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Context. The extensive stellar spectroscopic datasets that are available for studies in Galactic Archeaology thanks to, for example, the Gaia-ESO Survey, now benefit from having a significant number of targets that overlap with asteroseismology projects such as Kepler, K2, and CoRoT. Combining the measurements from spectroscopy and asteroseismology allows us to attain greater accuracy with regard to the stellar parameters needed to characterise the stellar populations of the Milky Way. Aims. The aim of this Gaia-ESO Survey special project is to produce a catalogue of self-consistent stellar parameters by combining measurements from high-resolution spectroscopy and precision asteroseismology. Methods. We carried out an iterative analysis of 90 K2@Gaia-ESO red giants. The spectroscopic values of Teff were used as input in the seismic analysis to obtain log g values. The seismic estimates of log g were then used to re-determine the spectroscopic values of Teff and [Fe/H]. Only one iteration was required to obtain parameters that are in good agreement for both methods and, thus, to obtain the final stellar parameters. A detailed analysis of outliers was carried out to ensure a robust determination of the parameters. The results were then combined with Gaia DR2 data to compare the seismic log g with a parallax-based log g and to investigate instances of variations in the velocity and possible binaries within the dataset. Results. This analysis produced a high-quality catalogue of stellar parameters for 90 red giant stars from K2@Gaia-ESO that were determined through iterations between spectroscopy and asteroseismology. We compared the seismic gravities with those based on Gaia parallaxes to find an offset which is similar to other studies that have used asteroseismology. Our catalogue also includes spectroscopic chemical abundances and radial velocities, as well as indicators for possible binary detections. [ABSTRACT FROM AUTHOR]

Analyses of data from spectroscopic and astrometric surveys have led to conflicting results concerning the vertical characteristics of the Milky Way. Ages are often used to provide clarity, but typical uncertainties of >40 per cent from photometry restrict the validity of the inferences made. Using the Kepler APOKASC sample for context, we explore the global population trends of two K2 campaign fields (3 and 6), which extend further vertically out of the Galactic plane than APOKASC. We analyse the properties of red giant stars utilizing three asteroseismic data analysis methods to cross-check and validate detections. The Bayesian inference tool PARAM is used to determine the stellar masses, radii, and ages. Evidence of a pronounced red giant branch bump and an [α/Fe] dependence on the position of the red clump is observed from the K2 fields radius distribution. Two peaks in the age distribution centred at ∼5 and ∼12 Gyr are found using a sample with σage < 35 per cent. In comparison with Kepler , we find the older peak to be more prominent for K2. This age bimodality is also observed based on a chemical selection of low-[α/Fe] (≤0.1) and high-[α/Fe] (>0.1) stars. As a function of vertical distance from the Galactic mid-plane (| Z |), the age distribution shows a transition from a young to old stellar population with increasing | Z | for the K2 fields. Further coverage of campaign targets with high-resolution spectroscopy is required to increase the yield of precise ages achievable with asteroseismology. [ABSTRACT FROM AUTHOR]