Warp, waves, and wrinkles in the Milky Way

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 Vϕ, and angular momentum Lz for stars in the Galactic centre and anticentre directions. The resulting mean vertical motion W shows a linear increase with both Vϕ and Lz at 10σ significance. Such a trend is expected from and consistent with the known Galactic warp. This signal extends to stars with guiding centre radii Rg < R0, placing the onset of the warp at R ≲ 7 kpc. At equally high significance, we detect a previously unknown wave-like pattern of W over guiding centre Rg with an amplitude ~1 kms-1 and a wavelength ~2.5 kpc. 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 Rg ~9 kpc (|Lz| ~2150 kpc km s-1)