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The second data release of the Gaia mission includes an advance catalog ofvariable stars. The classification of these stars are based on sparsephotometry from the first 22 months of the mission. We set out to investigatethe purity and completeness of the all-sky Gaia classification results with thehelp of the continuous light curves of the observed targets from the Kepler andK2 missions, focusing specifically on RR Lyrae and Cepheid pulsators, outsidethe Galactic Bulge region. We crossmatched the Gaia identifications with theobservations collected by the Kepler space telescope. We inspected the lightcurves visually, then calculated the relative Fourier coefficients and periodratios for the single- and double-mode K2 RR Lyrae stars to further classifythem. We identified 1443 and 41 stars classified as RR Lyrae or Cepheidvariables in Gaia DR2 in the targeted observations of the two missions and 263more RR Lyre targets in the Full-Frame Images (FFI) of the original mission. Weprovide the crossmatch of these sources. We conclude that the RR Lyrae cataloghas a completeness between 70-78%, and provide a purity estimate between 92-98%(targeted observations) with lower limits of 75% (FFI stars) and 51% (K2worst-case scenario). The low number of Cepheids prevents us from drawingdetailed conclusions but the purity of the DR2 sample is estimated to be around66%.

Gaia Data Release 2: Validation of the classification of RR Lyrae and Cepheid variables with the Kepler and K2 missions