in differences between our results for the benchmark stars library and those values that have been deemed acceptable.

Appendix A.9: Nice

The Nice Node analysis is based on the automated stellar parametrization pipeline developed for the AMBRE Project (Worley et al. 2012). At the core of the pipeline is the stellar parametrization algorithm MATISSE (MATrix Inversion for Spectrum SynthEsis), developed at the Observatoire de la Côte d’Azur primarily for use in the Gaia RVS (Radial Velocity Spectrometer) stellar parametrization pipeline (Recio-Blanco et al. 2006), and the Gaia-ESO synthetic spectrum grid (see Sect. 5.3).

MATISSE is a local multilinear regression method that simultaneously determines the stellar parameters (θ) of an observed spectrum O(λ) by the projection of the spectrum onto vector functions B_θ(λ). A B_θ(λ) function is constructed as an optimal linear combination of the local synthetic spectra S(λ). The stellar parameters determined by the Nice Node are T_eff, log g, a global metallicity [M/H], and a global α-element abundance over iron ([α/Fe]: α = O, Ne, Mg, Si, S, Ar, Ca, and Ti).

To minimize the impact of mismatches between the observed and synthetic spectra, a solar flux spectrum (Wallace et al. 1998) and an Arcturus spectrum (Hinkle et al. 2000) are compared with corresponding Gaia-ESO synthetic spectra in the UVES spectral range. About 24% of the UVES domain is discarded because of telluric/instrumental contamination. A further 4% is discarded for differences between the observed and synthetic normalized fluxes greater than 10% for the Sun or 20% for Arcturus. These limits grossly reject discrepant spectral features (errant lines or blatant mismatched regions) between the observed and synthetic spectra. The resulting comparison prior to any normalization optimisation shows for the remainder that 95% (resp. 80%) of the pixels have less than 5% difference between the Sun (resp. Arcturus) and the corresponding synthetic spectrum, while 94% of the pixels have flux differences less than 10% in the case of Arcturus. As MATISSE uses all the available pixels for the parameter determination, any few discrepant pixels remaining after the full iterative normalisation have little effect on the result.

The final wavelength domain totals 1447 Å between 4790 Å and 6790 Å with 18 080 pixels at a sampling of 0.08 Å/px. The synthetic spectra are convolved with a Gaussian kernel (FWHM = 0.2254 Å) for a resolution range from R~ 21 000 (4790 Å) to R~ 30 000 (6790 Å). The observed spectra are convolved to the same resolution using a transformation FWHM based on the measured spectral FWHM and grid FWHM.

The Nice pipeline consists of spectral processing (v_rad correction; cleaning/slicing/convolution; normalization to synthetic spectra), and stellar parameter determination by MATISSE (SPC stage in Fig. 4 of Worley et al. 2012). At each iteration of these last two stages, improved estimates of the stellar parameters provide new synthetic spectra for use in the normalization until there is convergence on the final stellar parameters.

Calibration and validation of the pipeline was undertaken using three key samples: the Gaia-ESO Benchmarks (see Sect. 7.1); the spectral library of Jofré et al. (2014); and the AMBRE:UVES#580 PASTEL data set (Worley et al., in prep.), a sample of 2273 slit spectra that have high quality spectroscopic stellar parameters cited in the PASTEL catalog. These three samples were used to calibrate the convolution and normalization in the spectral processing by comparison of processed spectra with synthetic spectra and by comparing the MATISSE parameters with the accepted parameters for each sample.

Appendix A.10: Paris-Heidelberg

The Paris-Heidelberg Node uses the automatic parameter determination and abundance analysis code MyGIsFOS (Sbordone et al. 2014). MyGIsFOS strictly replicates a “traditional”, or “manual”, parameter determination and abundance analysis method in a fully automated fashion. To do so, MyGIsFOS determines EWs and abundances for a number of Fe i and Fe ii features, and looks for the atmospheric parameters (T_eff, log g, ξ) that satisfy the excitation and ionization equilibrium, and that minimize trends of abundance with EW. MyGIsFOS uses a precomputed grid of synthetic spectra instead of relying on on-the-fly synthesis or on a priori EW measurements. By fitting against synthetic spectra, MyGIsFOS can use moderately blended features in abundance measurements, or treat directly HFS-affected lines. A summary of how MyGIsFOS works follows:

• 1.

  A grid of synthetic spectra varying (in the most general case) inT_eff, log g, ξ, [Fe/H], and [α/Fe] is provided to the code together with the input spectra (for which initial guess parameters have to be provided), and a set of spectral “regions” to be used either as pseudocontinuum ranges (for normalization) or as spectral features of various kinds (e.g., Fe i lines).

• 2.

  The observed spectrum, and each spectrum in the synthetic grid, are pseudonormalized using the continuum intervals, then the synthetic grid is collapsed (by interpolation) at the initial guess values for T_eff, log g, ξ and [α/Fe], leaving a grid whose sole dimension is [Fe/H].

• 3.

  The provided Fe i and Fe ii lines are fitted (by χ²-minimization) against the collapsed grid, deriving best-fit Fe i abundances for each line. EWs are also measured in the process. In a series of nested loops, the aforementioned diagnostics (excitation and ionization equilibrium, etc.) are evaluated, and if needed, the stellar parameters are altered, and the whole process repeated, until convergence is achieved.

• 4.

  To measure abundances of other elements, the respective features are fitted against the same grid, collapsed at the final values of T_eff, log g, ξ, and thus varying in [Fe/H]. The best fitting metallicity value is used as the element [X/H] (this is in principle inconsistent but leads to generally accurate values, see Sbordone et al. 2014). A special case is α-elements, which are measured first after T_eff, log g, and ξ have been set, and used to estimate the last grid parameter, [α/Fe]. The derived value of [α/Fe], if different enough from the estimated, triggers a new estimation of the other parameters. Finally, all the other elements are measured.

After processing, the output is examined for signs of problems: nonconverging objects are checked individually and eventually rerun. MyGIsFOS does not estimate or vary the spectrum broadening: the grid is provided broadened at the nominal resolution of R = 47 000. Stars showing extra-broadening (essentially moderately rotating objects) are detected by inspecting the quality of line fits, and reprocessed with appropriate broadening.

For GESviDR1Final, T_eff was not iterated within MyGIsFOS, since this was not yet implemented. Instead, T_eff was determined from the available photometry by applying the González Hernández & Bonifacio (2009) relations. Full T_eff iteration is now in place and was used in the analysis of iDR2. In addition, MyGIsFOS is using the Gaia-ESO grid of synthetic spectra that does not include a ξ dimension, but relies on a single, precalibrated ξ value depending on T_eff, log g, and [Fe/H]. Thus, MyGIsFOS is not determining ξ for the Gaia-ESO data. In the future, when a new grid of synthetic spectra with the ξ dimension is available, this quantity will also be determined.

Appendix A.11: UCM

The UCM Node employs the automatic code StePar (Tabernero et al. 2012) to determine the stellar atmospheric parameters (T_eff, log g, ξ) and metallicity. StePar computes the stellar atmospheric parameters using MOOG (v.2002). Although designed to make use of a grid of Kurucz ATLAS9 plane-parallel model atmospheres (Kurucz 1993), StePar has been now modified to operate with the spherical and nonspherical MARCS models.

The atmospheric parameters are inferred from a previously selected Fe i-Fe ii line list. The code iterates until it reaches the excitation and ionization equilibrium and minimizes trends of abundance with log (EW /λ). StePar employs a Downhill Simplex Method (Press et al. 1992). The function to minimize is a quadratic form composed of the excitation and ionization equilibrium conditions. The code performs a new simplex optimization until the metallicity of the model and the iron abundance are the same.

Uncertainties for the stellar parameters are derived as described in Tabernero et al. (2012). In addition, a 3σ rejection of the Fe i and Fe ii lines is performed after a first determination of the stellar parameters. StePar is then rerun without the rejected lines.

The EW determination of all the lines was carried out with the ARES code. The approach of Sousa et al. (2008) to adjust the parameters of ARES according to the S/N of each spectrum was followed. Regarding the individual abundances, two line lists were prepared: one for dwarfs (log  g≥ 4.0) and one for giants (log  g≤ 4.0). To get the individual abundances, the EWs are fed to MOOG and then a 3σ-clipping for each chemical element is performed.

Appendix A.12: ULB

The ULB Node uses the BACCHUS (Brussels Automatic Code for Characterizing High accUracy Spectra) code, which consists of three different modules designed to derive EWs, stellar parameters, and abundances, respectively. The current version relies on (i) a grid of MARCS model atmospheres; (ii) a specific procedure for interpolating among the model atmosphere thermodynamic structure within the grid (Masseron 2006); and (iii) the radiative transfer code Turbospectrum.

The stellar parameters determination relies on a list of selected Fe lines. The first step consists in determining accurate abundances for the selected lines using the abundance module for a given set of T_eff and log g values. The abundance determination module proceeds in the following way: (i) a spectrum synthesis, using the full set of (atomic and molecular) lines, is used for local continuum level finding (correcting for a possible spectrum slope); (ii) cosmic and telluric rejections are performed; (iii) local S/N is estimated; and (iv) a series of flux points contributing to a given absorption line is selected. Abundances are then derived by comparing the observed spectrum with a set of convolved synthetic spectra characterized by different abundances. Four different diagnostics are used: χ² fitting, core line intensity comparison, global goodness-of-fit estimate, and EW comparison. A decision tree then rejects the line, or accepts the line and keeps the best matching abundance.

The second step consists in deducing the EWs of Fe lines using the second module. One asset of the code is precisely this computation of EWs from best-matching synthetic spectra, because the EW of only the considered line is taken into account (excluding the contribution from nearby, blending lines). Indeed, EWs are computed not directly on the observed spectrum, but internally from the synthetic spectrum with the best-matching abundance. This way, the information about the contribution of blending lines is known, allowing a clean computation of the EW of the line of interest.

The last step of the procedure consists in injecting the derived EWs in Turbospectrum to compute abundances for a grid of 27 neighbor model atmospheres (including three values of effective temperature, three of gravity, and three of microturbulence velocity), covering the parameter space of interest. For each model, the code computes the slopes of abundances against excitation potential and against EWs, as well as Fe i and Fe ii lines abundances.

The final parameters are determined by requesting that the ionization equilibrium is fulfilled, and that simultaneously null slopes for abundances against excitation potential and against EWs are obtained. The whole procedure is iterated once per star, after a first guess of stellar parameters has been refined and a new seed model computed.

Appendix A.13: Vilnius

The Vilnius Node uses a traditional EW based method for the stellar parameters determination. Effective temperature is derived by minimizing the slope of abundances obtained from Fe i lines with respect to the excitation potential. Surface gravity is determined by forcing the measured Fe i and Fe ii lines to yield the same [Fe/H] value. Microturbulence is determined by forcing Fe i abundances to be independent of the EWs of the lines. A custom wrapper software was developed to measure EWs, and compute the main atmospheric parameters and abundances automatically.

Equivalent widths were measured using the DAOSPEC software. The atomic and molecular data provided by the Gaia-ESO line list group were used. Only lines corresponding to the best quality criteria (flags provided together with the line list) were used. Different subsamples of lines were used for giant stars and for metal-poor stars.

The stellar atmospheric parameters were computed using MOOG (v.2010) and the MARCS atmospheric models. The interpolation code provided with the MARCS grid was modified to make possible an automatic selection of the required sets of models and the extraction of the final interpolated model in the WEBMARCS format for MOOG.

The wrapper code performs an iterative sequence of abundance calculations using a simultaneous quadratic minimization of: (i) abundance dependency on the line excitation potential; (ii) difference between neutral and ionized iron abundances; and (iii) scatter of neutral iron abundances. Iterations were performed on each step until a stable solution was reached. The minimization procedure was based on the Nelder-Mead method (Nelder & Mead 1965). During this iterative procedure, the code searches for possible outliers in abundances determined using different lines. Every resulting abundance for every single line that departed from the mean by more than 2σ was flagged as outlier and was omitted from further calculations.

A starting point was selected randomly in a vicinity of T_eff = 5500 K, log g = 4.0, [Fe/H] = −0.5 and ξ = 1.5 km s^-1. The final values of atmospheric parameters for a specific star do not depend on the starting point of the calculations. The final abundances of all other elements were derived omitting possible outliers using a 2σ criteria.

The uncertainties of the stellar parameter were determined using error estimations of the line profile fitting and the standard deviations of the abundances. The uncertainty for the effective temperatures was estimated by obtaining the boundary temperature values of the possible satisfactory parameter space, using the error of the linear regression fit. The uncertainty of the gravity was obtained using the possible boundary values of log g, using the standard deviations of the abundances from Fe i and Fe ii lines. The uncertainty of the microturbulence velocity is obtained by employing the error of the standard deviation of the neutral iron abundances. The [Fe/H] standard deviation is adopted as the metallicity uncertainty.

Appendix B: The science verification analysis

	Fig. B.1 Distribution of the median S/N of the spectra in iDR1 (508 FGK-type stars) observed with UVES. Each of the two UVES spectrum parts (from each CCD) is counted separately (thus, two spectra per star). Red dashed lines indicate S/N = 20. Samples of the solar neighborhood (GES_MW), open clusters (GES_CL), and calibration targets (GES_SD) are shown separately.
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The science verification analysis was the first full analysis cycle of the Survey. The first few papers with Gaia-ESO data are based on results of this first analysis (e.g., Bergemann et al. 2014; Cantat-Gaudin et al. 2014b; Donati et al. 2014; Friel et al. 2014; Magrini et al. 2014; Spina et al. 2014). We therefore believe it is important to document the details, achievements, and shortcomings of this analysis. We document in particular the differences between this analysis and the analysis of iDR2, described in the main text. The data analyzed was part of the first internal data release (iDR1), described below:

• Internal Data Release 1 (iDR1): this data release consists ofspectra obtained up to the end of June 2012 and includes spectra of576 FGK-type stars observed with UVES. Of these stars, 68 arepart of young open clusters (age <100 Myr). They were not analyzed by WG11 but by the working group responsible for pre-main-sequence stars (Lanzafame et al. 2014). For the moment, the results have been released only internally to the Gaia-ESO collaboration and are referred to as GESviDR1Final (Gaia-ESO Survey verification internal data release one). We point out that the reduced spectra for part of the stars observed in the first six months are already available through the ESO data archive²⁶.

The S/N distribution of the iDR1 data are shown in Fig. B.1. Table B.1 summarizes the number of stars part of iDR1. Figure B.2 shows how the stars targeted in the first six months of Gaia-ESO observations are distributed in the T_eff − log g plane. Atmospheric parameters were determined for 421 stars out of the 508 in the sample. For the remaining stars, the analysis failed for different reasons (low S/N, fast rotation, reduction artefacts, etc.). Flags will be provided indicating the reason for the failure.

In the sections that follow, we discuss separately the data products determined in the analysis of the iDR1 data, i.e., EWs (Appendix B.1), stellar atmospheric parameters (Appendix B.2), and elemental abundances (Appendix B.3). The differences between this analysis and that of iDR2 are highlighted.

Appendix B.1: EWs in iDR1

Fig. B.2 Distribution of 421 FGK-type stars from GESviDR1Final in the Teff − log g plane. The stars were observed with UVES during the first six months of the Survey and had atmospheric parameters determined as described in this paper. The panels are divided according to metallicity. Black stars represent field stars, red crosses stars observed in open-cluster fields, and blue circles stars observed in globular-cluster fields.

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The Nodes that determined EWs for the iDR1 data set were: Bologna, CAUP, Concepcion, EPInArBo, UCM, ULB, and Vilnius. Three codes were used to measure EWs automatically: ARES, BACCHUS (T. Masseron, unpublished, see Sect. A.12), and DAOSPEC. Of these codes, BACCHUS was not included in the iDR2 discussion.

We include here figures similar to those discussed in the main text about iDR2. A comparison between these plots can show the evolution of the measurements between one iDR and the next.

Figure B.3 shows the comparison between the EWs of Fe i lines measured by different groups in the two stars discussed in Sect. 6 (the metal-poor dwarf HD 22879 with S/N ~ 260 and the metal-rich giant Trumpler 20 MG 781 with S/N ~ 50).

The EWs measured with the same code by different Nodes (left and center-left plots in Fig. B.3) tend to agree to within 2σ, although a systematic difference is present in some case. When comparing the EWs measured with ARES and DAOSPEC (center-right plots in Fig. B.3), it is noticeable that the scatter increases. As discussed before, this is probably related to the different ways that the continuum is defined in each code (global vs. local continuum for DAOSPEC and ARES, respectively).

The comparison between BACCHUS and the other two codes (right plots in Fig. B.3) show systematic differences that are under investigation. BACCHUS measures the EWs not from the observed spectrum, but from a best fitting synthetic spectrum once the abundance and the parameters are fixed. It removes from the line the contribution of any known blending feature that is included in the line list. The synthetic line is computed in 1D LTE, using all the line information possible: line broadening, HFS, and blends. In this sense, the BACCHUS EWs should be the more robust measurements (assuming that the atmospheric parameters are perfectly known and that the blends are perfectly synthesized). The continuum placement might be another source of error. BACCHUS fits the continuum relying on the synthetic spectrum, adapting it from star to star, and from wavelength region to wavelength region. However, if the continuum match is poor around the measured line, the continuum may be wrong, and so will the final abundance and EW. The issue is complex and we are investigating the causes of the discrepancies and improving the measurements for future releases.

Fig. B.3 Comparison between Fe i equivalent widths measured by different Nodes for two stars. Top row: star HD 22879, a benchmark star used for calibration with Teff = 5786 K, log g = 4.23, and [Fe/H] = −0.90. The median S/N of its spectra are 239 and 283 for the blue and red part of the spectra, respectively. Red lines indicate the typical 1σ (solid line) and 2σ (dashed line) uncertainty of the EW computed with the Cayrel (1988) formula, adopting FWHM = 0.190 Å, pixel size = 0.0232 Å, and S/N = 260.Bottom row: a clump giant in the open cluster Trumpler 20(Trumpler 20 MG 781 in the numbering system of McSwain & Gies 2005), with Teff = 4850 K, log g = 2.75, and [Fe/H] = +0.15. The median S/N of its spectra are 36 and 68 for the blue and red part of the spectra, respectively. Red lines indicate the typical 1σ (solid line) and 2σ (dashed line) uncertainty of the EW computed with the Cayrel (1988) formula, adopting FWHM = 0.190 Å, pixel size = 0.0232 Å, and S/N = 50. In each panel, the average difference of the EWs and its dispersion are also given.

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Fig. B.4 Left panel: histogram of per star, taking into account the measurements of all Nodes. Also shown are lines indicating the 2σ uncertainty calculated with Cayrel (1988) formula for S/N = 40 (dotted line at 5.31 mÅ), S/N = 70 (dashed line at 3.04 mÅ), and S/N = 100 (solid line at 2.12 mÅ). Right panel: the dependence of with respect to S/N. Also shown is the expected 2σ value given by the Cayrel (1988) formula (as a red line).

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Figure B.4 depicts the behavior of measured in GESviDR1Final. For each Fe i line of a star, the average value of the EW is computed, together with its standard deviation. For each star, we define as the mean of all the standard deviations of the Fe i lines in that star. For most stars, the standard deviations are small (<3 mÅ), with a few cases reaching up to ~20 mÅ. Figure B.4 shows that for the majority of the stars, the multiple measurements of EWs tend to agree within the expected statistical uncertainty given by the S/N of the spectra.

	Fig. B.5 Mean of all the standard deviations of the Fe i lines in a star, , as a function of the atmospheric parameters.
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In Fig. B.5, is plotted against the atmospheric parameters, T_eff, log  g, and [Fe/H]. Most of the stars where > 10 mÅ tend to be warm, metal-rich subgiants or dwarfs. Many of these stars display significant rotation (Fig. B.6).

The ULB results for EWs (using the BACCHUS code), and finally for atmospheric parameters and abundances for iDR2, were not used to compute the final recommended values that will be released, as the Node withdrew its results.

Appendix B.2: Atmospheric parameters in iDR1

Appendix B.2.1: Benchmark stars

For the iDR1 analysis, only eight benchmark stars were available²⁷ and they did not cover the parameter space as well as the 21 stars used in iDR2. The accuracy of the Node results was judged by evaluating if the Node could reproduce T_eff and log  g of most benchmark stars to within ±150 K and ±0.30 dex, respectively. If yes, the Node results were considered to be accurate. If not, the Node results were disregarded. In practice, only the results of one Node were discarded.

For iDR1, weights were not computed and the parameter space was not divided in three regions. The individual results were then combined using a simple median. The comparison with the fundamental parameters of the benchmark stars ensures that the final parameters are also in the scale defined by them, to within the accuracy level adopted above (±150 K for T_eff and ±0.30 dex for log  g).

Appendix B.2.2: Calibration clusters

The number of calibration clusters available during the iDR1 analysis was also smaller. Four calibration globular clusters (NGC 1851, NGC 2808, NGC 4372, and NGC 5927) and one calibration open cluster (NGC 6705) were analyzed. The NGC 6705 AB-type stars were mostly found to be fast rotators. The results for them were deemed uncertain and were excluded during quality control. In Fig. B.7, we show the final recommended parameters of the stars observed in the cluster fields in comparison with isochrones. The agreement is very good, lending confidence in the final recommended parameters of iDR1.

Appendix B.2.3: Method-to-method dispersion

As for iDR2, we compare the results of different Nodes and quantify the method-to-method dispersion of each parameter using the associated median absolute deviation (MAD). The MAD is defined as the median of the absolute deviations from the median of the data.

	Fig. B.6 Mean of all the standard deviations of the Fe i lines in a star, , as a function of the rotational velocity of the star.
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For the GESviDR1Final results, the median of the method-to-method dispersion is 78 K, 0.17 dex, and 0.07 dex for T_eff, log g, and [Fe/H], respectively. These values are slightly larger than for iDR2. The third quartile of the distribution has values of 108 K, 0.23 dex, and 0.10 dex for T_eff, log g, and [Fe/H], respectively. Histograms of these dispersions are shown in Fig. B.8. For T_eff, the dispersion is within reasonable expectations. For the surface gravity, the dispersion is perhaps too high. However, the surface gravity is a quantity notoriously difficult to derive for field stars with uncertain distances. For the metallicity, there is a very good agreement among the Nodes.

Appendix B.2.4: Recommended atmospheric parameters

Based on comparisons of individual Node results with the calibrators, as shown above, the following scheme has been adopted to calculate the recommended values of atmospheric parameters of the FGK-type stars with UVES spectra for iDR1:

• 1.

  The accuracy of the Node results is judged using the eightavailable benchmark stars as reference, with a tolerance of ±150 K and ±0.30 dex, for T_eff and log g, respectively.

• 2.

  Further consistency tests of the Node results are conducted using the calibration clusters.

• 3.

  Nodes which fail to reproduce the reference atmospheric parameters of most of the benchmark stars, or that produce unreliable results for the calibration clusters, are disregarded.

• 4.

  The median value of the validated results is adopted as the recommended value of that parameter. The median should minimize the effect of eventual outlier results.

• 5.

  The MAD is computed to quantify the method-to-method dispersion (analysis precision) and is adopted as an indicator of the uncertainties.

• 6.

  The number of results on which the recommended value is based is also reported.

	Fig. B.7 Recommended parameters of the stars in the calibration clusters of iDR1 in the Teff − log  g plane. No attempt was made to identify nonmember stars. The plots include all stars observed in the field of the clusters. The ages, metallicities, and isochrones are the same as in Fig. 9.
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	Fig. B.8 Histograms showing the distribution of the method-to-method dispersion of the atmospheric parameters of the 421 stars that are part of GESviDR1Final. Left: the dispersion of Teff. Center: the dispersion of log g. Right: the dispersion of [Fe/H].
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Fig. B.9 Difference between the recommended values of Teff, log g, and [Fe/H] for the benchmark stars of GESviDR1Final and the reference values. The error bars are the method-to-method dispersions. The stars are sorted in order of decreasing [Fe/H] (left to right). Dotted red lines indicate limits of ±150 K for Teff, of ±0.30 dex for log g, and of ±0.10 dex for [Fe/H]. Star HD 140283 appears twice because two different spectra of this star (based on different exposures) were produced and analyzed separately.

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Table B.2 summarizes the number of stars for which atmospheric parameters were determined during the science verification analysis and are part of the GESviDR1Final internal release. The analysis of a fraction of the stars (~17%) was not completed for different reasons (e.g., high-rotation, double-lined signatures, too low S/N).

A comparison of the recommended values of the atmospheric parameters of the benchmark stars (computed as described above) with the reference values is shown in Fig. B.9. All recommended values of T_eff are within ±150 K of the reference values. Good agreement is also present for log g (within ±0.30 dex), except for HD 140283, a metal-poor subgiant (two spectra of this star were analyzed separately and thus it appears twice in the plot). Gravity values for metal-poor stars are known to be affected by NLTE effects (see, e.g., Bergemann et al. 2012), therefore, it is no surprise that the results of LTE-based analyses shown here are discrepant when compared to the reference values, since the latter are independent from spectroscopy. The results included in GESviDR1Final for metal-poor stars should be used with care. The recommended [Fe/H] values agree with the reference values to within ±0.15 dex.

Appendix B.3: Abundances

Fig. B.10 Comparison of two sets of abundances for the stars of calibrating globular and open clusters included in iDR1. Points are the averages for all stars observed in the field of a given cluster. No attempt was made to identify nonmembers. Symbols in black are the abundances computed with the recommended atmospheric parameters. Symbols in blue are the abundances computed with the atmospheric parameters of the Nodes. Error bars are the standard error of the mean.

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	Fig. B.11 Histograms with the method-to-method dispersion of selected species included in the iDR1 results.
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As for the atmospheric parameters, the elemental abundances were computed in different ways for the iDR1 and the iDR2 datasets.

Multiple determinations of the abundances were conducted. All Nodes that have tools for abundance determinations performed the analysis in parallel for all the stars. For iDR1, the Nodes were asked to compute abundances using two sets of atmospheric parameters for each star, i.e., i) the atmospheric parameters derived by the Node itself; and ii) the set of recommended atmospheric parameters, computed as described above.

We then computed the median of the multiple determinations for each of these two cases. For iDR1, we did not homogenize the line-by-line abundances, but only the final values of each element in each star. In Fig. B.10, we compare the two sets of abundances for a few elements in stars of globular and open clusters. It is clear from this plot that there is no significant difference between the final abundances computed with the two sets of atmospheric parameters.

In addition, it is apparent that the star-to-star scatter of the abundances does not seem to increase when using one or the other set of atmospheric parameters. This lends confidence to the approach adopted here, of having multiple abundances determined by different groups and adopting the median values as the recommended best values.

For the final set of recommended abundances included in GESviDR1Final, we decided to adopt the median of the results calculated using as input the recommended values of T_eff, log g, [Fe/H], and ξ. The MAD was again adopted as an indicator of the uncertainties (as it is a measurement of the precision with which multiple methods agree). The following 16 elements were analyzed and abundances for at least a handful of stars are included in GESviDR1Final: Li, O, Na, Mg, Al, Si, S, Ca, Ti, Cr, Fe, Ni, Zn, Y, Zr, and Ce. Except for Li, O, S, Zn, Zr, and Ce, all the abundances have been determined by at least three different Nodes. Elements that have important hyperfine structure were not included, as this kind of data were not part of the Gaia-ESO line list (version 3.0) when the abundances were calculated.

Appendix B.3.1: Method-to-method dispersion

The method-to-method dispersion of the abundances can be used as an indicator of the precision with which the results were derived. In Fig. B.11, we show the histogram of the MADs of a few selected elements. The third quartile of the method-to-method dispersion distribution is equal to or below 0.05 dex for the elements: Al i, Ti i, Fe i, and Ni i. The third quartile of the dispersion is between 0.06 and 0.10 dex for the other elements with multiple measurements: Na i, Mg i, Si i, Ca i, Ti ii, Cr i, Cr ii, and Fe ii. The MADs were adopted as the typical uncertainties.

© ESO, 2014