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. 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. 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. This analysis produced a high-quality catalogue of stellar parameters for 90 red giant stars observed by both K2 and 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.
33 pages, 26 figures