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Description
We derive unbiased distance estimates for the Gaia-TGAS data set by correcting for the bias due to the distance dependence of the selection function, which we measure directly from the data. From these distances and proper motions, we estimate the vertical and azimuthal velocities, W and V_{phi}_, and angular momentum L_z_ for stars in the Galactic centre and anticentre directions. The resulting mean vertical motion W^-^ hows a linear increase with both V_{phi}_ and L_z_ at 10{sigma} significance. Such a trend is expected from and consistent with the known Galactic warp. This signal extends to stars with guiding centre radii R_g_<R_0_, placing the onset of the warp at R<=7kpc. At equally high significance, we detect a previously unknown wave-like pattern of W^-^ over guiding centre R_g_ with an amplitude ~1km/s and a wavelength ~2.5kpc. This pattern is present in both the centre and anticentre directions, consistent with a winding (corrugated) warp or bending wave, likely related to known features in the outer disc (TriAnd and Monoceros overdensities), and may be caused by the interaction with the Sgr dwarf galaxy ~1Gyr ago. The only significant deviation from this simple fit is a stream-like feature near R_g_~9kpc (|L_z_|~2150kpc.km/s).
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