SIMBAD references

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_φ, and angular momentum L_z for stars in the Galactic centre and anticentre directions. The resulting mean vertical motion  shows a linear increase with both V_φ and L_z 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 R_g < R₀, placing the onset of the warp at R <= 7 kpc. At equally high significance, we detect a previously unknown wave-like pattern of  over guiding centre R_g with an amplitude ∼1 km s^–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 ∼1 Gyr ago. The only significant deviation from this simple fit is a stream-like feature near R_g ∼ 9 kpc (|L_z| ∼ 2150 kpc km s^–1).