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The Gaia-ESO Survey: Separating disk chemical substructures with cluster models

(Abridged) Recent spectroscopic surveys have begun to explore the Galactic disk system outside the solar neighborhood on the basis of large data samples. In this way, they provide valuable information for testing spatial and temporal variations of disk structure kinematics and chemical evolution. We used a Gaussian mixture model algorithm, as a rigurous mathematical approach, to separate in the [Mg/Fe] vs. [Fe/H] plane a clean disk star subsample from the Gaia-ESO survey internal data release 2. We find that the sample is separated into five groups associated with major Galactic components; the metal-rich end of the halo, the thick disk, and three subgroups for the thin disk sequence. This is confirmed with a sample of red clump stars from the Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey. The two metal-intermediate and metal-rich groups of the thin disk decomposition ([Fe/H]>-0.25 dex) highlight a change in the slope at solar metallicity. This holds true at different radial regions. The distribution of Galactocentric radial distances of the metal-poor part of the thin disk ([Fe/H]<-0.25 dex) is shifted to larger distances than those of the more metal-rich parts. Moreover, the metal-poor part of the thin disk presents indications of a scale height intermediate between those of the thick and the rest of the thin disk, and it displays higher azimuthal velocities than the latter. These stars might have formed and evolved in parallel and/or dissociated from the inside-out formation taking place in the internal thin disk. Their enhancement levels might be due to their origin from gas pre-enriched by outflows from the thick disk or the inner halo. The smooth trends of their properties (their spatial distribution with respect to the plane, in particular) with [Fe/H] and [Mg/Fe] suggested by the data indicates a quiet dynamical evolution, with no relevant merger events.