We explore the possibility of detecting and characterising the warp of the stellar disc of our Galaxy using synthetic Gaia data and two available proper motion catalogues namely UCAC4 and PPMXL. We develop a new kinematic model for the galactic warp. With Gaia, 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 realisations 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 work we have developed a first and simplified kinematic model for our Galactic warp. The simplicity of the model has allowed us to evaluate the efficacy and limitations of the use of Gaia data to characterise the warp. These limitations have been fully explored and quantified. From the work done so far, we expect that the Gaia database, together with the methods presented here, will be a very powerful combination to characterise the warp of the stellar disc of our Galaxy. Moreover, We introduce LonKin methods that help us detect the kinematic signature of the warp in the vertical motions of stars as a function of galactic longitude. Applying this method to the UCAC4 proper motions, we do not obtain a similar trend as the one we expect from our warp model. We explore a possible source of this discrepancy in terms of systematics caused by a residual spin of the reference frame with respect to the extra- galactic inertial one. We also look into a deeper proper motion survey namely the PPMXL. The effect of systematics in this catalogue was reduced using hundreds of thousand quasars present in this survey. An analytical fit to the vertical velocity trend of red clump stars suggests a vertical oscillation in the southern warp with a rather high frequency that tends to decrease the amplitude of the warp. We analysed this trend in the context of our warp model and an abrupt decrease of the warp’s amplitude in a very short time of about one hundred Myr could explain this trend.
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