THE RADIAL VELOCITY EXPERIMENT (RAVE): FOURTH DATA RELEASE

The recent work of Kordopatis et al. (2011a, hereafter K11) on spectra with a resolution R ⩽ 10, 000 has shown that the Ca ii wavelength range suffers from spectral degeneracies that, if not appreciated, can introduce serious biases in spectroscopic surveys that use automated parameterization pipelines. These degeneracies are mostly important for cool main-sequence stars and stars along the giant branch. On the one hand, the spectral signatures that are used to determine the surface gravities for the main-sequence stars are insensitive to small log g variations, hence reducing the accuracy of the measurement of that parameter. On the other hand, the spectra of stars along the giant branch can be identical for different sets of parameters. In this case, the degeneracy is due to the fact that the spectral signatures sensitive to variations of effective temperature, surface gravity, and metallicity are the same. The degeneracy works as follows: the spectrum corresponding to a given T_eff, log g, and [M/H] is almost identical to a spectrum corresponding to a lower (higher) temperature, lower (higher) surface gravity, and lower (higher) metallicity.

Automated parameterization pipelines try to find the model template that minimizes the distance function, defined as the difference between the observation and a set of reference (model) spectra. In the case where not enough information is available in the data, the distance function can become non-convex, and secondary minima can appear, in which the parameterization algorithms can falsely converge. If these secondary minima are close in the parameter space, the resulting parameter estimation will have a large scatter around the true value, whereas if they are distant in the parameter space, the algorithms might converge randomly to one or the other according to where the noise is placed in the spectrum.

In K11 it has been shown that for low- and medium-resolution spectra around the IR Ca ii, decision-tree methods manage to better find the absolute minimum of the distance function, compared to other algorithms, like the projection methods (e.g., principal component analysis) or the ones trying to solve an optimization problem (e.g., minimum χ²), in particular when the S/N is low. For that reason, the pipeline presented in K11 iteratively renormalizes the spectra and obtains the atmospheric parameters using a combination of a decision-tree algorithm called DEGAS (Bijaoui et al. 2012) and a projection method called MATISSE (Recio-Blanco et al. 2006), which allows us to better interpolate between the grid points.

Both DEGAS and MATISSE have a learning phase based on a nominal library of synthetic spectra (i.e., the templates), described in Section 3.4. Here we describe briefly the pipeline and the two algorithms, but we refer the reader to Recio-Blanco et al. (2006), Bijaoui et al. (2012), and Kordopatis et al. (2011a) for further details.

In the limit of the sampling precision of a learning grid (i.e., the parameter steps), parameter estimation is a pattern recognition problem. The grid of synthetic spectra can be treated as a known set of patterns among which the observed spectra should be identified. The DEGAS algorithm is an oblique 3D decision tree (in our case T_eff, log g, and [M/H]), for which the decisions result from the projection of the observations onto N node vectors noted D_n(λ) (n = 1, ..., N). These node vectors are associated with a subset of spectra of the nominal library, in the sense that the result of the projection of an observed spectrum on that node will select half of the subset which most closely resembles the observation.

The recognition rules of DEGAS, at each node, are established during the learning phase as follows:

• 1.  
  The mean vector M(λ) of the flux values per pixel of all the reference spectra in the subset is computed.
• 2.  
  For each reference spectrum S_j(λ) associated with the node, the scalar product c_j = ∑_λS_j(λ) · M(λ) is calculated. Let $\tilde{\rm c}$ be the median value of c_j.
• 3.  
  The reference spectra are bisected in two new subsets, T₁ and T₂, according to the following criteria:S_j belongs to the subset T₁ if $c_j \leqslant\tilde{\rm c}$S_j belongs to the subset T₂ if c_j $> \tilde{\rm c}$.
• 4.  
  The difference vector D(λ) = M₁(λ) − M₂(λ) is determined, where M₁(λ) and M₂(λ) are the mean vectors of the flux values of each subset.
• 5.  
  If the correlation coefficient between M(λ) and D(λ) is too small (typically, smaller than 0.999), the initial subset of reference spectra is re-separated by the hyperplane defined by D(λ), iterating until convergence (going back to step 2, replacing M(λ) by D(λ)).

When the previous procedure has converged for a particular node n, the final adopted projection node vector D_n(λ) is determined, which will display the features that allow the separation of the subset of learning spectra at that node. The final median value $\tilde{c_n}$ of c_j = ∑_λS_j(λ) · D_n(λ) that will allow us to make the decisions is also set.

In this way, the recognition tree is built, having log₂(N) levels, where N is the number of spectra of the learning grid. At the lowest level nodes of the tree, only one training spectrum remains associated with each node. During the application phase, the target data O_i(λ) pass through all the levels of the recognition tree, and a template is associated with it.

Of course, noise can induce misclassifications. The exploration of the branches, even if the decision threshold $\tilde{c_n}$ does not allow it, is accomplished thanks to an activation function on the directions of the tree. Let us consider

$$\begin{equation} u_i=\frac{c_i-\tilde{c_n}}{\sigma _{c_i}}, \end{equation} \tag{ 2 }$$

where c_i = ∑_λO_i(λ) · D_n(λ), $\sigma _{c_i}=S_f \cdot \sqrt{\Sigma _\lambda D_n(\lambda)^2}$, and S_f is an arbitrary constant chosen in order to explore optimally the branches. If u_i ⩽ −k, we decide that the correct direction is 1. If u_i ⩾ k, the direction 2 is chosen. If −k < u_i < k, both directions are considered.

After the scanning of all the nodes, a subset of synthetic templates is selected, and their distances (in terms of the difference with the observed spectrum) are computed. Then, the parameters of the observed spectrum are determined by computing a weighted mean on the selected spectra, taking into account these distances, setting

$$\begin{equation} W_{i}^{n} =\left(1- \left[\sum _\lambda O_i(\lambda) - S_n(\lambda) \right]^2 \right)^{p}. \end{equation} \tag{ 3 }$$

The value p of the exponent is rather arbitrary. Following K11, where it was found that p = 64 gave the best results, the same value was adopted in what follows.

DEGAS has a key role in the pipeline used for the RAVE DR4 analyses. Because of its pattern recognition approach, it is exploring more efficiently the parameter space than other mathematical methods and, as a consequence, is less affected by secondary minima in the distance function. Hence, given a roughly normalized spectrum at the rest frame, DEGAS is used in order to achieve a good normalization for the data, using the synthetic spectrum corresponding to the intermediate solution found.

Once DEGAS has converged on a set of parameters, the new parameters are used to re-normalize the spectrum given the intermediate solution template. The re-normalization process might need several iterations until the shape of the continuum stays unchanged from one normalization to another. The number of needed iterations may vary from 3 to 10. In the case where the distance function has many secondary minima (low-S/N spectra and/or low-metallicity stars), the results of DEGAS at that stage are the most accurate among the other methods. Nevertheless, it has been shown in K11 that MATISSE manages to better interpolate between the grid points when the astrophysical information is sufficient in the spectra. Thus, once the shape of the continuum has converged, the mean S/N per pixel is estimated in the same way as in Zwitter et al. (2008), and in the case of high-S/N spectra MATISSE is run to get more precise atmospheric parameters. The S/N threshold at which MATISSE is run has been established in K11 to be S/N =30 pixel⁻¹.

The MATISSE algorithm is a local multi-linear regression method. It estimates a $\hat{\theta _i}$ stellar atmospheric parameter (i ≡ T_eff, log g, [M/H]) by projecting the observed spectrum O(λ) on a particular vector B_θ(λ) associated to a theoretical θ_i parameter, as follows:

$$\begin{equation} \hat{\theta _i}=\sum _\lambda B_{\theta _i}(\lambda) \cdot O(\lambda). \end{equation} \tag{ 4 }$$

These vectors, called B_θ(λ) functions hereafter, are computed during a learning phase. They relate, in a quantitative way, the pixel-to-pixel flux variations in a spectrum to a given variation of the θ_i parameter. In the case where the B_θ(λ) are orthogonal, the effects due to each parameter affect the spectrum in an independent way, and hence the atmospheric parameters are derived accurately. When this is not the case (as in most applications), possible degeneracies in the parameter space can occur, causing a correlation of the parameter errors.

The B_θ(λ) functions are computed within a given range of parameters, from an optimal multi-linear combination of theoretical, synthetic spectra S(λ), as follows:

$$\begin{equation} B_{\theta _i}(\lambda)=\sum _j \alpha _{ij} \cdot S_j(\lambda), \end{equation} \tag{ 5 }$$

where the α_ij factor is the weight associated with each synthetic spectrum S_j(λ), in order to retrieve the $\hat{\theta _i}$ parameter. The weights are computed during the learning phase by applying Equation (4) to a subset of synthetic spectra. Thus, combining Equations (4) and (5), one obtains

$$\begin{equation} \Theta _i = C \alpha _i, \end{equation} \tag{ 6 }$$

where $C=[c_{jj^{\prime }}]$ is the correlation matrix and Θ_i the vector of the parameters θ_i for all the considered spectra. The weights α_ij are then obtained by inverting the correlation matrix C. As explained in K11, a direct inversion of C would take into account all the available spectral signatures, including the smallest ones. Nevertheless, in the case of noisy spectra some lines become insignificant and should hence be discarded from the analysis. In order to achieve that, we adopt here the same approach as in K11, which used the Landweber algorithm to iteratively invert C. By stopping the inversion procedure at different convergence values, smaller weights are then applied to the most insignificant lines, which allows the solution to be less affected by secondary minima in the distance function. Extensive analysis of the parameter space for spectra of different S/N values allowed adoption of a different set of B_θ(λ) functions for different S/N values and hence achieved enhanced accuracy in the parameter determination (see K11 for further details).

The convergence of the algorithm works as follows: if the projection of the observed spectrum on a set of B_θ(λ) gives results that are not within the parameter ranges for which these B_θ(λ) have been computed, then a new set of B_θ(λ) is used, centered on the previous solution. This step is repeated until the results stay within the parameter range of applicability of the projection vectors. In the case where the distance function is convex, less than five iterations are usually needed to reach the absolute minimum, but in some cases of degeneracy in the distance function, the algorithm might not converge (these spectra are then flagged and should not be used from the catalog; see Section 6.1).

As noted previously, MATISSE has the advantage of interpolating accurately between the learning grid points, achieving a good parameter estimation at the high-S/N regimes. Nevertheless, local projection methods such as MATISSE have, in general, two main disadvantages. The first consists in not exploring entirely the parameter space and hence being easily trapped in secondary minima of the distance function if there is a lot of noise in the spectrum. The second disadvantage is that it can extrapolate results outside the boundaries of the learning grid. These two undesired effects are attenuated with the parallel use of DEGAS. Indeed, as described in Section 3.2, DEGAS is first used to converge toward a sub-region of the parameter space. Then, for the lowest S/N spectra or when the derived MATISSE parameters are outside the grid's limits, the results of DEGAS are adopted, and MATISSE is not implemented.²⁶

The very high resolution grid computed in K11 has been convolved with a Gaussian kernel, in order to obtain a new synthetic library at R = 7500,²⁷ with a constant wavelength step of 0.35 Å and covering the wavelength range of 8450.80–8746.55 Å. In addition, the cores of the Ca ii lines have been removed from the synthetic spectra, corresponding to 1 pixel for the first Ca ii line and 2 pixels for the other two lines. This removal is justified since the cores of the lines are formed in the upper stellar atmospheric layers where some modeling assumptions like the local thermodynamical equilibrium (LTE) or hydrostatic equilibrium might not be valid hypotheses anymore. The flux disagreement with real spectra for these pixels can induce the algorithms to converge to false minima, and hence the cores must be discarded (see K11 for further details).

We recall that the synthetic library has been computed using the one-dimensional, LTE and hydrostatic equilibrium MARCS model atmospheres (Gustafsson et al. 2008), in combination with the Turbospectrum code (Alvarez & Plez 1998). The atomic line list has been calibrated on high-S/N and high-resolution spectra of the Sun and Arcturus (Brault & Neckel 1987; Hinkle et al. 2003), assuming the solar abundances of Grevesse (2008), except for CNO, where we used the values of Asplund et al. (2005). The molecular line list includes ZrO, TiO, VO, CN, C2, CH, SiH, CaH, FeH, and MgH lines with their corresponding isotopic variations (kindly provided by B. Plez).

The reference grid spans effective temperatures from 4000 K to 8000 K with a constant step of 250 K and surface gravities from 0.0 dex to 5.0 dex with a constant step of 0.5 dex. In addition, the library spans with a constant step of 200 K effective temperatures from 3000 K to 4000 K and surface gravities from 0.0 dex to 5.5 dex. As far as the metallicities are concerned, the number of grid models has increased compared to K11. Instead of having a variable metallicity step, ranging from 0.25 dex for the most metal-rich stars to 1 dex for the stars with [M/H] <−3 dex, the new grid has a constant metallicity step of 0.25 dex for all the metallicities ranging from [ − 5.0; +1.0] dex. These new spectra, whose atmospheric models did not exist in the MARCS database, have been linearly interpolated from the existing synthetic spectra.

One of the noticeable differences between previous data releases and DR4 is that, in this work, only three parameters are independent in the grid: the effective temperature, T_eff, the logarithm of the surface gravity, log g, and the overall metallicity, [M/H]. This restriction decreases the number of the secondary minima of the distance function, hence increasing the accuracy of the parameter derivation. It should be noted though that the microturbulent velocity (ξ) is not constant within the grid, but is changed in lock-step with the gravity of the stars. Dwarfs (log g ⩾3.5 dex) have a microturbulent velocity of ξ = 1 km s⁻¹, whereas giants have ξ = 2 km s⁻¹. Abundances of the α-elements²⁸ are also changed systematically with metallicity, being scaled on the iron abundance, [Fe/H], following the standard α-enhancement found for the metal-poor stars of the Milky Way (thick disk and halo):

• 1.  
  [α/Fe] = 0.0 dex for [Fe/H] ⩾0.0 dex
• 2.  
  [α/Fe] = −0.4 ×[Fe/H] dex for −1 ⩽[Fe/H]⩽0 dex
• 3.  
  [α/Fe] = +0.4 dex for [Fe/H] ⩽ −1.0 dex.

In addition, spectra for which the parameter combinations did not correspond to realistic astrophysical stars have been removed from the learning grid and hence from the solution space as well. To minimize the importance of our astrophysical priors in the derived parameters, we removed only the templates with log g =5 dex and T_eff >6250 K, those with T_eff ⩽4250 K and 4 ⩽ log g ⩽3 dex, as well as all stars with [M/H] ⩽ −3 dex, T_eff ⩽4000 K, and log g ⩽4 dex. These criteria correspond to excluding very young stars with extremely metal-poor abundances (age < 0.5 Gyr and [Fe/H] <−2.5 dex), as well as old stars that are extremely metal-rich (age > 14 Gyr and [Fe/H] >0.75 dex). The final grid contains 3580 spectra of 839 pixels each.

Based on this grid, a subset of reference models can be selected, according to the additional information that is available for each data set to be treated. In the case of RAVE, the 2MASS photometric information that is available for the observed targets is used to exclude some parameter combinations from the solution space corresponding to derived temperature ranges which are grossly inconsistent with the photometric color. In practice, the RAVE spectra have been separated into four different color ranges. Then, according to their 2MASS (J − K_s) color, a set of solutions has been imposed as soft photometric priors for every analyzed spectrum, defining:

• 1.  
  (J − K_s) > 0.75⇒ T_eff <4500 K
• 2.  
  0.4 < (J − K_s) < 0.75⇒3750 < T_eff <6000 K
• 3.  
  (J − K_s) < 0.4⇒ T_eff >5250 K.

The few stars for which no 2MASS photometry was available (less than 2%) form a fourth category for which there is no prior on the solution space.

The above-mentioned effective temperature ranges have been determined by requesting a color–magnitude diagram of the Galaxy from the web interface²⁹ of the Padova database with the 2MASS photometric system. Then, for the above three color ranges we inferred the full range of effective temperatures of the simulated stars and increased these limits by ±500 K. We note that the effective temperature bins have been made deliberately large, because neither the photometric errors nor the extinction have been taken into account when separating the spectra into color bins.

The total uncertainty of the pipeline for a given star is the quadratic sum of its internal and external errors. The internal uncertainties relate the capacity of an algorithm to treat spectral degeneracies and S/N, whereas external uncertainties concern the difference between the template synthetic spectra and the true stellar spectra (see Section 4.6).

Following K11, the internal uncertainties of the algorithm have been estimated by computing a set of spectra of realistic Galactic populations. Based on the Besançon Galactic model, a simulated catalog of stars toward three different Galactic directions (Galactic center, north Galactic pole, and intermediate Galactic latitudes) has been constructed, from which 10⁴ stars have been randomly selected to be our realistic Galactic sample. In addition, in order to explore different metallicity regimes, each star has been replicated in the catalog, with its partner having reduced (by −0.75 dex) metallicity. The 2 × 10⁴ synthetic spectra corresponding to these parameter combinations have been computed thanks to the interpolation capabilities of MATISSE, and four different values of white Gaussian noise were added to them (S/N = 100, 50, 20, 10 pixel⁻¹). Given these final 8 × 10⁴ spectra, the pipeline was run in order to retrieve the associated errors.

In order to simulate the way the RAVE spectra are analyzed, the pipeline was run twice: once without any photometric prior (see Table 1), and once by imposing soft priors (see Table 2), based on their temperatures. These priors have been selected in order to be similar with the ones that are applied in the analysis of the RAVE spectra (see Section 3.4). The error values for different stellar types, presented in Tables 1 and 2, have been computed as the 70th percentile of the error distribution. Indicative atmospheric parameter uncertainties for typical thin disk dwarfs, thick disk dwarfs, and halo giants are also given in the last three lines of these tables. A comparison of the uncertainty values with or without photometric priors shows that when the spectral degeneracy is important, the applied soft priors improve significantly the associated uncertainties (see, for example, the hot, metal-poor dwarfs). In addition, it has been noticed, as expected, that the use of the soft photometric priors improves the 90th percentile of most of the stellar categories considered in these tables.

The way the internal errors are associated with a specific parameter estimation is as follows: once the pipeline has converged toward a set of parameters, the final S/N is computed as in Zwitter et al. (2008), utilizing the associated solution template. According to the S/N, the stellar type, the luminosity class, its metallicity, and the use or not of 2MASS photometric prior, the equivalent internal error estimations in Table 1 or Table 2 are adopted. We note that this approach does not optimally take into account the properties of the distance function and hence the degeneracies. Nevertheless, we find that in the case of spectral degeneracy, the associated errors are larger, being consistent with what is expected.

The extraction and reduction procedures applied to the observed spectra are as described in Steinmetz et al. (2006) and Zwitter et al. (2008). As far as the normalization and rest-frame corrections are concerned, we have used the results and the raw data coming from DR3, details of which can be found in Siebert et al. (2011b) and for which the general properties are summarized in Section 8. In addition, in order to be able to perform a pattern recognition and a pixel-to-pixel comparison with the spectra of the learning grid, the RAVE spectra have been interpolated at the wavelengths of the templates and the cores of the IR Ca ii triplet lines have been removed (see Section 3.4).

Since the DR4 pipeline re-normalizes the observed spectra, initially erroneous or inaccurate continuum shapes do not influence the final parameter accuracy of DR4. One might worry about the accuracy of the RV of the stars and hence their rest-frame correction. Indeed, the radial velocities have been computed using cross-correlation with the solution template derived in DR3, whereas in the present work, the atmospheric parameters are recomputed, leading to different values. Nevertheless, the pipeline requires an RV precision only better than ∼7–10 km s⁻¹ (see K11) in order not to be affected by Doppler shifts in the parameter estimation. This threshold is much higher than the accuracy of the radial velocities coming from the DR3, where 95% of the sample has errors of less than ∼4 km s⁻¹ and 98% less than 7 km s⁻¹ (Siebert et al. 2011b, and Section 8). Thus, we can assume that the spectra are indeed at the rest frame for the purpose of our analysis.

First, the RAVE database has been explored to find spectra of stars that had atmospheric parameter determinations available from high-resolution spectroscopy. For that purpose, we made extensive use of the heterogeneous PASTEL catalog³⁰ to identify such targets, retrieving roughly 400 star candidates. Following Soubiran et al. (2010), we considered only the reference values coming from Fuhrmann (1998a, 1998b, 2004, 2008), Gratton et al. (1996, 2003), Hekker & Meléndez (2007), Luck & Heiter (2006, 2007), McWilliam (1990), Mishenina & Kovtyukh (2001), Mishenina et al. (2004, 2006, 2008), Ramírez et al. (2007), and Valenti & Fischer (2005). These studies, when considered by author, all include a large number of stars (at minimum 222 stars) and are all analyzed in a homogeneous way. This allows us to minimize the discrepancies between the sub-catalogs of PASTEL. When for a given star several measurements were available, the mean was computed and the dispersion of the parameters has been considered as the uncertainty on the reference values. We kept only those stars for which measurements were available for the three parameters from a single study, and for which the dispersions among the literature values were less than 100 K, 0.2 dex, and 0.1 dex for T_eff, log g, and [M/H], respectively. In total, 169 stars were selected that way, mainly dwarfs of intermediate metallicity.

In order to investigate the pipeline's behavior in the low-metallicity regime for giant stars, we chose to use the parameters of 229 thick disk stars analyzed by Ruchti et al. (2011), as well as 163 stars observed by J. P. Fulbright et al. (in preparation). The targets of both of these data sets are drawn from RAVE, while the stellar parameters have been obtained from an equivalent-width (EW) analysis of high-resolution spectra. In addition, the very metal-poor giant star CD-38245 ([M/H] =−4.2 dex; Cayrel et al. 2004), which has been observed twice by RAVE, has been included in the list, in order to calibrate the results at the very metal-poor regime.

Metal-rich giant stars have been explored thanks to the CFLIB library (Valdes et al. 2004). The entire spectral library was downloaded from the Web site³¹ of that project, excluding only spectra that did not include the wavelength range around the IR Ca ii triplet. The final comparison catalog is the same as in K11, where once again we used the updated values that can be found in the PASTEL database and discarded the stars for which the dispersions in the literature values were greater than 100 K, 0.2 dex, and 0.1 dex for T_eff, log g, and [M/H], respectively.

Finally, in order to have a more significant statistical sample at the high-metallicity regime, we used the 2.3 m telescope at the Siding Spring Observatory (SSO) to obtain spectra of stars belonging to open clusters. Although the data have not been obtained with the same instrument, the same reduction pipeline has been used as for the RAVE spectra. For calibration purposes, we have used 16 RAVE-like SSO spectra of giant stars belonging to the open cluster M67 and 12 RAVE-like SSO spectra of giants belonging to the open cluster IC 4651, with a few additional data sets used as testing sets (see Section 4.5). These targets were selected given their positions, colors, and radial velocities when available, prioritizing bright stars in order to have high-S/N spectra. For these stars, no individual atmospheric parameters were available, but their metallicity is expected to have a small dispersion around their mean open cluster metallicity value.

In total, 809 stars are used as calibrators, each having S/N >40 pixel⁻¹. The final number of spectra used from each data set is summarized in Table 3, and their reference and retrieved T_eff–log g diagrams are plotted in Figure 5.

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Figures 5 and 6 show the comparison between the reference values found in the literature and those found with the present pipeline for all the data sets except those for open cluster members (where no reference values were available). As far as the effective temperature is concerned, good agreement is found, with a mean offset of 15 K and a dispersion of roughly 400 K. On the other hand, the agreement is less good for the surface gravity, with a rather big scatter for the giant stars. This effect is a manifestation of the previously cited spectral degeneracy that is present for the low- and intermediate-resolution spectra around the IR Ca ii triplet. According to the stochastic position of the noise on the spectrum, a metal-rich turn-off star can be easily confused with a star on the sub-giant branch of lower metallicity. Unless precise photometric temperatures are known, this degeneracy cannot be lifted using medium-resolution spectra alone and is a true degeneracy. Nevertheless, as noted in the previous sections, the DR4 pipeline takes advantage of the 2MASS photometric information (see Section 3.4), hence partly reducing the effect of these degeneracies.

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Discussion on the effective temperature scale. In order to verify the determination of the effective temperatures, we compared the DR4 values of RAVE spectra with S/N >20 pixel⁻¹ for 327 stars in common with the photometric effective temperatures from the Casagrande et al. (2010) calibration of the Geneva–Copenhagen Survey (GCS; Nordström et al. 2004). Figure 7 shows on one hand a small dispersion of the DR4 pipeline's effective temperatures when comparing with the values published by Casagrande et al. (2011) for the GCS, but on the other hand there is a constant underestimation of ∼170 K. Nevertheless, since the GCS covers only a limited range of the parameter space (only metal-rich dwarfs), and because any such offset is not seen with the other calibration data sets, it has been decided not to apply any correction to the RAVE T_eff scale. We note though that the user of the DR4 effective temperatures should be aware that in order to be in agreement with the Casagrande et al. (2010) effective temperature scale, for the type of stars analyzed by the GCS, an offset correction should be performed.

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In order to investigate the calibration needs for the metallicities, we used the iron abundances ([Fe/H]) from the literature. Indeed, we recall that the iron-peak and the α-element abundances of the synthetic spectra are scaled to the iron abundance. Since the metallicity measurement is dominated by the Ca ii lines (which correspond to an α-element), in our case and for standard Galactic α-abundances (i.e., following the trend defined in Section 3.4) we have [M/H]_DR4 ≈ [Fe/H]. Nevertheless, for non-standard stars, the overall metallicity will not be equal to the iron abundance, and hence it has been decided to keep in what follows the notation [M/H] instead of [Fe/H]. In what follows, the nomenclature of the DR3 paper is adopted, denoting the raw metallicity estimation of the DR4 pipeline as [m/H] and the calibrated (final) metallicity as [M/H]. Comparison of the reference values and those derived by the DR4 pipeline is presented in the left panel of Figure 8.

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The results of Figure 8 have been obtained with all the data sets of Table 3, assuming the metallicities given in the fourth column of that table. From the left panel of Figure 8 one can notice that there is an offset between the derived metallicities from the RAVE spectra and the reference iron abundances. This bias is not the same for all metallicities, and it is more important for metal-poor stars than in the metal-rich regime. We investigated the correlations of the errors and found that the main parameters driving the bias are the surface gravity and the metallicity itself. Figure 9 illustrates the covariance of the residual errors on the metallicity with respect to the surface gravity, for different metallicity ranges. In this figure, each point and error bar represent the median and the dispersion of the metallicity error for the stars inside each gravity bin. This binning approach smooths the errors, minimizes the impact of outliers, and highlights the general trends of the biases. On one hand, the results of Figure 9 show for the lowest metallicities a rather constant underestimation of the metallicity by 0.2 dex. On the other hand, there are some clear trends in the more metal-rich regimes, where the giant stars exhibit higher offsets than the dwarfs. These trends are too strong to be explained by a variation of microturbulent velocity along the giant branch, where the expected offsets should be less than 0.1 dex (see, e.g., Kirby et al. 2009).

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Using the binned points of Figure 9, the resulting fit of a quadratic surface for the errors in metallicity, taking into account the dependences on both the surface gravity and the metallicity, is

$$\begin{eqnarray} {\rm [m/H]}-{\rm [M/H]_{\mathrm{ref}}}&=& -0.076-0.006\times \log g + 0.003\nonumber\\ &&\times \log ^2 g - 0.021 \times {\rm [m/H] }\times \log g\nonumber\\ &&+0.582 \times {\rm [m/H]} + 0.205\times {\rm [m/H]}^2.\nonumber\\ && \end{eqnarray} \tag{ 7 }$$

Given this relation, the trend for the typical mean metallicity inside each box of Figure 9 has been plotted in blue. As expected, the fits are in good agreement with the offsets, hence assimilating the metallicity calibration relation to Equation (7). The right panel of Figure 8 shows the improvement that has been made on the metallicity determination thanks to the correction of Equation (7). We note, however, that due to the lack of reference stars with super-solar metallicities, our calibration is not optimal for [M/H] >+0.1 dex. This limitation will be addressed in a future study.

A more detailed investigation of the residuals for different gravity regimes and with respect to the calibrated metallicity is shown in Figure 10, for the Ruchti, Fulbright, PASTEL, and CFLIB libraries. As expected, there is no bias for the calibrated metallicity (lower plots), nor for the other parameters, except for the surface gravity of the lowest gravity giant stars (see also Section 6.1). The self-consistency of the calibration is hence validated.

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Previous RAVE data releases used the Munari et al. (2005) grid of synthetic spectra and a penalized χ² algorithm in order to determine the effective temperatures, surface gravities, overall metallicities, and α-abundances. The stellar rotational velocities (V_rot) and the microturbulent velocities (ξ) were also left as free parameters, although without attributing any constraint on these values in the end.³² Furthermore, the 2MASS photometric information was not used to help reduce spectral degeneracies, and the calibration data sets were not fully available.

The present DR4 pipeline reduces the parameter space to only the three free atmospheric parameters we are trying to measure. In addition to imposing a photometric effective temperature range, the new pipeline explores more efficiently the parameter space, thanks to the decision-tree algorithm. This makes the new results more robust and less susceptible to biases caused by spectral degeneracies.

Efficient exploration of the low-dimension parameter space is crucial for the accurate determination of the atmospheric parameters and calibration of the results. Indeed, tests done on the above-mentioned calibration data sets, using the DR3 pipeline output, showed that the metallicity biases could not be calibrated adequately, especially for the turn-off stars, where the degeneracy of the distance function is the most important (see Figure 11). As will be shown in Section 6.3, this led to biases and interdependences between the DR3 parameters and motivated the effort to develop the approach implemented here in DR4.

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Our proposed metallicity calibration relation (see Equation (7)) has been further verified on spectra that are not part of the calibration process. For that purpose, we used the 327 RAVE spectra of the GCS stars described previously, 105 non-RAVE spectra from the S⁴N library degraded to RAVE resolution (Allende Prieto et al. 2004), and 65 RAVE-like spectra of open and globular cluster stars obtained by the 2.3 m telescope at the SSO, listed in Table 4. We note though that the reference metallicity values that have been adopted for these test spectra are not as reliable as the calibration data sets. Indeed, except for the S⁴N library, all the other data sets do not have individual spectroscopically measured metallicities. In addition, non-member stars might be included in the cluster data sets. Finally, the mean metallicity value has been considered for the stars belonging to the globular clusters, whereas dispersions up to few tenths of a dex (Gratton et al. 2004) can be expected in some cases.

The three plots of Figure 12 show the recovered T_eff–log g diagram of the total considered sample (left), the log g versus residuals in [m/H] (middle), and versus residuals in calibrated [M/H] (right). Despite the relatively large dispersion due to the heterogeneous quality of the data sets, one can see that the bias is greatly reduced in all the samples, and for all gravities, providing a sanity validation check of the calibration relation established previously.

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The errors described in Section 3.5 concern only the internal accuracies of the method. To estimate the total uncertainties of the pipeline, one needs also to estimate the external errors.

We used all the spectra with S/N ⩾50 pixel⁻¹ of the previously described calibration data set to estimate the external uncertainties for different ranges of stellar parameters. Given the total number of spectra in the data set, we divided the sample into cool (T_eff ⩽6000 K) and hot (T_eff >6000 K) dwarfs (log g ⩾3.5 dex) and giants (log g <3.5 dex). Furthermore, we also divided into metal-rich ([M/H] ⩾−0.5 dex) and metal-poor ([M/H] <−0.5 dex) regimes, except for the hot giants, for which not enough stars were available in the sample. The dispersion of the residual differences is presented in Table 5, together with the number of stars that have been considered in order to compute these uncertainties.

Using the values presented in Table 5, the total uncertainties of the pipeline parameter determinations are then estimated by adding in quadrature the external errors with the internal errors given in Tables 1 and 2.

The EW library is built using the driver ewfind of the spectrum synthesis code MOOG (Sneden 1973), which computes the EW of every line as if they were isolated. Nevertheless, line blends when not carefully taken into account can lead to abundance overestimations. In the case of lines instrumentally (but not physically) blended, the observed blend has a total EW that is the sum of the EWs of the two isolated lines, and thus no problem arises. However, when two lines are physically blended (i.e., not instrumentally), the quantity of radiation absorbed by one line is affected by the opacity of the neighboring line, and the total EW of the blend is smaller than the sum of the two isolated EWs. In this case the blend in the constructed model is too strong, leading to abundance overestimations. In order to avoid such overestimation, we corrected the EWs of the blended lines in the EW library with the following procedure:

• 1.  
  Consider the line l₀ having EW₀, blended with some lines l_i with EW_i. Compute the ratio EW_r = EW₀/∑EW_i with EW₀ and EW_i computed as if they were isolated.
• 2.  
  Synthesize the blend composed by l₀ and all l_i, and measure the overall EW_tot.
• 3.  
  Compute the corrected EW of the line l₀ as ${\rm EW}_0^{{\rm corr}}={\rm EW}_r\cdot {\rm EW}_{{\rm tot}}$.

Two lines are considered blended if they are closer than 0.2 Å. In addition, we applied this correction to lines that are blended with one or more lines having EW > 10 mÅ. Lines with EWs smaller than 10 mÅ would affect the EW of the neighboring lines by less than 0.7%, which can be considered negligible. Although ${\rm EW}_0^{{\rm corr}}$ is only an approximation, the constructed blends with such corrected EWs match the synthesized blend better than 1% of the normalized flux. This correction replaces the previous one adopted in the B11 chemical pipeline.

Most of the absorption lines in the RAVE wavelength range and resolution have an intrinsic width smaller than the RAVE instrumental profile. Therefore, their line profile is dominated by the instrumental one, which is Gaussian. Nevertheless, this is not the case for the strongest lines, where the broad wings extend beyond the instrumental profile. In that case, the line is better approximated by a Voigt profile.

Compared to B11, the new chemical pipeline drops the simplistic Gaussian assumption and now uses an improved line profile. Because of the difficulties of implementing a real Voigt profile, we use the approximation implemented by Bruce et al. (2000):

$$\begin{equation} V(x)={\rm EW}\cdot [rL(x)+(1-r)G(x)], \end{equation} \tag{ 8 }$$

where L and G are the Lorentzian and Gaussian functions, respectively, and EW is expressed in Å. The r parameter rules the linear combination between L and G, so that when r = 0, V(x) is a pure Gaussian, and when r = 1, V(x) is a pure Lorentzian. The FWHM of L and G is forced to be identical and varies as a function of the EW with the following relation:

$$\begin{equation} {\rm FWHM}={\rm FWHM}_{{\rm best}}+{\rm EW}/4, \end{equation} \tag{ 9 }$$

where FWHM_best is the best-matching FWHM found by the minimization routine during the best-matching model searching. Unlike Bruce et al. (2000), we make the parameter r dependent from the EW:

$$\begin{equation} r=0.5\cdot \exp \left(\frac{-1}{(3{\rm EW})^2+0.001} \right) \end{equation} \tag{ 10 }$$

so that for small EW the line profile is Gaussian and for large EW the line profile approximates a Voigt profile.

Kielkopf (1973) showed that the difference between the real and the pseudo-Voigt profile described by Equation (8) is always smaller than 1.2% for EW = 0.5 Å, which corresponds to an error smaller than 0.72% in EW (Bruce et al. 2000).

In order to remove some fringing effects that sometimes affect the initial input RAVE spectra (the same ones as used by the DR4 pipeline; see Section 3.6), the chemical pipeline has its own internal re-normalization algorithm. It can be summarized as follows (a more detailed discussion can be found in Section 2.5 and Figure 3 of B11):

• 1.  
  A preliminary metallicity estimation is performed and the modeled metallic lines are subtracted from the observed spectrum.
• 2.  
  The strong lines belonging to the Ca ii and H i are fitted with a Lorentzian profile and subtracted from the observation.
• 3.  
  The continuum profile is then defined by a box-car smoothing of the residuals obtained after the previous two steps.
• 4.  
  The strong Ca ii and H i lines are added to the continuum profile to obtain the new "continuum." The chemical pipeline does not measure the broad lines of the Ca ii and H i, and their profiles are considered part of the continuum level. Therefore, by adding them to the classical continuum, they are excluded from the chemical analysis. It is by comparison with this level of "continuum" that the metallic lines are measured.

This re-normalization permits better continuum placement around the absorption lines for a better elemental abundance estimation. In particular, the new adopted Voigt profile (see Section 5.2) contributes to improve the continuum placement thanks to the superior fit of the line's wings, which can now be properly subtracted during the re-normalization procedure.

The present chemical pipeline applies the continuum placement like the chemical pipeline outlined in B11 (see their Section 2.5), with the difference that it is applied twice for spectra with S/N ⩾ 40 pixel⁻¹ and only once for S/N < 40 pixel⁻¹. Indeed, thanks to the pseudo-Voigt profile, the continuum placement process becomes more stable at S/N ⩾ 40 pixel⁻¹, and when applied iteratively the continuum estimation converges after two iterations. On the other hand, for S/N < 40 pixel⁻¹ the continuum estimation cannot converge to the right level. The noise spikes (mistaken as metallic lines by the code) lead to a too high continuum placement and, consequently, to a too high metallicity estimation. Thus, the re-normalization is applied only once for low-S/N spectra.

In order to evaluate the precision and accuracy of the new chemical pipeline, we ran tests on synthetic and real spectra with known chemical abundances and compared the results with the expected abundances. The samples of synthetic and real spectra used are the same as those employed in B11. This allows us to have a clear view of the achieved improvement between the two pipelines.

Unlike the work presented in B11, we present here the tests and results for only six elements (aluminum, magnesium, silicon, titanium, nickel, and iron). We rejected the calcium abundance as not being reliable (see Section 6.3.1).

5.4.1. Internal Errors: Tests on Synthetic Spectra

The tests have been performed on a sample of 1353 synthetic spectra. The values for the effective temperature and the surface gravity for these spectra have been taken from a mock sample of RAVE observations created using the Besançon model, whereas the adopted chemical abundances have been taken from the Soubiran & Girard (2005) catalog, whose star metallicities span from −1.5 dex to +0.4 dex (for further details on how the sample has been constructed, see B11). This ensures plausible stellar parameters and chemical abundance distributions of the synthetic spectra.

We evaluated the precision and accuracy of the results at S/N = 100, 40, 20 pixel⁻¹. In Figures 13 and 14 we report the detailed results.

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Results at S/N = 100 pixel⁻¹. While the B11 chemical pipeline gave slightly underestimated abundances, the present one reduces or removes such underestimation for most of the elements at S/N = 100 pixel⁻¹. [Ni/H] is underestimated by ∼0.1 dex, whereas the [Ti/H] estimate is good for giants but should be rejected for dwarfs (for which Ti lines are too weak for a good estimation).

Results at S/N = 40 pixel⁻¹. All the elements have reliable abundances, except for [Si/H] and [Ti/H], which look overestimated by ∼+0.1 and ∼+0.2 dex, respectively.

Results at S/N = 20 pixel⁻¹. [Fe/H], [Si/H], and [Al/H] are reliable, with uncertainties of ∼0.15–0.20 dex. [Mg/H] and [Ti/H] show significant systematics, and [Ni/H] cannot be measured because its lines are too weak.

For Ni and Ti the selection effect due to the S/N is particularly evident. Moving to lower S/N, the number of spectra with Ti and Ni estimations decreases, because the lines of Ti (in dwarfs stars) and Ni are weak in the RAVE wavelength range and do not overcome the noise at low S/N. This selection bias is further discussed in Section 6.3.1.

In general, the new chemical pipeline suffers smaller systematics with respect to the old one. Underestimations are reduced, and abundances of important elements (Fe, Si, Al, and Mg) do not correlate with the effective temperature (see Figure 15) as they did with the previous pipeline. [Ti/H] appears reliable only for cool giants.

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We further tested the robustness of our results by repeating the abundance measurements after adjusting randomly the initial T_eff, log g, and [M/H] by values normally distributed around their true values with $\sigma _{\rm T_{{\rm eff}}}=250$ K, σ_log g = 0.5 dex, and σ_[M/H] = 0.2 dex, respectively. The results are shown in Figure 14. The shifts in stellar parameters (representing the input errors) simply inflate the errors in abundances seen in the test without stellar parameters errors, without introducing any new systematics.

The overall uncertainties have been estimated by computing the elemental abundances of 98 RAVE spectra of dwarf stars from Soubiran & Girard (2005, hereafter SG05) and 233 RAVE spectra of 203 giant stars from Ruchti et al. (2011, hereafter R11). Most of the SG05 stars have RAVE spectra with S/N >100 pixel⁻¹, whereas the R11 stars have RAVE spectra with S/N ranging between 30 pixel⁻¹ and 90 pixel⁻¹. Hence, the results are representative of the medium–high S/N regime. Figures 16 and 17 show the results obtained for the six elements in common with SG05 and the four in common with R11.

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Adopting the RAVE DR4 stellar parameters, the RAVE chemical pipeline delivers slightly underestimated abundances for Mg, Al, and Ti (∼−0.1 dex). There is a general improvement in precision for most of the elements with respect to the B11 pipeline (dispersions smaller than ∼0.05–0.07 dex for Mg, Ti, and Fe) with no visible systematic offsets. The estimated errors in abundance depend on the element and range from 0.17 dex for Mg, Al, and Ti to 0.3 dex for Ti and Ni. The error for Fe is estimated as 0.23 dex. We note that the errors reported here are conservative estimations of the RAVE abundance errors, because we are comparing our results with other more precise but still uncertain measurements, and we have not corrected the variance for the second contribution. For illustration, assuming an uncertainty in the reference abundances of 0.1 dex, our estimated RAVE errors decrease by 0.03–0.05 dex.

The following criteria need to be understood as the confidence limits for selection based on observational (S/N) and pipeline limitations (mainly the boundaries of the grid).

We selected all the stars that had S/N >20 pixel⁻¹, had errors in the RV estimation of less than 8 km s⁻¹ (measured by RAVE DR3; see Section 8), had derived log g > 0.5 dex, determined T_eff >3800 K, and calibrated metallicity [M/H]>−5 dex (measured by the DR4 pipeline), and for which the DR4 algorithm had converged toward a stable solution.³³ In total, roughly 19% (∼8.7 × 10⁴) of the spectra have been rejected after these quality criteria. We are working toward the next DR5 RAVE data release, with work that we hope will improve the parameters for at least some of these currently non-reliable stars.

The cut on the error on the RV (ΔV_HRV <8 km s⁻¹, 12,974 spectra) has been defined based on the results of Kordopatis et al. (2011a), where it has been shown that for Doppler shifts larger than approximately half a pixel, the results of the pipeline were seriously degraded. Nevertheless, a criterion based on the Tonry–Davis correlation coefficient (R) might be preferred in some cases, since some stars can have large errors but good R (due, for example, to strong hydrogen lines) and vice versa (small errors but R < 5).

The removal of the stars with gravities lower or equal to 0.5 dex (25,882 spectra), T_eff lower than 3800 K (20,143 spectra), and/or calibrated [M/H] lower than −5 dex (1282 spectra) has been decided because the results are considered both unrealistic (the synthetic spectra computed with the MARCS atmospheric models at such log g have not been carefully compared to real spectra) and less reliable (e.g., missing models in the reference grid). Finally, the cut on the convergence of the DR4 algorithm (14,454 spectra) is made in order to minimize cases badly affected by the spectral degeneracies. Indeed, these degeneracies can cause, in some cases, an impossibility for the algorithm to converge due to a negative gradient in the distance function between the spectrum and the templates. MATISSE can in some cases oscillate between two solutions (∼11% of the published sample). We decided to keep these solutions because, in general, they are close in the parameter space. Nevertheless, in case the user decides not to use them, we have flagged these stars in the algo_conv parameter, which is also published with this data release (see the Appendix).

An additional cut, based on the velocity width parameter of the spectral lines, V_rot, has been applied, since our algorithm cannot treat fast rotators. We discarded empirically stars at the high-velocity tail of the distribution (V_rot > 100 km s⁻¹, 11,735 in total). We recall that the estimation of the V_rot is made through the DR3 pipeline, as a free parameter, at the same moment as the first estimation of T_eff, log g, and [M/H] is made. Nevertheless, the rather low resolving power of RAVE spectra (∼1.2 Å or 30 km s⁻¹) does not allow the determination of rotational velocities for slow rotators, which represent the vast majority of RAVE stars. Hence, this parameter is not published, but true fast rotators will be discussed in a separate paper.

Finally, we note that targets at low Galactic latitudes should also be treated with caution, since the possibly high interstellar extinctions in these directions are not taken into account in the photometric constraints imposed by the DR4 pipeline.

From the whole RAVE internal data set, we measured chemical abundances only for spectra with the following features:

• 1.  
  Effective temperature 4000 ⩽ T_eff (K)⩽7000 K
• 2.  
  S/N > 20 pixel⁻¹
• 3.  
  Rotational velocity V_rot < 50 km s⁻¹.

Such limitations are due to the following facts. First, the EW library (and the B11 line list on which it is based) is reliable only in this effective temperature range. In addition, the line measurement and stellar parameters are reliable only for S/N larger than 20 pixel⁻¹. Finally, the absorption lines can be reliably measured only if their FWHM does not significantly exceed the RAVE instrumental FWHM (∼1.2 Å), which corresponds to a rotational velocity of 30 km s⁻¹. Such criteria leave 313,874 spectra selected from the RAVE database.

Besides the chemical abundances of this selected sample, we provide some extra statistical quantities and flags to be employed for further quality selection:

• 1.  
  χ² between best-matching model and observed spectrum. The lower the values, the better the expected abundance precision. We suggest a user reject spectra with χ² > 2000.
• 2.  
  The value frac, which represents the fraction of the observed spectrum that satisfactorily matches the model. We suggest a user reject spectra with frac < 0.7 (see B11 for further details).
• 3.  
  Classification flags by Matijevič et al. (2012). We suggest a user select spectra classified as "normal" by Matijevic et al. in order to avoid peculiar objects on which the chemical pipeline fails.
• 4.  
  $Algo\_Conv$ value. This value indicates if the DR4 pipeline has converged or if the stellar parameters were either outside the grid boundaries or MATISSE was oscillating between two values. The higher quality data have $Algo\_Conv=0$.

The application of these quality flags is left to the user. The number of spectra that meet all such quality flags is 187,305. In Figure 19 we show the distribution of the chemical abundances, given the above-mentioned criteria, for S/N > 20 pixel⁻¹ and S/N > 40 pixel⁻¹.

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A description of Galactic properties based on the published parameters of this catalog is beyond the scope of this paper. Nevertheless, as a sanity check, we explore in this section the general properties of the catalog, by analyzing the correlation of the parameters and the change of the metallicity properties according to the S/N, the effective temperature, or the surface gravity. By comparing the behaviors of the DR3 and the DR4 pipelines, we show that although the differences between the atmospheric parameters of the two methods are relatively subtle, DR4 better reproduces the expected behavior for different subpopulations of stars and thus is the method of choice for most Galaxy evolution studies.

Figure 20 compares the resulting T_eff–log g diagrams of the DR4 and the DR3 pipelines as selected according to the criteria of Section 6.1. One can notice that besides the well-understood and described discretization due to the DEGAS algorithm, there are some additional subtle differences in the parameters of the two pipelines. In particular, hot dwarfs, as well as turn-off stars, have now smaller surface gravities and the main sequence is better defined. Finally, giants have slightly higher effective temperatures.

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The DR4 and DR3³⁴ calibrated metallicity trends, as a function of the surface gravity and the effective temperatures, can be seen in Figure 21. As far as the T_eff dependencies are concerned, one can notice that the metallicity distribution functions (MDFs) of the DR4 pipeline get broader when the effective temperature lowers. In particular, the DR4 pipeline finds that the hottest stars have a narrow metallicity distribution with a mean value at slightly super-solar values, as expected for the young stars in the solar neighborhood. This is not the case for the results of the DR3 pipeline, where metallicities as low as [M/H] ∼−0.5 dex are obtained. Furthermore, from the isocontours of the log g versus [M/H], we can see that despite the mild pixelization of the values, there are no trends of the metallicities as a function of the surface gravity for the dwarfs, as derived by the DR4 pipeline. This is not the case for the DR3 pipeline results, where a shift is noticed.

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In order to investigate whether this shift is real and justified given our classical view of the Milky Way, we explored the stellar heliocentric radial velocities and the evolution of the MDFs for different surface gravity bins. Figure 22 shows the resulting histograms for the calibrated metallicities of the DR4 (in black solid lines) and the DR3 pipelines (red dashed lines). The RV dispersions of the selected stars have also been reported inside each box. For the lower panels, corresponding to the dwarf stars (3.5 < log g <5 dex), the RV dispersion stays constant. Considering that each Galactic population (thin disk, thick disk, and halo) is characterized by a different velocity dispersion, the constant $\sigma _{V_{\rm HRV}}$ that is found indicates that the same proportions of Galactic populations are probed for these gravity bins. As a result, the MDFs should not vary inside these bins. This is the case only for the DR4 MDFs, the DR3 ones shifting by 0.2 dex in this range of log g. As far as the sub-giant and giant stars are concerned, a good agreement is found between the DR3 and DR4 MDFs, with a shift toward lower metallicities with decreasing log g and at the same time an increase in the RV dispersion. This is in agreement with a change in the mixture of the probed Galactic populations as a function of the probed volume, passing from an old thin disk dominated population to the presence of more halo stars for the larger volume probed by the more luminous giant stars.

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To show the correlations between the parameters, we select among the DR4 catalog those stars that are observed multiple times, and for which several independent spectra and derived parameter sets are available. In the panels we plot the differences between the several determinations of the measured T_eff, log g, and calibrated metallicities. Figure 23 shows the results for the stars with S/N >20 pixel⁻¹, for both DR4 and DR3 pipelines. From that figure one can see that the new DR4 pipeline is more robust than the DR3 one, since the bulk of the stellar parameters show a very small discrepancy between the repeated observations, as well as a negligible parameter correlation. This validates once more the robustness of our calibration relation of Equation (7). However, we note that correlations between the parameter estimations still exist for some stars. This is expected, due to the intrinsic spectral degeneracy: an underestimation of the T_eff leads to a similar underestimation of the log g and the [M/H].

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The robustness of the DR4 pipeline in terms of better treatment of the spectral degeneracies can also be seen in Figure 24. The evolution of the mean metallicity as a function of the S/N (yellow points on Figure 24) shows no trends down to S/N >15 pixel⁻¹. Nevertheless, the cost for this better treatment is the pixelation of the results for the most metal-poor stars or the ones having low S/N. In particular, the pixelization effect can be clearly seen in Figure 24 below the threshold of S/N =30 pixel⁻¹. Indeed, we recall that for all the observed spectra DEGAS is first used to find the nominal template spectrum of the learning grid in order to re-normalize the observed one. Then, on one hand, for the high-S/N regime, the MATISSE algorithm is used on these optimally re-normalized spectra in order to obtain the final parameters. On the other hand, for the low-S/N data (<30 pixel⁻¹) and at the boundaries of the learning grid, tests on synthetic spectra have shown that the projection method was giving less accurate results than the decision tree. Given these facts, Kordopatis et al. (2011a) showed that DEGAS is preferred over the projection approach of MATISSE for S/N <30 pixel⁻¹, even if a pixelization of the parameters is introduced.

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6.3.1. Chemical Abundance Reliability: Element by Element

Besides the quality indicators described in Section 6.2, the number of measured absorption lines for an element can be a good indicator of the reliability and precision of the abundance estimation (as illustrated in Figure 25). We outline here a summary of the expected precision of the abundance element by element.

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Magnesium yields reliable results on synthetic and real spectra with no significant correlation with stellar parameters. We expect errors σ_Mg ⩽ 0.15 dex for S/N > 40 pixel⁻¹ and σ_Mg ∼ 0.25 dex for 20 < S/N < 40 pixel⁻¹. Tests on synthetic spectra show that magnesium suffers a systematic error when measured at low S/N. Such an error has not been confirmed with real spectra.

Aluminum gives a reliable abundance although obtained with only two isolated lines. Abundance errors expected are σ_Al ⩽ 0.15 dex for S/N > 40 pixel⁻¹ and σ_Al ∼ 0.25 dex for 20 < S/N < 40 pixel⁻¹.

Silicon is among the most reliably determined elements. Abundance errors expected are σ_Si ⩽ 0.15 dex for S/N > 40 pixel⁻¹ and σ_Si ∼ 0.25 dex for 20 < S/N < 40 pixel⁻¹ with a small overestimation of ∼0.1 dex.

Titanium gives reliable estimates at high S/N for cool giants (T_eff < 5500 K and log g < 3). We suggest rejecting Ti abundances for dwarf stars. Tests on synthetic and real spectra suggest an expected error of σ_Ti ⩽ 0.2 dex for S/N > 40 pixel⁻¹ and σ_Ti ∼ 0.3 dex for 20 < S/N < 40 pixel⁻¹.

Iron gives robust and precise abundances thanks to its large number of measurable lines at all stellar parameter values. Expected errors are σ_Fe ⩽ 0.1 dex for S/N > 40 pixel⁻¹ and σ_Fe ∼ 0.2 dex for 20 < S/N < 40 pixel⁻¹.

Nickel abundances have to be used with care because of the few lines that are measurable. From synthetic spectra we infer that Ni should be used for cool stars only (T_eff < 5000 K) and high S/N. In this regime, the abundances are reliable (despite being underestimated by ∼0.1 dex) with an expected error of $\sigma _{_{\rm Ni}}\sim 0.25$ dex. The mean abundance correlates with the number of measured lines (i.e., with S/N) as highlighted in Figure 25.

α-enhancement is the average of [Mg/Fe] and [Si/Fe], and it proved to be a robust estimation, particularly useful at low S/N, where the measurements are more uncertain. The expected error is ∼0.15 dex for S/N > 40 pixel⁻¹ and ∼0.2 dex for 20 < S/N < 40 pixel⁻¹.

Thanks to the improved line profile and the correction of the EW library for the opacity of the neighboring lines, the continuum re-normalization has improved. The new abundances are now less affected by systematic errors than the previous ones, and their correlations with T_eff are now negligible. On the other hand, the new continuum re-normalization reveals the scarcity of information for elements with weak and few visible lines like [Ca/H] (which has been dropped in this data release) and [Ti/H] on dwarf stars, which turns out to be not reliable. A slight correlation between abundances and S/N is present, as shown in Figure 26. Such correlation is negligible for giant stars, whereas for dwarf stars [m/H]_chem (computed with the formula given by Salaris et al. 1993, see Section 3.4 of B11) increases by ∼0.1 dex from S/N = 80 pixel⁻¹ to S/N = 40 pixel⁻¹. The different re-normalization procedure for the two S/N regimes generates the step in average metallicity seen at S/N = 40 pixel⁻¹.

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The accuracy of the RAVE abundances depends on many variables, often inter-dependent in a non-linear way, which makes difficult the accuracy estimation of the individual abundances. Indeed, on one hand the abundance accuracy depends on the number of measured absorption lines. On the other hand, the number of measurable lines (i.e., strong enough to be identified in the noise) depends on S/N and on the stellar parameters. In Figure 25 the dispersion of the residuals between measured and expected abundances (for the sample of synthetic spectra) decreases as the number of measured lines increases. This number is a useful index of goodness of the abundance accuracy, although it must be considered together with S/N. In Figure 27 we illustrate the fraction of spectra having an abundance estimation (i.e., at least one absorption line measured) for different elements, and how this fraction decreases when S/N and/or metallicity decrease. This is a selection effect due to the measurement process, and it must be taken into account during data analysis and interpretation.

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6.3.2. Comparison between [M/H] and [m/H]_chem

In order to measure the chemical abundances, the RAVE chemical pipeline uses on one hand the estimation of T_eff and log g of the RAVE pipeline, and on the other hand [M/H] is employed only as a first guess. This means that the metallicity [m/H]_chem (computed as explained in Section 3.4 of B11) and any elemental abundance provided by the chemical pipeline are independent of [M/H]. It is, therefore, interesting to compare [M/H] with [m/H]_chem as much as with [Fe/H], because the latter is the element of reference used to calibrate [M/H]. In Figure 28 the residuals between [M/H], [m/H]_chem, and [Fe/H] are shown as a function of T_eff, log g, and [M/H] for spectra with S/N > 40 pixel⁻¹. In general, [M/H] appears to lie between [Fe/H] and [m/H]_chem, in the order [Fe/H] ⩽ [M/H] ⩽ [m/H]_chem. More specifically, there are some differences: for dwarf stars this difference is slightly larger (∼0.1 dex) than for giants (⩽0.05 dex). This can be due to the higher number of strong and narrow absorption lines available in giants with respect to hot dwarfs, which allows better measurements over the whole S/N range. In addition, the [Fe/H] deviation can be due to the α-enhanced stars, which do not follow the enhancement relation of the learning grid (see Section 3.4) and for which [Fe/H] ≠ [M/H]. Indeed, roughly 25% of the stars with S/N > 40 pixel⁻¹ deviate more than 1σ (0.15 dex) from the enhancements of the learning grid of Section 3.4.

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To verify the quality of the RAVE data, a fraction of the survey time is devoted to multiple observations of RAVE targets with time intervals between observations ranging from a few hours to 4 yr. In the present release, 23,288 stars belong to this program, for a total of 61,457 measurements, some stars having been observed up to 13 times. The distribution of the number of observations per star is presented in the left panel of Figure 30. The distribution of the time interval Δt between re-observations is presented in Figure 30, right panel, where the Δt are binned using intervals of 1 day. As seen from this figure, the distribution is not random. A quasi-logarithmic spacing is used to sample optimally the possible orbital state of the spectroscopic binaries with an enhancement of the observations at specific intervals of 1 day, 2 weeks, 1, 2, 3, and 6 months, and 1, 2, 3, and 4 yr.

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The comparison between the RV measurements for the different observations is given in Figure 31. In the top panel, the color coding follows the density per bin of 2 km s⁻¹. For each star, the velocity of the observation with the highest S/N is used as the reference velocity along the x-axis (HRV₁), while subsequent observations are along the y-axis (HRV₂). The measurements are convolved with a Gaussian function along each direction. The dispersion of the Gaussian is the internal error associated with the measurement along each axis. The general trend follows closely the one-to-one relation, showing no sign of any systematic effects.

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Another way to look quantitatively at the RV difference is presented in the bottom panel of Figure 31, which shows the histogram of the RV difference normalized to the errors $\Delta _{{\rm HRV}}=({\rm HRV}_1-{\rm HRV}_2) / (\sqrt{\sigma _1^2+\sigma _2^2})$. If our measurements were perfect, this distribution should follow a Gaussian function of zero mean and unit dispersion. Binaries and problematic measurements contribute to the tail and can be assumed to follow a Gaussian function with a larger dispersion. In the case of our RAVE data, a sum of two Gaussians is used to fit the histogram, setting the dispersion of the first Gaussian function to one. Also, we remove the central bin from the fit. This central bin is mostly populated by repeat observations without delay in time. The best fit is shown as a continuous black line, the contribution of each Gaussian function being represented by a dashed line. Apart from the central bin, the fit provides an adequate representation of the observed histogram. The respective contributions of the two Gaussian functions are 77% for the standard population and 23% for the spectroscopic binaries/problematic observations. This fraction is in agreement with our finding for DR3 data (26%).

As for the DR3 and previous releases, the RV solutions are corrected for potential zero-point offsets due to change in temperature in the spectrograph room. The procedure uses the available sky lines in the RAVE spectra to construct a smooth solution of the zero-point offset across the field plate. This procedure is fully described in Siebert et al. (2011b), and the relevant measurements for each fiber are given in the catalog. To verify the validity of our velocity zero-point solution, comparison to independent measurements is made. Our comparison sample comprises data from seven different sources: the GCS (Nordström et al. 2004) data and high-resolution echelle follow-up observations of RAVE targets at the ANU 2.3 m telescope, Asiago Observatory, Apache Point Observatory from Ruchti et al. (2011), and Observatoire de Haute Provence using the Elodie and Sophie instruments. In total, the sample of RAVE stars with external RV measurements contains 1265 stars. Their distributions in DENIS I magnitude and 2MASS J−H versus H−K color–color diagram are presented in Figure 32. Stars with I < 9 are mostly custom RAVE observations of bright GCS stars. At fainter magnitudes the sample consists primarily of high-resolution re-observations of RAVE targets. In the 2MASS color–color diagram, we observe that this sample covers the two main peaks (representing dwarf and giant stars) present in the RAVE catalog. However, dwarfs are over-represented compared to the RAVE distribution due to the large number of GCS stars observed in this sample that are Hipparcos dwarfs.

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The summary of the comparison to the control samples is given in Table 6. This table reports the number of objects in each sample, the total number of observations, the mean ΔRV = RV_DR4 − RV_ext, and the standard deviation. ΔRV is computed using an iterative σ-clipping technique to remove the contamination by spectroscopic binaries or problematic measurements. No other quality cut was applied on the samples. The clipping parameter and the number of stars rejected for each sample are given in the last column of the table.

We note that the agreement between RAVE and the external sources is better than 1 km s⁻¹ in all the cases. Figure 33 (top panel) presents the direct comparison of the DR4 radial velocities to the external source measurements. The blue circles are the known spectroscopic binaries and show a broader distribution than the remainder of the sample. Figure 33 (bottom panel) shows the histogram of the RV difference. This distribution can be adequately reproduced by the sum of two Gaussian functions, the peak representing the single stars being of zero mean with a dispersion of 1.5 km s⁻¹, consistent with our expectation for RAVE data.

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As a final test, we check the dependence of the RV difference as a function of the Tonry–Davis correlation coefficient (R) and S/N of the RAVE data (Figure 34). Although an increase in the dispersion is observed for S/N < 30 pixel⁻¹, or R of 40, the absence of an apparent bias indicates that our RV measurements are reliable.

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