We explore the possibility of detecting and characterizing the warp of the stellar disc of our Galaxy using synthetic Gaia data. The availability of proper motions and, for the brightest stars radial velocities, adds a new dimension to this study. A family of Great Circle Cell Counts (GC3) methods is used. They are ideally suited to find the tilt and twist of a collection of rings, which allow us to detect and measure the warp parameters. To test them, we use random realizations of test particles which evolve in a realistic Galactic potential warped adiabatically to various final configurations. In some cases a twist is introduced additionally. The Gaia selection function, its errors model and a realistic 3D extinction map are applied to mimic three tracer populations: OB, A and Red Clump stars. We show how the use of kinematics improves the accuracy in the recovery of the warp parameters. The OB stars are demonstrated to be the best tracers determining the tilt angle with accuracy better than ∼ 0.5 up to Galactocentric distance of ∼ 16 kpc. Using data with good astrometric quality, the same accuracy is obtained for A type stars up to ∼ 13 kpc and for Red Clump up to the expected stellar cut-off. Using OB stars the twist angle is recovered to within < 3 • for all distances.

In this first paper we simulate the population of disc Red Clump stars to be observed by Gaia. We generate a set of test particles and we evolve it in a 3D barred Milky Way like galactic potential. We assign physical properties of the Red Clump trace population and a realistic 3D interstellar extinction model. We add Gaia observational constraints and an error model according to the pre-commissioning scientific performance assessments. We present and analyse two mock catalogues, offered to the community, that are an excellent test bed for testing tools being developed for the future scientific exploitation of Gaia data. The first catalogue contains stars up to Gaia G∼20, while the second is the subset containing Gaia radial velocity data with a maximum error of σ Vr = 10km s −1 . Here we present first attempts to characterise the density structure of the Galactic bar in the Gaia space of observables. The Gaia large errors in parallax and the high interstellar extinction in the inner parts of the Galactic disc prevent us to model the bar overdensity. This result suggests the need to combine Gaia and IR data to undertake such studies. We find that IR photometric distances for this Gaia sample allow us to recover the Galactic bar orientation angle with an accuracy of ∼ 5 • .

Aims. We derive the vertical velocities of disk stars in the range of Galactocentric radii of R = 5−16 kpc within 2 kpc in height from the Galactic plane. This kinematic information is connected to dynamical aspects in the formation and evolution of the Milky Way, such as the passage of satellites and vertical resonance and determines whether the warp is a long-lived or a transient feature. Methods. We used the PPMXL survey, which contains the USNO-B1 proper motions catalog cross-correlated with the astrometry and near-infrared photometry of the 2MASS point source catalog. To improve the accuracy of the proper motions, the systematic shifts from zero were calculated by using the average proper motions of quasars in this PPMXL survey, and we applied the corresponding correction to the proper motions of the whole survey, which reduces the systematic error. From the color-magnitude diagram K versus (J − K) we selected the standard candles corresponding to red clump giants and used the information of their proper motions to build a map of the vertical motions of our Galaxy. We derived the kinematics of the warp both analytically and through a particle simulation to fit these data. Complementarily, we also carried out the same analysis with red clump giants spectroscopically selected with APOGEE data, and we predict the improvements in accuracy that will be reached with future Gaia data. Results. A simple model of warp with the height of the disk z w (R, φ) = γ(R − R ) sin(φ − φ w ) fits the vertical motions ifγ/γ = −34 ± 17 Gyr −1 ; the contribution toγ comes from the southern warp and is negligible in the north. If we assume this 2σ detection to be real, the period of this oscillation is shorter than 0.43 Gyr at 68.3% C.L. and shorter than 4.64 Gyr at 95.4% C.L., which excludes with high confidence the slow variations (periods longer than 5 Gyr) that correspond to long-lived features. Our particle simulation also indicates a probable abrupt decrease of the warp amplitude in a time of about one hundred Myr. Conclusions. The vertical motion in the warp apparently indicates that the main S-shaped structure of the warp is a long-lived feature, whereas the perturbation that produces an irregularity in the southern part is most likely a transient phenomenon. But we need higher accuracy in the systematic errors of proper motions to confirm this tentative detection of vertical motion in the outer disk. With the use of the Gaia end-of-mission products together with spectroscopically classified red clump giants, the precision in vertical motions can be increased by an order of magnitude at least.

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