Rotation of young solar-type stars as seen by Gaia and K2

Context. Accurate surface rotation measurements are crucial to estimate stellar ages and improve our understanding of stellar rotational evolution. Comparisons of datasets obtained from different space missions on common targets represent in this sense a way to explore the respective biases and reliability of the considered instruments, as well as a possibility to perform a more in-depth investigation of the properties of the observed stars.Aims. In this perspective, we used observations from the K2 mission to provide an external validation to Gaia rotation measurements, and confront observables available from Gaia, K2, and Kepler.Methods. We therefore cross-matched the Gaia rotation catalogue and the K2 mission Ecliptic Plane Input Catalogue (EPIC) in order to find Gaia stars with both measured rotation and periods and available K2 light curves. Using our cross-match, we analysed 1063 light curves from the K2 mission in order to characterise stellar rotational modulations and compare the recovered periods with Gaia reference values. The K2/Gaia cross-validated sample was used as a random-forest classifier training set to identify a subsample of Gaia stars with similar properties.Results. We validate the Gaia rotation measurements for a large fraction of the sample and we discuss the possible origin of the discrepancies between some K2 and Gaia measurements. We note that the K2 sample does not include members of the low-activity ultra-fast-rotating (UFR) population that was highlighted by Gaia observations, a feature that we explain considering the instrumental capabilities of K2. Placing our sample in perspective with the full Gaia rotation catalogues and Kepler observations, we show that the population for which both Gaia and K2 are able to measure rotation is composed of young late-type stars, a significant fraction of which are not yet converged on the slow-rotator gyrochronological sequence. In order to identify additional targets that have properties similar to the cross-validated K2 sample (considering in particular rotation and activity index), we computed the local outlier factor (LOF) of the stars in the Gaia DR3 rotation catalogue, considering the K2 stars as reference, and we identified 40 423 stars with a high degree of similarity, which can be useful for future statistical studies.Conclusions. For the purpose of characterising the properties of young solar-type fast rotators, future photometric space-borne missions such as PLATO will greatly benefit from the synergies with Gaia observations that we illustrate in this work.