The Sixth Data Release of the Radial Velocity Experiment (Rave). II. Stellar Atmospheric Parameters, Chemical Abundances, and Distances

Rave DR6 employs the exact same procedure to derive stellar atmospheric parameters from spectroscopy as DR5 (Kunder et al. 2017). In short, the pipeline MADERA uses a combination of (i) a decision tree (DEGAS; Bijaoui et al. 2012), which normalizes the spectrum iteratively as well as parameterizing the low-S/N spectra, and (ii) a projection algorithm (MATISSE; Recio-Blanco et al. 2006) which is used to obtain the stellar atmospheric parameters for the high-S/N spectra (>30).

Both methods are used with the grid of 3580 synthetic spectra first calculated in the framework of Kordopatis et al. (2011) and adjusted for DR4 (Kordopatis et al. 2013a) assuming the solar abundances of Grevesse (2008) and Asplund et al. (2005). This grid has been computed using the MARCS model atmospheres (Gustafsson et al. 2008) and Turbospectrum (Plez 2012) under the assumption of local thermodynamic equilibrium (LTE). The atomic data were taken from the VALD⁴¹ database (Kupka et al. 2000), with updated oscillator strengths from Gustafsson et al. (2008). The line-list was calibrated primarily on the solar spectrum of Hinkle et al. (2003) and with adjustments to fit also the Arcturus spectrum to an acceptable level (see Kordopatis et al. 2011 for further information). Furthermore, the grid excludes the cores of the Ca triplet lines, as they can suffer, depending on spectral type, from non-LTE effects or emission lines owing to stellar activity. The grid has three free parameters: effective temperature, ${T}_{\mathrm{eff}}$, logarithm of the surface gravity, $\mathrm{log}g$, and metallicity,⁴² [m/H]. These free parameters are thus the parameters that MADERA determines.

We note that the α-enhancement [α/Fe] varies across the grid, but is not a free parameter. Indeed, only one [α/Fe] value is adopted per [m/H] grid-point:

$$\begin{eqnarray}&&\left[\displaystyle \frac{\alpha }{\mathrm{Fe}}\right]=\left\{\begin{array}{c}\,+0.4\quad :\ \left[\tfrac{{\rm{m}}}{{\rm{H}}}\right]\leqslant -1\\ -0.4\times \left[\tfrac{{\rm{m}}}{{\rm{H}}}\right]\quad :\ -1\lt \left[\tfrac{{\rm{m}}}{{\rm{H}}}\right]\lt 0\\ \,0\quad :\ \left[\tfrac{{\rm{m}}}{{\rm{H}}}\right]\geqslant 0.\end{array}\right.\end{eqnarray} \tag{ 1 }$$

This implies that the [m/H] value of the grid can be thought of as the content of all the metals in the star, except the α elements. The derived value of [m/H] from an observed spectrum, denoted by [m/H]_u, should hence be considered as an overall metallicity estimator assuming an α-enhancement. This should be discriminated from methods and grids based on the total metallicity including an α-enhancement, like those used in Sections 3.3 and 3.4; we refer to those metallicity estimators as [M/H].

Finally, with [Fe/H] we refer to direct measurements of the iron content by fitting iron lines, e.g., with the GAUGUIN method (Section 4) or when using high-resolution data for validation (see Section 6).

3.1.1. MADERA's Quality Flags

3.1.2. Calibration of the Stellar Atmospheric Parameters

Several tests performed for DR4, as well as the subsequent science papers, have indicated that the stellar parameter pipeline is globally robust and reliable. However, being based on synthetic spectra that may not match the real stellar spectra over the entire parameter range, the direct outputs of the pipeline need to be calibrated on reference stars in order to minimize possible systematic offsets.

To calibrate the DR6 outputs of the pipeline, the same calibration data set and polynomial fit compared to literature values have been used as for DR5. For completeness reasons, we review the relations in the following subsections, but refer the reader to DR4 and DR5 for further details. We performed tests with additional subsets (coming from, e.g., asteroseismic surface gravities) or/and more complex polynomials to calibrate the pipeline's output and obtained results that did not show any significant improvement over the approach that was adopted in DR4 and DR5.

Metallicity calibration. The calibration relation for DR6 is

$$\begin{eqnarray}\begin{array}{rcl}{[{\rm{m}}/{\rm{H}}]}_{\mathrm{DR}6} & = & {[{\rm{m}}/{\rm{H}}]}_{{\rm{u}}}+(0.276-0.044\,\mathrm{log}{g}_{{\rm{u}}}\\ & & +\,0.002\,\mathrm{log}{g}_{{\rm{u}}}^{2}-0.248\,{[{\rm{m}}/{\rm{H}}]}_{{\rm{u}}}\\ & & +\,0.007\,{[{\rm{m}}/{\rm{H}}]}_{{\rm{u}}}\,\mathrm{log}{g}_{{\rm{u}}}-0.078\,[{\rm{m}}/{\rm{H}}{]}_{{\rm{u}}}^{2}),\end{array}\end{eqnarray} \tag{ 2 }$$

where ${[{\rm{m}}/{\rm{H}}]}_{\mathrm{DR}6}$ is the calibrated metallicity, and ${[{\rm{m}}/{\rm{H}}]}_{{\rm{u}}}$ and $\mathrm{log}{g}_{{\rm{u}}}$ are, respectively, the uncalibrated metallicity and surface gravity (both the raw output from the pipeline). The adopted calibration corrects for a rather constant underestimation of 0.2 dex at the lowest metallicities, while also correcting trends in the more metal-rich regimes, where the giant stars exhibit higher offsets than the dwarfs. As already described in the earlier DR papers, this relation has been calibrated against [Fe/H] values from the literature. This implies that ${[{\rm{m}}/{\rm{H}}]}_{\mathrm{DR}6}$ is a proxy for [Fe/H] only if all of the elements in the targeted star are solar-scaled and if the α abundances are following the same relation as adopted for the synthetic grid at the [Fe/H] value of the star of interest. ${[{\rm{m}}/{\rm{H}}]}_{\mathrm{DR}6}$ should therefore be rather thought of as a metallicity indicator, i.e., to depend on a combination of elements. ${[{\rm{m}}/{\rm{H}}]}_{\mathrm{DR}6}$ is, however, not equal to the overall metallicity of the star, as discussed above—see also Equation (5) in Section 3.3).

Surface gravity calibration. The following quadratic expression defines our surface gravity calibration:

$$\begin{eqnarray}&&\mathrm{log}{g}_{\mathrm{DR}6}=\mathrm{log}{g}_{{\rm{u}}}+(0.515-0.026\,\mathrm{log}{g}_{{\rm{u}}}-0.023\,\mathrm{log}{g}_{{\rm{u}}}^{2}).\end{eqnarray} \tag{ 3 }$$

This relation increases gravities of supergiants by ∼0.5 dex, and of dwarfs by ∼0.75 dex.

Effective temperature calibration. The adopted calibration for effective temperature is

$$\begin{eqnarray}&&{T}_{\mathrm{eff},\mathrm{DR}6}={T}_{\mathrm{eff},{\rm{u}}}+(285\,{\rm{K}}-0.073{T}_{\mathrm{eff},{\rm{u}}}+40\,{\rm{K}}\times \mathrm{log}{g}_{{\rm{u}}}).\end{eqnarray} \tag{ 4 }$$

Corrections reach up to 200 K for cool dwarfs, but are generally much smaller.

Effective temperatures from the infrared flux method (IRFM; Casagrande et al. 2006, 2010) are derived in a manner similar to that carried out in Rave DR5, where a detailed description can be found. Briefly, our implementation of the IRFM uses APASS and 2MASS photometry to recover stellar bolometric and infrared fluxes. The ratio of these two fluxes for a given star is compared to that predicted from theoretical models, for a given set of stellar atmospheric parameters, and an iterative approach is used to converge on the final value of ${T}_{\mathrm{eff}}$. The advantage of comparing observed versus model fluxes in the infrared is that this region is largely dominated by the continuum and is thus very sensitive to ${T}_{\mathrm{eff}}$, while the dependence on surface gravity and metallicity is minimal. Here, we adopt for each star the calibrated $\mathrm{log}{g}_{\mathrm{DR}6}$ and ${[{\rm{m}}/{\rm{H}}]}_{\mathrm{DR}6}$ from the MADERA pipeline, but if we were instead to use the parameter values from the SPARV pipeline the derived value of ${T}_{\mathrm{eff}}$ would differ by a few tens of Kelvin at most. Since the IRFM simultaneously determines bolometric fluxes and effective temperatures, stellar angular diameters can be derived, and are also provided in DR6. Extensive comparison with interferometric angular diameters to validate this method is discussed in Casagrande et al. (2014). We are able to provide ${T}_{\mathrm{eff}}$ from the IRFM for over 90% of our sample, while for about 6% we have to resort to color–temperature relations derived from the IRFM. For less than 3% of our targets effective temperatures could not be determined due to the lack of reliable photometry.

In a photometric method such as the IRFM, reddening can have a non-negligible impact. We rescale the reddening from Schlegel et al. (1998) as described in Rave DR5, but for stars with $\mathrm{log}(g)\lt 3.5$ and $E(B-V)\gt 0.3$ we now use the relation $E(B-V)=0.918(H-W2-0.08)/0.366$ from the Rayleigh–Jeans color excess method (Majewski et al. 2011).

Rave DR6 includes for the first time stellar atmospheric parameters derived using the Bayesian framework demonstrated in McMillan et al. (2018), along with derived distances, ages, and masses, which have also been derived for previous data releases. We refer to the method as the BDASP (Bayesian Distances Ages and Stellar Parameters) code. This follows the pioneering work deriving (primarily) distances by Burnett & Binney (2010) and Binney et al. (2014).

This method takes as its input the stellar atmospheric parameters ${T}_{\mathrm{eff}}$ (taken from the IRFM, Section 3.2), $\mathrm{log}g$ taken from the MADERA pipeline, an estimate of the overall metallicity taken from MADERA (see below), J, H, and K_s magnitudes from 2MASS, and, for the first time, parallaxes from Gaia DR2. For a detailed description of the method, the interested reader should refer to McMillan et al. (2018), where parallaxes from Gaia DR1 (Gaia Collaboration et al. 2016a) were used for the 219,566 Rave sources that entered the Tycho-Gaia astrometric solution (TGAS) part of the Gaia catalog (Michalik et al. 2015). Here we simply give a brief overview and note differences in the methodology used here and by McMillan et al. (2018).

BDASP applies the simple Bayesian statement

$$\begin{eqnarray*}&&P(\mathrm{model}| \mathrm{data})=\displaystyle \frac{P(\mathrm{data}| \mathrm{model})P(\mathrm{model})}{P(\mathrm{data})},\end{eqnarray*}$$

where in our case "data" refers to the inputs described above for a single stars, and "model" comprises a star of specified initial mass ${ \mathcal M }$, age τ, metallicity [M/H], and location, observed through a specified line-of-sight extinction. $P(\mathrm{data}| \mathrm{model})$ is determined assuming uncorrelated Gaussian uncertainties on all inputs, and using PARSEC isochrones (Bressan et al. 2012) to find the values of the stellar atmospheric parameters and absolute magnitudes of the model star. The uncertainties of the stellar atmospheric parameters are assumed to be the quadratic sum of the quoted internal uncertainties and the external uncertainties, as found for Rave DR5 (Kunder et al. 2017, Table 4). $P(\mathrm{model})$ is our prior, and $P(\mathrm{data})$ is a normalization that we can safely ignore. We adopt the "density" prior from McMillan et al. (2018), which is the least informative prior considered in that study. Even with the significantly less precise Gaia DR1 parallax estimates, the choice of prior has a limited impact on the results, and this is reduced still further because of the very high precision of the Gaia DR2 parallax estimates.

As discussed above, the MADERA pipeline provides [m/H], the metal content except the α-elements, which is calibrated against [Fe/H]. To provide an estimate of the overall metallicity [M/H] we assume that we can scale all abundances with [m/H] except those of α-elements, which we assume all scale in the same way assumed by MADERA (i.e., following Equation (1)). A proxy for the overall metallicity including α-elements, denoted by [M/H], can then be inferred by applying a modified version of the Salaris et al. (1993) formula, derived using the same technique as in Valentini et al. (2019):

$$\begin{eqnarray}&&\left[\displaystyle \frac{{\rm{M}}}{{\rm{H}}}\right]={\left[\displaystyle \frac{{\rm{m}}}{{\rm{H}}}\right]}_{\mathrm{DR}6}+{\mathrm{log}}_{10}(C\times {10}^{[\alpha /\mathrm{Fe}]}+(1-C)),\end{eqnarray} \tag{ 5 }$$

with C = 0.661. Within this approximation [M/H] corresponds to the composition assumed by the PARSEC isochrones.

As was made clear at the time of Gaia DR2, astrometric measurements from Gaia have small but significant systematic errors (including an offset of the parallax zero-point), which vary across the sky on a range of scales, and are dependent on magnitude and color (Arenou et al. 2018; Lindegren et al. 2018). This has been demonstrated for a variety of comparison samples since Gaia DR2 (Sahlholdt & Silva Aguirre 2018; Stassun & Torres 2018; Zinn et al. 2019; Graczyk et al. 2019; Khan et al. 2019). The parallaxes used in BDASP are therefore corrected for a parallax zero-point of −54 μas, following the analysis of Schönrich et al. (2019). This study determined this zero-point offset for stars with Gaia DR2 RVs, which cover a similar magnitude range to Rave, and have a larger zero-point offset than the fainter quasars considered by Lindegren et al. (2018). We also add a systematic uncertainty of 43 μas in quadrature with the quoted parallax uncertainties to reflect a best estimate of the small-scale spatially varying parallax offsets as found by Lindegren et al. (2018).

In DR5 we provided an improved description of the distances to stars with a multi-Gaussian fit to the probability density function (pdf) in distance modulus. This was particularly important for stars with multi-modal pdfs, for example stars where there was an ambiguity over whether they were subgiants or dwarfs. With the addition of Gaia parallaxes, these ambiguities have become rare. Fewer than one percent of the sources required multi-Gaussian pdfs under the selection criteria used in McMillan et al. (2018). These are generally pdfs with a narrow peak associated with the red clump and an overlapping broader one associated stars ascending the red giant branch, rather than truly multi-modal pdfs (see Binney et al. 2014 for a discussion and examples). In the interests of simplicity, we therefore do not provide these multi-Gaussian pdfs with DR6. Extinction is taken into account in the same way as in Binney et al. (2014) and McMillan et al. (2018), and is relatively weak for the majority of Rave stars. The median extinction we find corresponds to A_V ∼ 0.2 mag, which is ∼0.06 mag in the J-band (the band that suffers the most extinction of all those we consider).

We can use the Gaia DR2 parallaxes to validate our Bayesian distance-finding method in the same way as McMillan et al. (2018) did with the TGAS parallaxes: comparing the parallax estimates using BDASP, without including the Gaia parallax, to the Gaia DR2 parallax. Since these are independent estimates, we would expect that if we take the difference between these values divided by their combined uncertainty (the two uncertainties summed in quadrature), it will be distributed as a Gaussian, with average zero and standard deviation unity.

In Figure 1 we plot histograms showing this comparison for the parallax estimates from Rave DR5 (using the same techniques described here, and using MADERA ${T}_{\mathrm{eff}}$), or using BDASP but taking the IRFM ${T}_{\mathrm{eff}}$ as input (as this was shown to be a better approach by McMillan et al. 2018). In both cases we show the comparison to the quoted values from Gaia DR2, and a comparison to the "adjusted" values, where we have corrected the Gaia parallaxes for their assumed zero-point offset and systematic uncertainties. This figure demonstrates that the parallax zero-point offset of Gaia is significant, even for these relatively nearby stars. Including the zero-point offset brings the Gaia parallaxes more in line with those from Rave. We also see that the use of IRFM temperatures significantly improves the BDASP parallaxes. In all cases we see more outlying values than we would expect for a Gaussian distribution. One could, therefore, reasonably argue that we should be using the median, rather than a sigma-clipped mean (as in Figure 1) to quantify the bias of the values. The median values, compared to the zero-point-adjusted Gaia parallaxes, are 0.136 and 0.011 using MADERA ${T}_{\mathrm{eff}}$ or IRFM ${T}_{\mathrm{eff}}$, respectively.

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We can compare the precision we achieve for stellar atmospheric parameters with BDASP in Rave DR6 to that achieved with MADERA. The most interesting of these is the precision in $\mathrm{log}g$, where the Gaia parallax provides the greatest value. This comparison is shown in Figure 2, and we see that we improve by more than a factor of two (median precision 0.16 dex for MADERA, 0.07 dex for BDASP). The dwarf stars, which are nearby and therefore have precise parallax estimates from Gaia, dominate the narrow peak at the smaller BDASP log g uncertainties of ∼0.04 dex while giants make up most of the broader peak of larger log g uncertainties. We can also compare the distance uncertainty BDASP found without Gaia DR2 parallax input in Rave DR5, as compared to the distance uncertainty now. Here we find a dramatic improvement, from a typical distance uncertainty of 30% in DR5 to one of 4% in DR6. Furthermore, Gaia DR2 parallaxes are available for 99.8% of Rave spectra, as opposed to only 49% in Rave DR5/Gaia DR1. At this point the only significant gain in precision of using spectro-photometric information to derive distances for Rave stars is for the red clump and high on the giant branch (the latter being known to be problematic for Rave: McMillan et al. 2018). Otherwise the distance estimates are, to a fairly close approximation, derived directly from Gaia parallaxes, so it makes little difference whether these distances, or those derived directly from Gaia parallaxes alone are used. This reflects the extraordinary precision of Gaia DR2, and emphasizes the value of combining the Gaia data with Rave.

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The surface gravity provided by asteroseismology ($\mathrm{log}{g}_{{\rm{S}}}$) is now widely used for testing the accuracy of $\mathrm{log}g$ measured from spectroscopy. The seismic $\mathrm{log}{g}_{{\rm{S}}}$ can easily be computed starting from the scaling relations, two relations that directly connect stellar mass and radius to the effective temperature (${T}_{\mathrm{eff}}$) and two seismic observables Δν (average frequency separation) and ${\nu }_{\max }$(frequency of maximum oscillation power). The seismic $\mathrm{log}{g}_{{\rm{S}}}$ depends only on ${T}_{\mathrm{eff}}$ and ${\nu }_{\max }$, and it is defined as

$$\begin{eqnarray}&&\mathrm{log}{g}_{{\rm{S}}}=\mathrm{log}{g}_{\odot }+\mathrm{log}\left(\displaystyle \frac{{\nu }_{\max }}{{\nu }_{\max \odot }}\right)+\displaystyle \frac{1}{2}\mathrm{log}\left(\displaystyle \frac{{T}_{\mathrm{eff}}}{{T}_{\mathrm{eff}\odot }}\right)\end{eqnarray} \tag{ 6 }$$

where the solar values are $\mathrm{log}{g}_{\odot }=4.44$ dex, ${\nu }_{\max \odot }\,=3090$ μHz, and ${T}_{\mathrm{eff}\odot }=5777$ K (Huber et al. 2011).

Large spectroscopic surveys as APOGEE, Gaia–ESO, LAMOST, and GALAH observed seismic targets with the purpose of testing and calibrating, if necessary, the $\mathrm{log}g$ measured by their spectroscopic pipelines. Thanks to the recommissioned Kepler satellite, the K2 mission (Howell et al. 2014), Rave had the opportunity to incorporate seismic data starting in DR5 (Kunder et al. 2017), where a set of 87 red giant stars, observed by K2 in Campaign 1, were used as calibrators and for an ad hoc calibration for red giant stars only (Valentini et al. 2017). In DR6, 699 red giants observed during the first six K2 campaigns are used (see Table 1, showing the number of targets per campaign). This allowed for an improved coverage of the parameter space (in particular, effective temperature and metallicity). We use the procedure as outlined in DR5, but use ${T}_{\mathrm{eff},\mathrm{IRFM}}$ as the prior for the effective temperature. We also allow a larger flexibility interval (±450 K instead of 350 K as in Valentini et al. 2017). The calibration adopted in this case turned out to be very similar to that in DR5, confirming the robustness of the method, given the larger seismic data set. For the catalog presented in the later part of this work (Section 7.3):

$$\begin{eqnarray}&&\mathrm{log}{g}_{{\rm{S}}}=\mathrm{log}{g}_{{\rm{u}}}-{0.76}_{0.74}^{0.80}\times \mathrm{log}{g}_{{\rm{u}}}+{1.98}_{1.90}^{2.06},\end{eqnarray} \tag{ 7 }$$

where $\mathrm{log}{g}_{{\rm{u}}}$ is the uncalibrated $\mathrm{log}g$ delivered by the MADERA pipeline. Further details on the seismic and spectroscopic data analysis are presented in M. Valentini et al. (2020, in preparation).

Asteroseismology can be also used for providing estimates of the mass of red giants, and hence their age (since the age of a red giant corresponds to the time it spent on the main sequence, and therefore its mass). In M. Valentini et al. (2020, in preparation) we derive mass, radius, and distance of the K2-Rave stars using PARAM (Rodrigues et al. 2017), a Bayesian tool that infers stellar properties using both atmospheric and seismic parameters as input.

GAUGUIN was originally developed in the framework of the Gaia/RVS analysis developed within the Gaia/DPAC for the estimation of the stellar atmospheric parameters (for the mathematical basis, see Bijaoui et al. 2010). For first applications, see Bijaoui et al. (2012) and Recio-Blanco et al. (2016). A natural extension of GAUGUIN's applicability to the derivation of stellar chemical abundances was then initiated within the context of the Gaia/RVS (DPAC/Apsis pipeline, Bailer-Jones et al. 2013), the AMBRE Project (de Laverny et al. 2013; Guiglion 2015; Guiglion et al. 2016, 2018b), and the Gaia–ESO Survey (Gilmore et al. 2012). Currently, GAUGUIN is integrated into the Apsis pipeline at the Centre National d'Études Spatiales (CNES), for Gaia/RVS spectral analysis (Bailer-Jones et al. 2013; Recio-Blanco et al. 2016; Andrae et al. 2018).

GAUGUIN determines chemical abundance ratios for a given star by comparing the observed spectrum to a set of synthetic spectra. In order to both have a fast method and be able to deal with large amounts of data, it is best to avoid synthesizing model spectra on-the-fly. GAUGUIN is therefore based on a pre-computed grid of synthetic spectra, which we interpolate to the stellar atmospheric parameters of the star, in order to create a set of synthetic models for direct comparison with the observation.

The triplet of calibrated $\{{T}_{\mathrm{eff}},\mathrm{log}g,[{\rm{m}}/{\rm{H}}]\}$ from MADERA is used as input stellar atmospheric parameters for GAUGUIN.

4.1.1. Preparation of the Observed Rave Spectra for Abundance Analysis

In order to maintain consistency between the MADERA stellar atmospheric parameters and chemical abundances of non-α-elements, we employed the synthetic spectral grid as used by MADERA (Section 3.1; see also Kordopatis et al. 2013a; Kunder et al. 2017). For the elemental abundance analysis we restricted the range of effective temperatures to be within 4000 ≤ ${T}_{\mathrm{eff}}$ ≤ 7000 K (in steps of 250 K), thus avoiding stars that are too cool (owing to considerable mismatches between spectral templates and the Rave spectrum) or too hot (with spectral features that are too weak). We kept the same ranges in $\mathrm{log}g$ and [m/H] as the MADERA grid, i.e., 0.5 ≤ $\mathrm{log}g$ ≤ 5.0 (in steps of 0.5 dex) and $-5.0\leqslant [{\rm{m}}/{\rm{H}}]\leqslant 1.0$ dex in steps of 0.25 dex. The spectral resolution of the synthetic spectra matched that of the observational data (R ∼ 7500), with binning of 0.35 Å. We refer the reader to Section 3.4 of Kordopatis et al. (2013a) for more details concerning this grid of synthetic spectra.

The intermediate resolution and wavelength domain of the Rave spectra provides a unique scenario for determining chemical abundances, which is in synergy with the processing of the Gaia mission. In this framework, we were able to obtain chemical abundances of three elements: Fe, Al, and Ni. In order to get the abundance [X/H] for each of these three elements, we vary for a given Rave spectrum the metallicity around the metallicity ${[{\rm{m}}/{\rm{H}}]}_{\mathrm{DR}6}$ at fixed ${T}_{\mathrm{eff},\mathrm{DR}6}$ and $\mathrm{log}{g}_{\mathrm{DR}6}$ until the best match to an absorption line of element X is achieved. In the following, we refer to the varied metallicity parameter as μ. In practice, we create a 1D grid of synthentic spectra $S{1}_{i}(\lambda )\,=S({\mu }_{i},\lambda )$ for seven grid points μ_i: the central point is obtained by a trilinear interpolation from the eight neigboring grid points in ${T}_{\mathrm{eff}}$, $\mathrm{log}g$, and [m/H] from the MADERA 3D grid of synthetic spectra. The other six grid points of the 1D grid are then obtained by applying the same interpolation procedure to the atmospheric parameters sets with $\mu =[{\rm{m}}/{\rm{H}}]\pm 0.2$, $[{\rm{m}}/{\rm{H}}]\pm 0.4$, and $[{\rm{m}}/{\rm{H}}]\pm 0.6$, respectively, but keeping ${T}_{\mathrm{eff}}$ and $\mathrm{log}g$ unchanged. Then the best-matching spectrum is found by minimizing the quadratic distance between the observed spectrum S(λ) and and a synthetic one S1(μ, λ). The latter is obtained by interpolation in μ on the 1D grid S1_i(λ). The procedure is applied over a narrow wavelength range (typically from 4 to 9 pixels) around each spectral line (see Guiglion et al. 2016, and below). For each line of element X, we computed a χ² between the observed spectrum and its best synthetic spectrum. We averaged those χ² values, weighted by the number of pixels used for the fit, providing then a mean χ². To search for the best lines, we made a careful examination of spectral features in the Rave wavelength region. A more detailed discussion of this procedure can be found in Guiglion et al. (2018a). The resulting selection of lines for the chemical abundance analysis with GAUGUIN are given in Table 2, and have been astrophysically calibrated by Kordopatis (2011). For a given element with several spectral lines, we averaged the individual line abundance measurements thanks to a sigma-clipped mean.

Table 2.  Ion, Wavelength (Line), Excitation Potential (χ_e) and $\mathrm{log}{gf}$ Values for the Spectral Lines Used in the Chemical Abundance Pipeline GAUGUIN

Ion	Line (Å)	χe	$\mathrm{log}{gf}$
Al i	8772.865	4.022	−0.39
Al i	8773.897	4.022	−0.20
Fe i	8514.794	5.621	−2.13
Fe i	8515.108	3.018	−2.13
Fe i	8526.669	4.913	−0.71
Fe i	8582.257	2.990	−2.36
Fe i	8592.951	4.956	−0.91
Fe i	8611.803	2.845	−2.06
Fe i	8621.601	2.949	−2.47
Fe i	8688.624	2.176	−1.33
Fe i	8698.706	2.990	−3.32
Fe i	8699.454	4.955	−0.54
Fe i	8713.187	2.949	−3.08
Fe i	8713.208	4.988	−1.04
Fe i	8757.187	2.845	−2.09
Fe i	8763.966	4.652	−0.33
Ni i	8579.978	5.280	−0.94
Ni i	8636.995	3.847	−1.94
Ni i	8702.489	2.740	−3.19
Ni i	8770.672	2.740	−2.79

Note. (Data are from Kordopatis (2011); see also Section 3.1)

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Because [α/Fe] is not a free parameter for a given metallicity in the synthetic spectral grid used by MADERA (Section 3.1), we adopted the 2014 version of the 4D Gaia–ESO Survey synthetic spectra grid (P. de Laverny et al. 2020, in preparation), which provides high-resolution synthetic spectra as a function of four input variables: ${T}_{\mathrm{eff}}$, $\mathrm{log}g$, [m/H], and [α/Fe]. The synthetic spectra grid adopted for the derivation of the α abundances is that specifically computed for the Gaia-ESO Survey (see the descriptions in Smiljanic et al. (2014) and Heiter et al. (2020)). In summary, the grid consists of 11,610 1D LTE high-resolution synthetic spectra (sampled at 0.0004 nm) for non-rotating FGKM spectral type stars, covering the Ca ii triplet region. The Gaia–ESO Survey atomic and molecular linelists (Heiter et al. 2020) were adopted for the computation of the synthetic spectra. The global metallicity ranges from [m/H] = −5.0 to +1.0 dex and five different [α/Fe]-enrichments are considered for each metallicity value. The effective temperature covers the domain 3600 ≤ ${T}_{\mathrm{eff}}$ ≤ 8000 K (in steps of 200 K from 3600 to 4000 K, and 250 K beyond), while the surface gravity covers the range 0.0 ≤ $\mathrm{log}g$ ≤ 5.5 (in steps of 0.5 dex). The grid computation adopts almost the same methodology as the one used for the AMBRE Project (de Laverny et al. 2013) described in de Laverny et al. (2012). MARCS model atmospheres (Gustafsson et al. 2008) and the Turbospectrum code for radiative transfer (Alvarez & Plez 1998; Plez 2012) are used, together with the solar chemical abundances of Grevesse et al. (2007). The grid also employs consistent [α/Fe]-enrichments in the model atmosphere and the synthetic spectrum calculation together with an empirical law for the microturbulence parameter (Smiljanic et al. 2014; M. Bergemann et al. 2020, in preparation). Plane-parallel and spherical assumptions have been used in the atmospheric structure and flux computations for dwarfs ($\mathrm{log}g\gt 3.5$) and giants ($\mathrm{log}g\leqslant 3.5$), respectively.

As mentioned previously, the overall metallicity and [α/Fe] ratios follow the same relation as Equation (1), but the grid includes extra [α/Fe]-enrichments at each metallicity, as illustrated in Figure 3. The spectral resolution of the Gaia–ESO Survey synthetic spectra have been degraded in order to match that of the observational data (R ∼ 7500) with a binning of 0.35 Å.

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In order to get the [α/Fe] abundance ratios, we follow an analogous procedure as in Section 4.2: we create a 1D grid $S{2}_{i}(\lambda )=S({[\alpha /\mathrm{Fe}]}_{i},\lambda )$ by trilinear interpolation from the eight neighboring grid points of the Gaia–ESO Survey 4D grid of synthetic spectra to the calibrated MADERA stellar atmospheric parameters ${T}_{\mathrm{eff},\mathrm{DR}6}$, $\mathrm{log}{g}_{\mathrm{DR}6}$, and ${[{\rm{m}}/{\rm{H}}]}_{\mathrm{DR}6}$ of the underlying Rave star. The initial [α/Fe] of the input spectrum is assumed to follow Equation (1). A 1D grid with nine elements is then created by applying the analogous interpolation to atmospheric parameters sets with ${[\alpha /\mathrm{Fe}]=[\alpha /\mathrm{Fe}]}_{\mathrm{initial}}\pm 0.1$, ${[\alpha /\mathrm{Fe}]}_{\mathrm{initial}}\,\pm 0.2$, ${[\alpha /\mathrm{Fe}]}_{\mathrm{initial}}\pm 0.3$, and ${[\alpha /\mathrm{Fe}]}_{\mathrm{initial}}\pm 0.4$, but keeping ${T}_{\mathrm{eff}}$, $\mathrm{log}g$, and [m/H] unchanged. We then compute the quadratic distance between the observed spectrum S(λ) and each of the interpolated synthetic spectra of S2_i(λ) over the whole spectral range. We exclude the cores of the Ca ii triplet lines as they can suffer from deviations owing to non-LTE effects or chromospheric emission lines depending on the spectral type. An example of such a 1D grid is shown in Figure 4 for a Rave spectrum.

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For both steps, derivation of the elemental abundances of Al, Ni, and Fe, as well as for the α overabundance, a rough minimum of the quadratic distance is given by the closest point to the true minimum (see Figure 4, right panel, dashed line). It is then refined using a Gauss–Newton algorithm (Bijaoui et al. 2012), as illustrated by the red dashed line in Figure 4. We provide a ${\chi }^{2}$ fit between the observed spectrum and a synthetic one, computed for the GAUGUIN abundance solution.

GAUGUIN was implemented combining C++ and IDL,⁴⁴ allowing it to derive 60 [α/Fe] ratios per second, and 1200 individual abundances per second. For the analysis of the whole data set with GAUGUIN (normalization, abundances + errors) the overall computation time was 29 hr, on a single CPU core.

The synthetic spectra adopted to derive [Fe/H], [Al/H], [Ni/H] ratios are calibrated with respect to the Sun and verified with respect to Arcturus and Procyon (Kordopatis 2011; Kordopatis et al. 2011). From line to line, small mismatches can occur between the observed solar and Arcturus spectra and their respective synthetic spectrum. We therefore chose to apply a zero-point correction to the GAUGUIN abundances. To do so, we determined with GAUGUIN the chemical abundances for the Sun and Arcturus, using the high-resolution library of Hinkle et al. (2003), degraded to match the Rave spectral resolution. The input stellar atmospheric parameters of both stars were chosen to be consistent with those obtained by MADERA. The MADERA zero-point correction was derived by feeding GAUGUIN with the uncalibrated stellar atmospheric parameters derived by MADERA from the solar and Arcturus spectra: Sun {${T}_{\mathrm{eff},{\rm{u}}}=5578$ K, $\mathrm{log}{g}_{{\rm{u}}}=4.09$, ${[{\rm{m}}/{\rm{H}}]}_{{\rm{u}}}=-0.24$ dex}; Arcturus {${T}_{\mathrm{eff},{\rm{u}}}=4318$K, $\mathrm{log}{g}_{{\rm{u}}}=2.04$, ${[{\rm{m}}/{\rm{H}}]}_{{\rm{u}}}=-0.35$ dex}.⁴⁵ The averaged zero-point corrections that we applied to the GAUGUIN-derived [Fe/H], [Al/H] and [Ni/H] abundances are presented in Table 3. The [Fe/H] corrections are minor as GAUGUIN tends to track the input metallicity very well. Arcturus zero-point abundances have been applied to giants ($\mathrm{log}g\leqslant 3.5$), while the solar zero-point abundances have been applied to dwarfs ($\mathrm{log}g\gt 3.5$), line by line. We note that such zero-point corrections will shift the global patterns in the [X/Fe] versus [Fe/H] plane, but their slope will remain mainly unchanged owing to very small $[\mathrm{Fe}/{\rm{H}}]$ corrections.

We provide individual error estimates on the GAUGUIN abundance ratios, while for the previous releases only a global error was provided (Kunder et al. 2017). To do so, we considered two main sources of uncertainty: propagation of the errors of the stellar atmospheric parameters ${\sigma }_{p}(p\pm {e}_{p})$, and the internal error of GAUGUIN due to noise ${\sigma }_{\mathrm{int}}({\rm{S}}/{\rm{N}})$ (internal precision, see the adopted procedure below). We combined them in a quadratic sum and obtained the total uncertainty of the GAUGUIN chemical abundances:

$$\begin{eqnarray}&&\sigma =\sqrt{{\sigma }_{p}^{2}(p\pm {e}_{p})+{\sigma }_{\mathrm{int}}^{2}({\rm{S}}/{\rm{N}})}.\end{eqnarray} \tag{ 8 }$$

We detail the way we computed ${\sigma }_{\mathrm{int}}({\rm{S}}/{\rm{N}})$ in the following section.

4.5.1. The Precision of GAUGUIN [α/Fe], [Fe/H], [Al/H], and [Ni/H] Abundances

The top row of Figure 5 presents the internal precision ${\sigma }_{\mathrm{int}}({\rm{S}}/{\rm{N}})$ as a function of S/N for [α/Fe], [Al/H], [Fe/H], and [Ni/H], derived by GAUGUIN. The internal precision was characterized by taking 500 measurements of the abundance from noisy synthetic spectra of Sun-like (${T}_{\mathrm{eff}}$ = 5750 K, $\mathrm{log}g$ = 4.5, $[{\rm{m}}/{\rm{H}}]=+0.0$, $[\alpha /\mathrm{Fe}]=+0.0$) and Arcturus-like stars (${T}_{\mathrm{eff}}=4250$ K, $\mathrm{log}g=1.5$, $[{\rm{m}}/{\rm{H}}]=-0.5$, $[\alpha /\mathrm{Fe}]\,=+0.3$), adopting S/N = 5 to 120, in steps of ${\rm{\Delta }}{\rm{S}}/{\rm{N}}=5$. We computed a simple standard deviation of the 500 abundance measurements, at a given S/N and for a given spectral line. Figure 5 clearly shows that the internal error is larger for dwarf stars than it is for giants. The overall [α/Fe] based on the overall fit of the spectrum appears to be relatively robust, with low σ (high precision). For [Ni/H] in dwarfs, the internal error varies strongly from one spectral line to another.

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4.5.2. The Accuracy of GAUGUIN [α/Fe], [Fe/H], [Al/H], and [Ni/H] Abundances

4.5.3. Total Uncertainty of GAUGUIN [α/Fe], [Fe/H], [Al/H], and [Ni/H] Abundances

Figure 6 shows the total uncertainty of the GAUGUIN [α/Fe], [Fe/H], [Al/H], [Ni/H] ratios, derived using Equation (8), using MADERA stellar atmospheric parameters as input. We show only stars with a quality flag equal to "0" (as described in Section 3.1.1). We observe that, while the total uncertainties of [α/Fe] abundances are very similar between dwarfs and giants (∼0.16 dex), the total uncertainties of the other abundances are systematically larger for dwarfs.

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When discarding stars with ${\rm{S}}/{\rm{N}}\lt 40$, we tend to remove the tail toward larger errors of the distributions. The typical errors for giants are of the order of 0.13 dex for Fe and Al, and >0.2 dex for Ni. We give the median errors of each distribution in Table 4. We note that even at high S/N, Ni suffers from larger uncertainties for dwarf stars. We strongly recommend the reader to use the individual total errors to select the most reliable GAUGUIN abundances for their specific science application.

Table 4.  Total GAUGUIN Error for All Elements, in the Whole Sample; Giants and Dwarfs

Elem	S/N	All	Giants	Dwarfs
[α/Fe]	all	0.16	0.16	0.17
	>40	0.13	0.13	0.13
[Fe/H]	all	0.16	0.14	0.21
	>40	0.14	0.13	0.18
[Al/H]	all	0.14	0.12	0.17
	>40	0.12	0.11	0.14
[Ni/H]	all	0.24	0.23	0.56
	>40	0.23	0.23	0.52

Note. The error is presented adopting MADERA inputs. We refer the reader to Figure 6 for a view of the distribution.

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4.5.4. Further Sources of Uncertainty

The internal error analysis presented above intrinsically assumes that the morphology of the observed Rave spectrum matches that of the synthetic grid. However, this condition does not necessarily need to be fulfilled, for example, owing to a peculiarity of the Rave spectrum, either of an astrophysical nature (e.g., significantly deviant abundance pattern of the underlying star or shortcomings of the synthetic grid, particularly in the less studied ranges of the parameter space), or for technical reasons (improper continuum normalization, e.g., owing to fringing).

The quality of the match between an actual Rave spectrum and the synthetic grids employed by the MADERA and GAUGUIN pipeline can be characterized by the two χ² values provided by the MADERA and GAUGUIN pipelines (see also Figure 7). A poor match of the MADERA pipeline will result in large residuals between the Rave and the template spectrum, which in turn will result in a poor fit of GAUGUIN and/or in excessive (and likely unphysical) deviation in [α/Fe]. In addition, a poor S/N will naturally lead to unreliable determinations using MADERA and/or GAUGUIN.

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Figure 7 illustrates this effect by showing, as a function of the S/N and color-coded by metallicity ${[{\rm{m}}/{\rm{H}}]}_{\mathrm{DR}6}$, the ${\chi }_{\mathrm{MADERA}}^{2}$ (left), and ${\chi }_{\mathrm{GAUGUIN}}^{2}$ value for all objects for which GAUGUIN provides a converged solution for [α/Fe]. The green line corresponds to the median χ² as a function of S/N, approximated by the following two relations:

$$\begin{eqnarray}&&{\chi }_{\mathrm{median},\mathrm{MADERA}}^{2}({\rm{S}}/{\rm{N}})=\displaystyle \frac{{10}^{5}}{-1.23\,{\rm{S}}{/{\rm{N}}}^{2}+227\,{\rm{S}}/{\rm{N}}+725}\end{eqnarray} \tag{ 9 }$$

and

$$\begin{eqnarray}&&{\chi }_{\mathrm{median},\mathrm{GAUGUIN}}^{2}({\rm{S}}/{\rm{N}})=\displaystyle \frac{1}{0.232\,{\rm{S}}{/{\rm{N}}}^{2}+27.7\,{\rm{S}}/{\rm{N}}-302},\end{eqnarray} \tag{ 10 }$$

for $10\lt {\rm{S}}/{\rm{N}}\lt 150$. respectively. The right plot shows the χ² values for MADERA and GAUGUIN against each other. The majority of the data points fall within a smooth distribution around the median value of either pipeline. Furthermore, as indicated by the right plot, usually both pipelines have a comparable quality of fit, i.e., stars for which the MADERA pipeline provides results within the main distribution of the quality of fit also fall within the main distribution for GAUGUIN. However, both pipelines show a sizeable number of stars with considerably poorer fits than average even for very high S/N values, usually associated with (MADERA-derived) very high super-solar metallicity. This is particularly prominent in the results for the MADERA pipeline. This finding is not very surprising as the aforementioned outliers predominantly correspond to very cool stars with a very dense forest of absorption lines, often also based on molecular lines, i.e., where the proper modeling of synthetic spectra and the matching to medium-resolution, medium-S/N data is particularly challenging.

A simple and convenient way to characterize the simultaneous fit of GAUGUIN and MADERA can be defined via

$$\begin{eqnarray}\begin{array}{rcl}{\bar{\chi }}^{2} & = & {\mu }_{\mathrm{MADERA}}\,\displaystyle \frac{{\chi }_{\mathrm{MADERA}}^{2}}{{\chi }_{\mathrm{median},\mathrm{MADERA}}^{2}({\rm{S}}/{\rm{N}})}\\ & & +\,{\mu }_{\mathrm{GAUGUIN}}\displaystyle \frac{{\chi }_{\mathrm{GAUGUIN}}^{2}}{{\chi }_{\mathrm{median},\mathrm{GAUGUIN}}^{2}({\rm{S}}/{\rm{N}})},\end{array}\end{eqnarray} \tag{ 11 }$$

with μ_MADERA and μ_GAUGUIN being being two arbitrary weighing factors. ${\bar{\chi }}^{2}$ is basically an effective χ² for the combined fit, and its inverse, i.e., $Q=1/{\bar{\chi }}^{2}$, can be seen as a quality parameter, i.e., a low value of ${\bar{\chi }}^{2}$ (a high value of Q) corresponds to a good fit. For the following we assume μ_MADERA = 1.25 and μ_GAUGUIN = 1, i.e., we are a little more restrictive with respect to the quality of the MADERA metallicity because of the poorer fits for some of the metal-rich stars.

In Figure 8 we consider the [α/Fe] versus iron relation for four different bins in the quality parameter ${\bar{\chi }}^{2}$, namely $0\leqslant {\bar{\chi }}^{2}\lt 1.4$, $1.4\leqslant {\bar{\chi }}^{2}\lt 2.5$, $2.5\leqslant {\bar{\chi }}^{2}\lt 4$, and ${\bar{\chi }}^{2}\geqslant 4$. The ([Fe/H], [α/Fe]) values are color-coded by S/N. We separate the population of stars into three categories based on the BDASP stellar parameters, hot stars (${T}_{\mathrm{eff}}\gt 5500$ K, top row), cool giants (${T}_{\mathrm{eff}}\gt 5500$ K and $\mathrm{log}g\lt 3.5$, middle row), and cool dwarfs (${T}_{\mathrm{eff}}\gt 5500$ K and $\mathrm{log}g\gt 3.5$, bottom row).

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The high-quality (${\bar{\chi }}^{2}\lt 1.4$) sample shows the expected behavior: for metallicities above $[\mathrm{Fe}/{\rm{H}}]\approx -1$, all stars follow the [α/Fe] versus [Fe/H] relation of the Galactic disk. Owing to the scatter in the abundance determination of about 0.15 dex even for the highest-quality sample, a separation into two disk components cannot obviously be seen (see, however, Section 8.1). Cool dwarfs, which owing to their low luminosity are mainly in the immediate neighborhood of the Sun, mainly have abundances comparable to the Sun; hot stars that can be identified to larger distances extend the [α/Fe] versus [m/H] relation toward considerably lower abundances. For cool giants, the data extend well into the metal-poor regime $[{\rm{m}}/{\rm{H}}]\lt -1$, and the transition to a constant α overabundance is nicely traced. Relaxing the quality criteria keeps these characteristics at first for all three populations, but increases the scatter. For the high-S/N end of the distribution, fairly confined and well defined relations can still be traced. A further relaxation of the quality parameter (${\bar{\chi }}^{2}\gt 2.5$) results in populating the area near the edges of the Gaia–ESO Survey grid, in particular for the lower-S/N data.

The aforementioned behavior is also reflected in Figure 9, which illustrates it now projected in bins of different S/N (and color coding by ${\bar{\chi }}^{2}$). In particular, it shows a systematic shift of the [α/Fe] versus [Fe/H] relation with decreasing S/N, with the lower-S/N subset seeming to have systematically higher [α/Fe]. This effect can be understood, as the pipeline reacts to the increasing noise level by interpreting this as a higher α abundance. Again this effect is more pronounced in situations where the match between the Rave spectrum and template is poorer.

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Overall, ${\bar{\chi }}^{2}\lt 2.5$ provides satisfactory results for hot stars, while for cooler stars and low S/N still some clustering at the grid boundaries, in particular at fairly negative [α/Fe] and high metallicity, can be observed. Such a quality cut also removes most targets from the first year of Rave observations that were still contaminated by light from second-order spectra (see DR6-1, Section 2.4). The residual presence of questionable abundance measurements at negative [α/Fe] and high metallicity can be suppressed by requiring a more stringent (lower) ${\bar{\chi }}^{2}$ value, in particular for lower S/N values. For example, the constraint ${\bar{\chi }}^{2}\lt 1.4$ for ${\rm{S}}/{\rm{N}}\lt 40$ basically removes all stars with $[\alpha /\mathrm{Fe}]\lt -0.1$ at $[\mathrm{Fe}/{\rm{H}}]\gt -0.4$. This is demonstrated in Figure 10, in which a critical threshold of ${\bar{\chi }}^{2}\lt {\bar{\chi }}_{\mathrm{crit}}^{2}=1.1\times \sqrt{{\rm{S}}/{\rm{N}}/10-1.5}$ is applied.

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Figure 12 shows the Rave sample defined by the different quality cuts in the ${T}_{\mathrm{eff}}$ versus $\mathrm{log}g$ plane (the "Kiel diagram"), where the blue scale is coded by the metallicity [m/H]. The quality cuts applied are (from top to bottom) for the left column (i) the MD sample, (ii) the MD40 sample, and (iii) MD60 sample, while for the right column, (i) the BD sample, (ii) the BD40 sample, and (iii) BD60 sample are shown, respectively. In the top left frame (MADERA), the stellar atmospheric parameters of the calibration sample are also plotted, color-coded by their origin (see the Appendix). In the top right frame (BDASP) we also show the validation sample used below for verifying the output of the GAUGUIN pipeline. As one can see, calibration and validation samples neatly cover the most relevant areas of the Kiel diagram, namely the main-sequence, main-sequence turn-off stars and subgiants, and the giant branch and the red clump region. For the Ruchti et al. (2011) sample, which was designed as a follow-up study of low-metallicity candidates drawn from earlier Rave data releases, the shift toward higher temperature when compared to the higher-metallicity Gaia–ESO DR5⁴⁷ sample is clearly visible, a feature that is nicely reproduced for the MADERA and BDASP pipelines. Furthermore, the pixelization of the MADERA pipeline (for a discussion see DR4, Section 6.3) is clearly visible.

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The results for the BDASP pipeline show a considerable sharpening of the distribution, with the main sequence and the position of the red clump being clearly defined. In particular, the region for $\mathrm{log}g\gt 3.5$ strongly benefits from the inclusion of Gaia parallaxes, as these dwarf stars are predominantly at lower distances ($d\lesssim 0.8$ kpc) and thus benefit from the accuracy of the parallax measurement.

For higher-S/N cuts, a clearly defined sequence nearly parallel to the main sequence but shifted by about +0.2 dex in $\mathrm{log}g$ becomes visible. This parallel sequence is mainly a product of unresolved binaries. These binaries form a second track in the color–magnitude diagram, about 0.7 mag brighter than main-sequence stars of the same color. BDASP assumes every target to be a single star, and therefore finds a poor match between stars on this track and main-sequence stars, instead finding close matches with pre-main-sequence stars which have lower $\mathrm{log}g$ at the same ${T}_{\mathrm{eff}}$. This explanation can be given more credence by the following observation: in Figure 13 we color-code the Kiel diagram by Gaia's re-normalized unit weight error (RUWE; Lindegren 2018), which is an indication of the quality of the Gaia DR2 astrometric fit. We see that the RUWE is noticeably higher in the parallel sequence, which is consistent with the astrometry being perturbed by the binary motion of the stars.

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We can both illustrate and verify the automated classification scheme (see Section 4 in DR6-1) by showing where stars of different classifications lie in the $\mathrm{log}g$ versus ${T}_{\mathrm{eff}}$ plane (Figure 14): The classification scheme clearly shows the transition to hot stars above a temperature of ${T}_{\mathrm{eff}}\approx 7000\,{\rm{K}}$ owing to the presence of strong Paschen line features, which dominate over the Ca triplet feature. On the main sequence, at effective temperatures below 5000 K, chromospheric emission lines become more prevalent in these cool and active stars (Žerjal et al. 2013). At temperatures below 4000 K, molecular lines lead to a classification of the star as cool or as having carbon features, in particular near the tip of the giant branch. A slightly pinkish color in the sequence parallel to the main sequence for temperatures above 4500 K also indicates a binary origin of stars in this part of the $\mathrm{log}g$ versus ${T}_{\mathrm{eff}}$ plane; for temperatures below 4500 K, the emission-line characteristics dominate the classification also in this part of the parallel sequence.

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6.2.1. Validation of Stellar Atmospheric Parameters

For an extensive validation of the pure spectroscopic MADERA stellar atmospheric parameters and their limitations we refer to DR4 and DR5.

Figure 15 compares ${T}_{\mathrm{eff}}$, $\mathrm{log}g$, and [m/H] derived from each of the MADERA and BDASP pipelines for the MD20 and BD20 sample with the values derived from 1094 external high-resolution observations (see the Appendix). For the BDASP sample, the metallcity [M/H] has been scaled to [m/H] using the inverse of Equation (5). Note that this comparison is not fully independent, as some of the external data set has been used to calibrate the outcome of the MADERA pipeline (see Section 3.1 and the Appendix). The effective temperatures of both methods give similar results in terms of uncertainties. However, the MADERA pipeline is more affected if low-S/N Rave targets are included in the comparison (for the MD00 sample, the standard deviation for MADERA increases to 320 K, while the value for BDASP remains basically unchanged). A closer inspection of the MADERA plot also reveals a tendency to somewhat overestimate the temperatures between 5000 and 6000 K by ≈250 K. This becomes more visible when the MADERA ${T}_{\mathrm{eff}}$ are compared with the temperatures derived via the infrared flux temperatures (see Figure 16). As expected, no such trend is visible in the effective temperature of the BDASP pipeline, which has used ${T}_{\mathrm{eff},\mathrm{IRFM}}$ as an input value.

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The surface gravities $\mathrm{log}g$ demonstrate the full potential of the parallax constraint from Gaia DR2. The derivation of $\mathrm{log}g$ has always been a major challenge for Rave because of the short wavelength interval and well known degeneracies (Kordopatis et al. 2011). The MADERA pipeline results for $\mathrm{log}g$ are on average unbiased, but exhibit a scatter of about 0.68 dex, while the BDASP pipeline can considerably reduce the uncertainty to only 0.33 dex and produce $\mathrm{log}g$ values that are unbiased, compared to asteroseismic estimates (see Section 6.4). Indeed, a comparison of the structure of the $\mathrm{log}g$ versus ${T}_{\mathrm{eff}}$ diagram with external data from the GALAH and APOGEE surveys (Section 6.3), plus the analysis of the repeat observations in Section 6.5 below, and the comparison with the asteroseismic information (Section 6.4) all lead to the conclusion that, as far as $\mathrm{log}g$ is concerned, much of the variation between the values obtained with BDASP and the external measurements may well need to be attributed to uncertainties in the external calibration sample.

In terms of the metallicity [m/H], both pipelines perform equally well, and indeed we recommend using the MADERA [m/H] as the metallicity estimate, as it is the only one that is directly derived spectroscopically.

6.2.2. Validation of GAUGUIN Abundances

[α/Fe] ratios. Figure 17 (top row) compares the [α/Fe] ratios obtained with GAUGUIN using the stellar atmospheric parameters ${T}_{\mathrm{eff}}$, $\mathrm{log}g$, and [Fe/H] of the calibration sample (see Section 6.2.1 and DR5 Section 7) against the [α/Fe] ratios of the calibration sample (defined as the average of [Si/Fe] and [Mg/Fe]). The abundances trace the pattern observed in the external reference stars very well, with a scatter of about 0.12 dex, and almost no bias. The bottom row of Figure 17 shows the analogous comparison when MADERA ${T}_{\mathrm{eff}}$, $\mathrm{log}g$, and [m/H] are used as input parameters. The abundances trace the pattern observed in the external reference stars still well, with a scatter somewhat increasing for lower-metallicity stars. Outliers can be directly mapped to large differences in ${T}_{\mathrm{eff}}$, $\mathrm{log}g$, and [m/H] between the calibration sample and the corresponding MADERA values. This is consistent with the poor ${\bar{\chi }}^{2}$ values for those outliers.

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The [Fe/H], [Al/H], and [Ni/H] ratios. The top row of Figure 18 compares [Fe/H], [Al/H], and [Ni/H] obtained with the GAUGUIN pipeline against those of the calibration sample. GAUGUIN was fed with the stellar atmospheric parameters of the calibration sample. For [Fe/H], the bias seems to slightly increase toward the [Fe/H]-poor regime, with a dispersion of 0.09 dex. For [Al/H] and [Ni/H] ratios, we notice a weak scatter as well, 0.13 and 0.08, respectively. For [Ni/H] we unfortunately have only very few stars. The biases and scatters observed here can be due to several factors, such as the different linelists and spectral resolution of Rave and the reference studies.

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In the bottom panel of Figure 18, we compare the GAUGUIN [Fe/H], [Al/H], and [Ni/H] values derived with MADERA input to those of the calibration sample (same stars as in the top row). For [Fe/H] and [Al/H], we notice an increase of the scatter for the Fe-poor regime. Basically, the comparison gives fairly satisfactory results, with an increased dispersion, driven by different input stellar atmospheric parameters.

Abundance trends in the Kiel diagram. Abundance trends for the [α/Fe], $[\mathrm{Al}/\mathrm{Fe}]$ and $[\mathrm{Ni}/\mathrm{Fe}]$ can neatly be followed by grouping them by $\mathrm{log}g$ and ${T}_{\mathrm{eff}}$ in the Kiel diagram. This is done in Figure 19 for [α/Fe] and for $[\mathrm{Al}/\mathrm{Fe}]$ and $[\mathrm{Ni}/\mathrm{Fe}]$ in Figures 20 and 21, respectively. In these diagrams we bin stars of the BD40 sample by their BDASP $\mathrm{log}g$ and ${T}_{\mathrm{eff}}$ in bins of size 1 dex and 500 K, respectively. We start with $4\lt \mathrm{log}g\leqslant 5$ and $4000\lt {T}_{\mathrm{eff}}\leqslant 4500$ in the lower right panel with ${T}_{\mathrm{eff}}$ increasing toward the left, and $\mathrm{log}g$ decreasing going upward. The leftmost plot includes all stars hotter than 7000 K. Each panel shows the [α/Fe] versus $[\mathrm{Fe}/{\rm{H}}]$ relation, and in addition shows an icon of the Kiel diagram in blue, with the respective subsample marked in red.

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The [α/Fe] versus [Fe/H] relation across the ${T}_{\mathrm{eff}}$–$\mathrm{log}g$ plane is shown in Figure 19. The figure nicely demonstrate how the GAUGUIN-derived abundances can track the systematically different behavior for different Galactic populations. For giants we probe predominantly the low-metallicity regime, which shows a successively increasing α overabundance with decreasing metallicity and the transition to a plateau at $[\alpha /\mathrm{Fe}]\approx 0.4$. Main-sequence stars, on the other hand, mainly test the thin disk behavior of the extended solar suburb.

Indeed, while we clearly see, as demonstrated in the next section, several populations of stars in terms of their combined chemical and kinematical properties, only in very few areas in the ${T}_{\mathrm{eff}}$–$\mathrm{log}g$ plane do we simultaneously see several components, most notably at ${T}_{\mathrm{eff}}\lt 5000$ K and $\mathrm{log}g\lt 2$, i.e., for red giants. There is also a trend that the slope of the [α/Fe]–[Fe/H]-relation is steeper for giants than it is on the main sequence. When comparing these findings with those of other surveys we have to alert the reader to properly take into account the different selection effects. For example APOGEE predominantly focuses on giants and has a large fraction of their targets at low Galactic latitudes (thanks to the near-infrared nature of this survey), while this area is almost completely excluded by the survey design of Rave. We also note that bright giants are a much rarer population in the Rave sample, reflecting the relatively bright magnitude limit of Rave compared with other ongoing surveys. Rave is basically dominated by two populations, main-sequence stars and red clump stars, as indicated by the density scale in Figure 19.

While not an α-element, aluminum is also predominantly formed in massive stars (Thielemann & Arnett 1985) and released to the interstellar medium via type-II supernovae. Therefore, similar abundance trends as observed for α-elements are expected. Indeed, while the scatter is considerably larger—we fit only very few lines in the CaT region, while for [α/Fe] we basically make use of the full spectrum—similar trends to those of α-elements can be observed (see Figure 20), in particular a relative-to-solar overabundance of Al for metal-poor giant stars, and a systematic trend of decreasing aluminum abundance for increasing metallicity. For the brightest red giants in our sample, as for [α/Fe], only aluminum-enriched very low-metallicity stars can be found in the sample, indicative that we trace the halo and metal-weak thick disk component. A kinematical analysis of this subset (see Section 8.2) shows that these stars are indeed on highly eccentric and inclined orbits.

As an iron group element, we would expect (within the accuracy expected by Rave) nickel to basically follow the same trends as the iron abundance, i.e., $[\mathrm{Ni}/\mathrm{Fe}]\approx 0$. This is indeed the case as illustrated by Figure 21, which shows systematic changes in the overall abundance as we move from red giants via red clump stars to main-sequence stars, but the relative abundance between Ni and Fe basically remains constant.

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APOGEE and GALAH are two high-resolution spectroscopic campaigns currently underway. APOGEE has R = 22,500 resolving power in the near-infrared, and mainly focuses on giant stars in the Galactic disk. Most of the publicly released APOGEE data cover Earth's northern hemisphere, so there is little overlap with Rave so far. The joint sample of Rave and APOGEE DR16 (Ahumada et al. 2020)—with the Rave quality constraints defined above and with abundances flagged by the APOGEE consortium as being reliable—amounts to 4859 objects.

GALAH is a high-resolution (R = 28,000) spectroscopic survey at optical wavelengths using the HERMES spectrograph and the 2dF fiber positioner facility at the AAO 3.9 m telescope. The GALAH second data release (Buder et al. 2018), published shortly before Gaia DR2, provides stellar atmospheric parameters and abundances for up to 342,682 stars in Earth's southern hemisphere. The Rave and GALAH data sets have 21,534 stars in common. Of these, 13,254 stars have a high-S/N (snr_med_sparv ≥ 20) Rave spectrum and a satisfactory-quality GALAH spectrum (flag_cannon = 0). Only these stars are used in the discussion below, with the further requirement that flag_x_fe = 0 when discussing individual element abundances [X/H].

It is illustrative to compare the outcome of the medium-resolution Rave data with the considerably higher-resolution APOGEE and GALAH data. When performing these comparisons one should, however, be aware that—unlike BDASP—neither the APOGEE nor the GALAH data pipeline has yet made use of the Gaia DR2 parallaxes. However, both surveys employed asteroseismic information from Kepler/K2 for constraining $\mathrm{log}g$.

Figure 22 compares ${T}_{\mathrm{eff}}$, $\mathrm{log}g$, and the abundances for Fe, Al, Ni, and α between Rave (BDASP) and APOGEE DR16 (upper two rows) and GALAH DR2 (lower two rows). Note that we plot all stars in common, irrespective of their possible classification. This simplification does not affect the general statistics of the comparison samples appreciably, but could be important when comparing individual objects, as discussed in DR6-1, Section 4.

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The comparison shows an excellent agreement in the derived values for $\mathrm{log}g$ and ${T}_{\mathrm{eff}}$. Indeed, the advantage of having Gaia DR2 parallax information available for Rave results in $\mathrm{log}g$ estimates that are at least comparable to those derived with higher-resolution spectroscopy. We compared Rave results also with new unpublished GALAH values of $\mathrm{log}g$ and [Fe/H], which make use of Gaia astrometry. This new information makes the $\mathrm{log}g$ values of both data sets almost identical (Δ = 0.03, σ = 0.10) and decreases the iron abundances for GALAH by ∼0.1 dex. For some elements like Fe, Al, and α, the trends between Rave and GALAH and between Rave and APOGEE appear qualitatively to be very similar, exhibiting a slight tilt in the residual in the sense that Rave tends to underestimate abundances for solar-type stars. Furthermore, unlike the Rave/APOGEE sample, the Rave/GALAH sample includes both dwarfs and giants, with each component having slightly different systematics, visible in a slight bimodality ($[\mathrm{Fe}/{\rm{H}}]\gt 0$ versus $[\mathrm{Fe}/{\rm{H}}]\lt 0$). Note that the expected modest decrease in [Fe/H] derived from GALAH when the surface gravity is constrained astrometrically affects also the abundances of other elements, as [X/H] = [X/Fe]+[Fe/H]. As a result, the comparison presented in Figure 22 seems rather conservative, with a suggestion that Rave values could show an even better agreement with high-resolution surveys when Gaia DR2 results will be used throughout. This is encouraging for future applications on medium-resolution data, like those that will come from WEAVE (Dalton et al. 2018), 4MOST (de Jong et al. 2019), or the Gaia RVS spectrometer. Considering the apparent differences between the two high-resolution surveys we feel confident that our pipelines have extracted the maximum possible from the Rave spectra, given the limitation of resolution and S/N.

Figure 23 compares the asteroseismic $\mathrm{log}g$ derived using Equation (6) and $\mathrm{log}g$ obtained from the MADERA and BDASP pipelines. This comparison shows the impact of Gaia DR2 parallaxes on the derived stellar atmospheric parameters, which remove the $\mathrm{log}g$–${T}_{\mathrm{eff}}$ degeneracy of the atmospheric stellar atmospheric parameters derived using only spectroscopy.

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A further way to validate the quality of the Rave data products is to compare the parameters derived for multiple observations of the same object (see Section 2.7 in DR6-1). In the following analysis we calculate for each property W under consideration (${T}_{\mathrm{eff}}$, $\mathrm{log}g$, [α/Fe], individual element abundances) and for each star k that has ${N}_{\mathrm{repeat}}^{k}\gt 1$ observations that fulfil the quality threshold, the difference between the observation i ($1\leqslant i\leqslant {N}_{\mathrm{repeat}}^{k}$)-derived properties W_i^k and the mean ${\bar{W}}^{k}$ for the respective repeat sequence. We then analyze the distribution function of ${\rm{\Delta }}{W}_{i}^{k}={W}_{i}^{k}-{\bar{W}}^{k}$ over all stars k and observations i. The distribution function is then approximated by a combination of two Gaussians using a least-squares fit.

Figure 24 shows the distribution function for ${T}_{\mathrm{eff}}$, $\mathrm{log}g$, and the elemental abundances for the MD20/BD20 sample in addition to a fit of the distribution with two Gaussians.

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Overall the distributions show very similar behavior: a core region that is well fit by two Gaussians, plus a wide exponential wing, which includes, however, only a few percent of the overall sample. The prominence of the wing and also the width of the wider Gaussian increase if we move from high (MD40) to lower-quality-constraint samples (like MD00). Occasionally, a spike at ΔW = 0 can be observed, in particular for the MADERA pipeline, reflecting the tendency of this pipeline to assign values close to the vertices of the spectral template grid ("pixelization"). Those spikes are excluded from the fitting procedure.

The distribution for the MADERA values for ${T}_{\mathrm{eff}}$, $\mathrm{log}g$, and [m/H], in the repeat sequence gives a result consistent with the differences between the MADERA value and the external data set, though overall the errors appear to be systematically smaller, reinforcing that a considerable uncertainty has to be assumed also for the stellar atmospheric parameters of the high-resolution sample, in particular for $\mathrm{log}g$. The uncertainties for the individual elements are also consistent with the errors quoted in Sections 4 and 6.2.2.

The on-first-sight surprisingly small variance in the BDASP values reflects the fact that these properties are predominantly not determined by Rave spectroscopic data. BDASP uses as temperature input ${T}_{\mathrm{eff},\mathrm{IRFM}}$, which is primarily determined by photometric data (which are the same for all members of a repeat sequence) and only weakly depends on the input $\mathrm{log}g$ from the MADERA pipeline. Variations thus come in only via [m/H]. $\mathrm{log}g$ is mainly determined by Gaia DR2 parallax information in the Bayesian framework, so again is only very weakly dependent on the MADERA input and thus on the spectral information.

The detailed use of the Rave DR6 data products and the quality criteria to be applied depend on the particular science case under consideration. A general recommendation thus cannot be made. Considering our experience working with Rave data over the past 15 years, and the various tests we performed in particular in the context of this data release, we recommend the following as a starting point in particular in the context of Galactic dynamics and Galactic archeology applications.

• 1.  
  Use the BDASP values for $\mathrm{log}g$, ${T}_{\mathrm{eff}}$, and the distance of the star, and the calibrated MADERA value for the overall metallicity [m/H]. In particular BDASP properties are recommended for the identification of subpopulations (dwarfs, giants, red-clump stars).
• 2.  
  For abundance ratios we recommend the α-enhancement and Al, Fe, and Ni values derived using GAUGUIN for $\mathrm{log}g$, ${T}_{\mathrm{eff}}$, and [m/H] taken from MADERA, as the MADERA/GAUGUIN combination provides an internally consistent pure spectroscopic framework. The use of BDASP-derived parameters as input parameters for a determination of the α-enhancement [α/Fe] should be taken with caution, as it introduces systematic inconsistencies in the templates used for the determination of [α/Fe] and the determination of the metallicity.
• 3.  
  For applications where a purely spectroscopically derived stellar parameter is sought, we recommend the calibrated MADERA values for $\mathrm{log}g$, ${T}_{\mathrm{eff}}$, and [m/H], and α-enhancements based on MADERA input parameters.

Stellar atmospheric parameters are derived using three pipelines and, consequently, assembled in three catalogs: DR6_MADERA (doi:10.17876/rave/dr.6/006, Table 7), DR6_IRFM (doi:10.17876/rave/dr.6/007, Table 8), and DR6_BDASP (doi:10.17876/rave/dr.6/008, Table 9). DR6_BDASP also provides an improved distance estimate and extinction measure combining Gaia, spectroscopic, and photometric data, as well as estimates for the mass and the age of the respective star based on a Bayesian isochrone comparison.

Table 7.  DR6_MADERA Catalog Description

Col	Format	Units	NULL	Label	Explanations
1	char	⋯	N	rave_obs_id	Rave spectrum designation
2	float	K	Y	teff_madera	Effective temperature
3	float	K	Y	teff_cal_madera	Calibrated effective temperature
4	float	K	Y	teff_error_madera	Error in effective temperature
5	float	dex	Y	logg_madera	log surface gravity
6	float	dex	Y	logg_cal_madera	Calibrated log surface gravity
7	float	dex	Y	logg_error_madera	Error in log surface gravity
8	float	dex	Y	m_h_madera	Uncalibrated metallicity ${[{\rm{m}}/{\rm{H}}]}_{{\rm{u}}}$
9	float	dex	Y	m_h_cal_madera	Calibrated metallicity ${[{\rm{m}}/{\rm{H}}]}_{\mathrm{DR}6}$
10	float	dex	Y	m_h_error_madera	Error in metallicity [m/H]
11	float	⋯	Y	algo_conv_madera	Quality flag for MADERA [0..4]a
12	float	⋯	Y	chisq_madera	χ2 of the best fit
13	float	⋯	Y	snr_madera	S/N employed in the MADERA pipeline
14	float	⋯	Y	chisq_madera	χ2 of the best fit

Note.

^aFlag of the MADERA stellar parameter pipeline: 0 = pipeline converged. 1 = no convergence. 2 = MATISSE oscillated between two values and the mean was calculated. 3 = results of MATISSE at the boundaries or outside the grid and the DEGAS value was adopted. 4 = the metal-poor giants with snr_madera < 20 were re-run by DEGAS with a scale factor (i.e., internal parameter of DEGAS) of 0.40.

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Table 9.  DR6_BDASP Catalog Description

Col	Format	Units	NULL	Label	Explanations
1	char	⋯	N	rave_obs_id	Rave spectrum designation
2	float	pc	N	distance_bdasp	Heliocentric distance estimate
3	float	pc	N	distance_error_bdasp	Heliocentric distance uncertainty
4	float	yr	N	age_bdasp	Age estimate
5	float	yr	N	age_error_bdasp	Age uncertainty
6	float	K	N	teff_bdasp	${T}_{\mathrm{eff}}$ estimate
7	float	K	N	teff_error_bdasp	${T}_{\mathrm{eff}}$ uncertainty
8	float	dex	N	logg_bdasp	$\mathrm{log}g$ estimate
9	float	dex	N	logg_error_bdasp	$\mathrm{log}g$ uncertainty
10	float	${M}_{\odot }$	N	mass_bdasp	Mass estimate
11	float	M⊙	N	mass_error_bdasp	Mass uncertainty
12	float	⋯	N	log_a_v_bdasp	Log of extinction (AV/mag) estimate
13	float	⋯	N	log_a_v_error_bdasp	Log of extinction (AV/mag) uncertainty
14	float	dex	N	m_h_bdasp	[M/H] estimate
15	float	dex	N	m_h_error_bdasp	[M/H] uncertainty
16	float	mas	N	parallax_bdasp	Parallax estimate
17	float	mas	N	parallax_error_bdasp	Parallax uncertainty
18	float	mag	N	dist_mod_bdasp	Distance modulus estimate
19	float	mag	N	dist_mod_error_bdasp	Distance modulus uncertainty
20	float	mag	N	a_v_inf_prior_bdasp	Prior on extinction (AV) at infinity used

Note. All parameter are determined using the BDASP pipeline.

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The asteroseismically calibrated red giant catalog is provided in the DR6_Seismo file (doi:10.17876/rave/dr.6/013), Table 10). We recommend to use DR6_Seismo only for targets that are classfied with flag1 = "n" and for which the difference between $\mathrm{log}{g}_{{\rm{S}}}$ and $\mathrm{log}{g}_{{\rm{u}}}$ is less then 0.5 dex.

Table 10.  DR6_Seismo, Asteroseismically Calibrated Red Giant Catalog Description

Col	Format	Units	NULL	Label	Explanations
1	char	⋯	N	rave_obs_id	Rave spectrum designation
2	float	K	N	teff_seismo	Effective temperature
3	float	K	N	teff_error_seismo	Error in effective temperature
4	float	dex	N	logg_seismo	$\mathrm{log}{g}_{{\rm{S}}}$
5	float	dex	N	logg_error_seismo	Uncertainty in $\mathrm{log}{g}_{{\rm{S}}}$
6	float	dex	N	m_h_seismo	${[{\rm{M}}/{\rm{H}}]}_{{\rm{S}}}$
7	float	dex	Y	m_h_error_seismo	Uncertainty in ${[{\rm{M}}/{\rm{H}}]}_{{\rm{S}}}$
8	float	dex	Y	fe_h_seismo	${[\mathrm{Fe}/{\rm{H}}]}_{{\rm{S}}}$
9	float	dex	Y	fe_h_error_seismo	Uncertainty in ${[\mathrm{Fe}/{\rm{H}}]}_{{\rm{S}}}$
10	float	dex	Y	mg_h_seismo	${[\mathrm{Mg}/{\rm{H}}]}_{{\rm{S}}}$
11	float	dex	Y	mg_h_error_seismo	Uncertainty in ${[\mathrm{Mg}/{\rm{H}}]}_{{\rm{S}}}$
12	float	⋯	Y	chisq_seismo	${\chi }^{2}$ of the best fit

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The abundances of the non-iron group elements (Al, Fe, and Ni) and of the α-enhancement [α/Fe] derived with the pipeline GAUGUIN and MADERA input are provided (doi:10.17876/rave/dr.6/009, Table 11). The analogous table for BDASP input (see comment above) can be found in (doi:10.17876/rave/dr.6/010.

Table 11.  DR6_GAUGUIN Catalog Description

Col	Format	Units	NULL	Label	Explanations
1	char	⋯	N	rave_obs_id	Rave spectrum designation
2	float	dex	N	alpha_de_gauguin	[α/Fe] estimate from GAUGUINa
3	float	dex	N	alpha_fe_error_gauguin	[α/Fe] error from GAUGUIN
4	float	⋯	N	alpha_fe_chisq_gauguin	${\chi }^{2}$ of the best fit
6	float	dex	N	fe_h_gauguin	[Fe/H] estimate from GAUGUIN
7	float	dex	N	fe_h_error_gauguin	[Fe/H] error from GAUGUIN
8	int	⋯	N	fe_h_nl_gauguin	Number of spectral lines used to derive [Fe/H]
9	float	⋯	N	fe_h_chisq_gauguin	χ2 of the best line fit
10	float	dex	N	al_h_gauguin	[Al/H] estimate from GAUGUIN
11	float	dex	N	al_h_error_gauguin	[Al/H] error from GAUGUIN
12	int	⋯	N	al_h_nl_gauguin	Number of spectral lines used to derive [Al/H]
13	float	⋯	N	al_h_chisq_gauguin	χ2 of the best line fit
14	float	dex	N	ni_h_gauguin	[Ni/H] estimate from GAUGUIN
15	float	dex	N	ni_h_error_gauguin	[Ni/H] error from GAUGUIN
16	int	⋯	N	ni_h_nl_gauguin	Number of spectral lines used to derive [Ni/H]
17	float	⋯	N	ni_h_chisq_gauguin	${\chi }^{2}$ of the best line fit

Note.

^aThis table is valid for both catalogs: DR6_GAUGUIN_MADERA and DR6_GAUGUIN_BDASP.

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For backward compatibility with the DR4 and DR5 data releases, we also provide a file with chemical abundances derived using the CDR pipeline (Boeche et al. 2011) using ${T}_{\mathrm{eff}}$, $\mathrm{log}g$, and [m/H] of the MADERA (DR6_CDR_MADERA, doi:10.17876/rave/dr.6/011) and BDASP (DR6_CDR_BDASP, doi:10.17876/rave/dr.6/012) pipeline as input, but in general recommend the use of elemental abundances from the GAUGUIN pipeline.

DR6_Orbits (doi:10.17876/rave/dr.6/014, Table 12) contains information on the orbits of the Rave stars, obtained under the assumption of a given Milky Way mass model (Section 5).

Table 12.  DR6_Orbits Catalog Description

Col	Format	Units	NULL	Label	Explanations
1	char	⋯	N	rave_obs_id	Rave target designation
2	float	kpc	N	helio_x	Heliocentric x position
3	float	kpc	N	helio_x_plus	–positive uncertainty
4	float	kpc	N	helio_x_minus	–negative uncertainty
5	float	kpc	N	helio_y	Heliocentric y position
6	float	kpc	N	helio_y_plus	–positive uncertainty
7	float	kpc	N	helio_y_minus	–negative uncertainty
8	float	kpc	N	helio_z	Heliocentric z position
9	float	kpc	N	helio_z_plus	–positive uncertainty
10	float	kpc	N	helio_z_minus	–negative uncertainty
11	float	$\mathrm{km}\,{{\rm{s}}}^{-1}$	N	helio_vx	Heliocentric velocity in x direction
12	float	km s−1	N	helio_vx_plus	–positive uncertainty
13	float	km s−1	N	helio_vx_minus	–negative uncertainty
14	float	km s−1	N	helio_vy	Heliocentric velocity in y direction
15	float	km s−1	N	helio_vy_plus	–positive uncertainty
16	float	km s−1	N	helio_vy_minus	–negative uncertainty
17	float	km s−1	N	helio_vz	Heliocentric velocity in z direction
18	float	km s−1	N	helio_vz_plus	–positive uncertainty
19	float	km s−1	N	helio_vz_minus	–negative uncertainty
20	float	kpc	N	galcyl_r	Galactocentric cylindrical radius
21	float	kpc	N	galcyl_r_plus	–positive uncertainty
22	float	kpc	N	galcyl_r_minus	–negative uncertainty
23	float	kpc	N	galcyl_z	Height above the Galactic plane
24	float	kpc	N	galcyl_z_plus	–positive uncertainty
25	float	kpc	N	galcyl_z_minus	–negative uncertainty
26	float	deg	N	galcyl_phi	Galactocentric azimuth
27	float	deg	N	galcyl_phi_plus	–positive uncertainty
28	float	deg	N	galcyl_phi_minus	–negative uncertainty
29	float	km s−1	N	galcyl_vr	Velocity in Galactocentric cylindrical radial direction
30	float	km s−1	N	galcyl_vr_plus	–positive uncertainty
31	float	km s−1	N	galcyl_vr_minus	–negative uncertainty
32	float	km s−1	N	galcyl_vz	Velocity perpendicular to the Galactic plane
33	float	km s−1	N	galcyl_vz_plus	–positive uncertainty
34	float	km s−1	N	galcyl_vz_minus	–negative uncertainty
35	float	km s−1	N	galcyl_vphi	Velocity in Galactocentric azimuth
36	float	km s−1	N	galcyl_vphi_plus	–positive uncertainty
37	float	km s−1	N	galcyl_vphi_minus	–negative uncertainty
38	float	kpc	N	min_galcyl_r	Minimum Galactocentric cylindrical radius on orbit
39	float	kpc	N	min_galcyl_r_plus	–positive uncertainty
40	float	kpc	N	min_galcyl_r_minus	–negative uncertainty
41	float	kpc	N	max_galcyl_r	Maximum Galactocentric cylindrical radius on orbit
42	float	kpc	N	max_galcyl_r_plus	–positive uncertainty
43	float	kpc	N	max_galcyl_r_minus	–negative uncertainty
44	float	kpc	N	max_galcyl_z	Maximum height above the Galactic plane on orbit
45	float	kpc	N	max_galcyl_z_plus	–positive uncertainty
46	float	kpc	N	max_galcyl_z_minus	–negative uncertainty
47	float	kpc	N	min_galsph_r	Minimum Galactocentric spherical radius on orbit
48	float	kpc	N	min_galsph_r_plus	–positive uncertainty
49	float	kpc	N	min_galsph_r_minus	–negative uncertainty
50	float	kpc	N	max_galsph_r	Maximum Galactocentric spherical radius on orbit
51	float	kpc	N	max_galsph_r_plus	–positive uncertainty
52	float	kpc	N	max_galsph_r_minus	–negative uncertainty
53	float	kpc	N	mean_galcyl_r	Orbit averaged Galactocentric cylindrical radius
54	float	kpc	N	mean_galcyl_r_plus	–positive uncertainty
55	float	kpc	N	mean_galcyl_r_minus	–negative uncertainty
56	float	km2 s−2	N	energy	Orbital energy
57	float	km2 s−2	N	energy_plus	–positive uncertainty
58	float	km2 s−2	N	energy_minus	–negative uncertainty
59	float	kpc km s−1	N	angmom	Angular momentum about Galactic z axis
60	float	kpc km s−1	N	angmom_plus	–positive uncertainty
61	float	kpc km s−1	N	angmom_minus	–negative uncertainty
62	float	⋯	N	eccentricity	Eccentricity
63	float	⋯	N	eccentricity_plus	–positive uncertainty
64	float	⋯	N	eccentricity_minus	–negative uncertainty
65	float	kpc km s−1	N	jr	Radial action
66	float	$\mathrm{kpc}\,\mathrm{km}\,{{\rm{s}}}^{-1}$	N	jr_plus	–positive uncertainty
67	float	kpc km s−1	N	jr_minus	–negative uncertainty
68	float	kpc km s−1	N	jz	Vertical action
69	float	kpc km s−1	N	jz_plus	–positive uncertainty
70	float	kpc km s−1	N	jz_minus	–negative uncertainty

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The Rave DR6 data release is complemented by two files cross-matching Rave DR6 with Gaia DR2 (DR6_GaiaDR2, doi:10.17876/rave/dr.6/015) and with a suite of other catalogs including Tycho-2, 2MASS, WISE, APASS9, and SKYMAPPER (DR6_XMatch, doi:10.17876/rave/dr.6/016).

In a first science application we show the changes in the iron abundance, α-enhancement, and kinematics throughout the volume probed by the Rave survey (for work with previous data releases, often employing a considerably smaller sample of stars; see, e.g., Williams et al. (2013), Boeche et al. (2013), Kordopatis et al. (2013b), Wojno et al. (2016, 2018), or Carrillo et al. (2018). We employ the full ${Q}_{\mathrm{high}}$ sample for giants ($\mathrm{log}g\lt 3.5$). BDASP stellar atmospheric parameters and abundances using GAUGUIN with MADERA input are used throughout this section.

The top row of Figure 25 shows a projection of Rave stars onto the R–z plane of the Galactocentric cylindrical coordinate system. Stars are binned using hexagonal bins of size 0.16 kpc. The upper left plot shows the clear decrease of the average iron abundance as we move from the Galactic plane to larger heights above the Galactic plane. Simultaneously, the composition becomes more α-enriched (second plot from the left). The change in abundances coincides with a change in kinematics: the average tangential velocity decreases (second plot from the right), while the disk is hotter, resulting in a higher RV dispersion ${\sigma }_{R}$ (rightmost plot). The center plot in the top row shows the Galactocentric RV, exhibiting a mild negative RV gradient, consistent with the finding by Siebert et al. (2011a) using Rave DR3.

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The next five rows dissect the Milky Way in slices and focus on the distribution in the x–y plane for each of these slices. The slices are for z > 1 kpc (first row) and $z\leqslant -1$ kpc (bottom row). In between, slices for −1 < z ≤ −0.2 kpc (second row), −0.2 < z ≤ 0.2 kpc (third row), and 0.2 < Z ≤ 1 kpc (forth row) are shown, respectively. The shrinking size of the slice in the x–y plane reflects the double-cone structure of the Rave survey volume, created by the exclusion of low Galactic latitude fields, in particular toward the Galactic center.

Each individual slice for [Fe/H], [α/Fe], v_ϕ, and σ_R shows a relatively homogeneous structure, with the changes with z as presented in the previous paragraph, reflecting the disk-like structure of the Milky Way. Only the central three slices exhibit some apparent radial gradient in the iron abundance with the distance from the Sun, an immediate result again of the Rave survey geometry: owing to the double conical layout of the survey volume, stars more distant in the central slices are predominantly from larger heights above the Galactic plane and thus have on average lower abundances than stars in the immediate solar neighborhood. The middle column again shows a mild outward-directed RV gradient, indicative of a non-axisymmetric gravitational potential.

In this section we repeat the analysis of Boeche et al. (2013) with the Rave DR6 data set. Unlike Boeche et al., we, however, only apply a very weak quality cut, namely the full ${Q}_{\mathrm{high}}$ giant sample with determinations of [Fe/H] and [α/Fe]. Consequently, the underlying sample could be increased by more than a factor of five from 9131 in Boeche et al. (2013) to 40,000 stars, respectively.

As in Gratton et al. (2003) or in Boeche et al. (2013) we begin with a kinematical decomposition into a so-called thin-disk component, dissipative-collapse component, and accretion component, based on the eccentricity e, the tangential velocity in cylindrical coordinates V_ϕ, and the maximum altitude from the Galactic plane z_max. The thin-disk component consists of stars with a low eccentricity (e < 0.25) and low maximum altitude (z_max < 0.8 kpc). The dissipative–collapse component, is composed of stars with higher eccentricity e > 0.25, traveling higher above the Galactic plane (z_max > 0.8 kpc), with V_ϕ > 40 $\mathrm{km}\,{{\rm{s}}}^{-1}$. This component is mainly composed of thick-disk and halo stars. The accretion component is mainly composed of halo stars and accreted stars. We adopted the criterion V_ϕ < 40 $\mathrm{km}\,{{\rm{s}}}^{-1}$, meaning that such stars are slowly rotating or even counter-rotating with respect to the Galactic disk. Based on the ${Q}_{\mathrm{high}}$ sample, we have at hand 39,130 stars of the thin-disk component, 12,354 stars in the dissipative–collapse component, and 1931 stars in the accretion component.

Figure 26 shows the [α/Fe] pattern for these three components. The thin-disk component is mainly confined at $[\mathrm{Fe}/{\rm{H}}]\gt -1$ dex, and shows an increase of its [α/Fe] with decreasing $[\mathrm{Fe}/{\rm{H}}]$. The dissipative–collapse component has a large range in iron abundance, with very few metal-rich stars and extends to very low metallicities down to $[\mathrm{Fe}/{\rm{H}}]\approx -3$ dex. Its [α/Fe] sequence is narrower, with an increased scatter toward the metal-poor end (owing to halo stars). The accretion component is mostly composed of metal-poor stars, in the range $-2.5\lt [\mathrm{Fe}/{\rm{H}}]\,\lt -0.5$, and is [α/Fe]-rich, but no trend is observed with $[\mathrm{Fe}/{\rm{H}}]$. The thin-disk component is the most metal-rich component ($\langle [\mathrm{Fe}/{\rm{H}}]\rangle =-0.18$ dex), while the dissipative–collapse component and the accretion component have an average metallicity of $\langle [\mathrm{Fe}/{\rm{H}}]\rangle =-0.64$ dex and $\langle [\mathrm{Fe}/{\rm{H}}]\rangle =-1.16$ dex, respectively. The mean [α/Fe] increases with decreasing metallicity, i.e., $\langle [\alpha /\mathrm{Fe}]\rangle =+0.11$ dex for the thin-disk component, $\langle [\alpha /\mathrm{Fe}]\rangle \,=+0.26$ dex for the dissipative–collapse component and $\langle [\alpha /\mathrm{Fe}]\rangle \,=+0.37$ dex for the accretion component.

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In a Toomre diagram, we clearly see that the dissipative–collapse component shows typical kinematics of thick-disk stars, but also halo-like kinematics (overlapping with the accretion component). We notice the presence as well of thin-disk-like stars belonging to the dissipative–collapse component. The eccentricity increases with decreasing metallicity, and the dissipative–collapse component and the accretion component show considerable overlap (likely due to halo stars). We characterized the gradients of V_ϕ as a function of $[{\rm{m}}/{\rm{H}}]$ in both thin-disk and dissipative–collapse components. In the thin-disk component, we measure a weak anti-correlation (${\rm{\nabla }}=-6\,\mathrm{km}\,{{\rm{s}}}^{-1}/\mathrm{dex}$), while a strong correlation is visible in the dissipative–collapse component (${\rm{\nabla }}=+55\,\mathrm{km}\,{{\rm{s}}}^{-1}/\mathrm{dex}$). Such gradients are consistent with previous works, like for example Lee et al. (2011) with SEGUE data or Wojno et al. (2018) for Rave.

We continue the strategy of Boeche et al. (2013) and analyze the orbits of disk giants in the $\epsilon -{z}_{{\max }}$ plane. We first separate the giant population into nine different bins with three ranges in orbital eccentricity (0 ≤  < 0.2, 0.2 ≤  < 0.4, and 0.4 ≤  < 0.6) and three ranges in maximum altitude, z_max, reached by a star in its orbit (0 kpc ≤ z_max < 1 kpc, 1 kpc ≤ _zmax < 2 kpc, and 2 kpc ≤ z_max < 3 kpc). We then investigate the distributions of the iron abundance [Fe/H] (Figure 27), of the α-enhancement [α/Fe] (Figure 28), and of the tangential velocity $| {V}_{\phi }|$ (Figure 29), as well as of the mean and minimum Galactocentric cylindrical radius R_m and R_min for these nine bins (Figure 30). Stars on orbits with  > 0.6 or z_max > 3 kpc are not considered in these plots, as we mainly focus on the thin and thick disks.

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We first concentrate on the stars in panel (a), i.e., those on orbits closest to local disk kinematics. Indeed, stars in this bin have a tangential velocity distribution that peaks near 227 $\mathrm{km}\,{{\rm{s}}}^{-1}$, at a mean Galactocentric distance of about 8 kpc. The abundances peak at [Fe/H] ≈ −0.280 dex (Figure 27), i.e., somewhat below the solar value and are slightly α-enhanced ($[\alpha /\mathrm{Fe}]=0.11$) compared to the immediate solar neighborhood (Figure 28). This reflects the fact that our sample consists of giant stars, which are therefore more distant than a few hundred parsecs. Indeed, a sample consisting of dwarf stars with the same orbital constraints exhibits a median abundance of $[\mathrm{Fe}/{\rm{H}}]=-0.06$ dex and an α-enhancement of $[\alpha /\mathrm{Fe}]=0.1$ dex.

As we go from less to more eccentric orbits (panels (a) → (c)) and from lower to higher height above the plane (panels (a) → (g)) or both (panels (a) → (i)), the distribution in the mean orbital radius R_m and in particular in the minimum distance R_min becomes broader and more skewed (Figure 30), peaking at considerably smaller Galactocentric cylindrical radii. The median tangential velocity decreases from about 230 $\mathrm{km}\,{{\rm{s}}}^{-1}$ to less than 135 $\mathrm{km}\,{{\rm{s}}}^{-1}$ (panel (i)) as expected from the increasing asymmetric drift with increasing velocity dispersion (see the previous section). The [Fe/H] distribution moves to successively lower values and reaches only $[\mathrm{Fe}/{\rm{H}}]\approx -0.75$ in panel (i), but the abundance mixture is now considerably more α-enriched with $[\alpha /\mathrm{Fe}]\approx 0.34$ (Figure 28), indicating that the sample is increasingly dominated by thick-disk and halo stars.

If we focus on the more eccentric orbital bins ((c), (f), and (i)), the distribution in velocity and radius is considerably more skewed, as expected, and the metallicity distribution exhibits a tail toward higher abundances (Figure 27). Owing to the high eccentricity, a significant fraction of the stars come from the inner disk, also resulting in a broader distribution in [Fe/H], indicating that this is a superposition of at least two populations, a low-[Fe/H] one with all the chemical characteristics of the thick disk, and a higher-[Fe/H] one more similar to the inner thin disk. Indeed, Figure 31 shows that, while samples with $[\mathrm{Fe}/{\rm{H}}]\lt -0.5$ dex and with $[\mathrm{Fe}/{\rm{H}}]\gt -0.4$ dex have little difference in their respective distribution of R_m and V_ϕ, they exhibit quite different patterns in [α/Fe], consistent with the findings in Boeche et al. (2013), but now reproduced for a much larger fraction of the Rave DR6 giant sample, as represented by the ${Q}_{\mathrm{high}}$ sample.

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We conclude our discussion by taking a tomographic look at the [α/Fe] versus Fe relation and its systematic changes as a function of location in the Galactic disk following the analysis of Hayden et al. (2015), which is based on higher-resolution APOGEE data (see, in particular, their Figure 4). Figure 32 shows a similar representation for the Rave DR6 ${Q}_{\mathrm{high}}$ giant sample. As we move away from the Galactic plane, we systematically depopulate the high-metallicity branch of the disk and start populating the very metal-poor and very α-enriched region of the [α/Fe] versus Fe relation. The respective distributions are, of course, a superposition of the chemical properties of the local environment convolved with that of other regions brought in by stars on highly eccentric and/or highly inclined orbits. Thanks to the astrometry provided by Gaia DR2, we are in the position to disentangle these effects, for example, rather than plotting the [α/Fe] versus [Fe/H] relation at the actual position space, we can use the average orbital radius (or guiding radius) R_m and the maximum height above the Galactic plane (z_max) as the respective spatial coordinates (see Figure 33). A comparison with Figure 32 reveals that the stars currently located in the Rave volume are drawn from a considerably larger volume, showing a clear transition from the local disk to the more metal-poor disk at larger heights above the plane to the more halo-type population seen at the largest distances. Also the systematic dependence of metallicity and α-enrichment on the eccentricity of the orbit (and/or vice versa) results in clear shifts toward metal-poorer and more α-enriched populations.

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