Context.The third data release ofGaia,has provided stellar parameters, metallicity [M/H], [α/Fe], individual abundances, broadening parameter from its Radial Velocity Spectrograph (RVS) spectra for about 5.6 million objects thanks to the GSP-Spec module, implemented in theGaiapipeline. The catalogue also publishes the radial velocity of 33 million sources. In recent years, many spectroscopic surveys with ground-based telescopes have been undertaken, including the public surveyGaia-ESO, designed to be complementary toGaia,in particular towards faint stars.Aims.We took advantage of the intersections betweenGaiaRVS andGaia-ESO to compare their stellar parameters, abundances and radial and rotational velocities. We aimed at verifying the overall agreement between the two datasets, considering the various calibrations and the quality-control flag system suggested for theGaiaGSP-Spec parameters.Methods.For the targets in common betweenGaiaRVS andGaia-ESO, we performed several statistical checks on the distributions of their stellar parameters, abundances and velocities of targets in common. For theGaiasurface gravity and metallicity we considered both the uncalibrated and calibrated values.Results.Overall, there is a good agreement between the results of the two surveys. We find an excellent agreement between theGaiaandGaia-ESO radial velocities given the uncertainties affecting each dataset. Less than 25 out of the ≈2100Gaia-ESO spectroscopic binaries are flagged as non-single stars byGaia.For the effective temperature and in the bright regime (G≤ 11), we found a very good agreement, with an absolute residual difference of about 5 K (±90 K) for the giant stars and of about 17 K (±135 K) for the dwarf stars; in the faint regime (G≥ 11), we found a worse agreement, with an absolute residual difference of about 107 K (±145 K) for the giant stars and of about 103 K (±258 K) for the dwarf stars. For the surface gravity, the comparison indicates that the calibrated gravity should be preferred to the uncalibrated one. For the metallicity, we observe in both the uncalibrated and calibrated cases a slight trend wherebyGaiaoverestimates it at low metallicity; for [M/H] and [α/Fe], a marginally better agreement is found using the calibratedGaiaresults; finally for the individual abundances (Mg, Si, Ca, Ti, S, Cr, Ni, Ce) our comparison suggests to avoid results with flags indicating low quality (XUncer = 2 or higher). These remarks are in line with the ones formulated by GSP-Spec. We confirm that theGaiavbroad parameter is loosely correlated with theGaia-ESOvsinifor slow rotators. Finally, we note that the quality (accuracy, precision) of the GSP-Spec parameters degrades quickly for objects fainter thanG≈ 11 orGRVS≈ 10.Conclusions.We find that the somewhat imprecise GSP-Spec abundances due to its medium-resolution spectroscopy over a short wavelength window and the faintGregime of the sample under study can be counterbalanced by working with averaged quantities. We extended our comparison to star clusters using averaged abundances, using not only the stars in common, but also the members of clusters in common between the two samples, still finding a very good agreement. Encouraged by this result, we studied some properties of the open-cluster population, using bothGaia-ESO andGaiaclusters: our combined sample traces very well the radial metallicity and [Fe/H] gradients, the age-metallicity relations in different radial regions, and allows us to place the clusters in the thin disc.
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