Warp, Waves, and Wrinkles in the Milky Way
  We derive unbiased distance estimates for the Gaia-TGAS dataset 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 anti-centre directions. The
resulting mean vertical motion $\overline{W}$ shows 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
$R\lesssim7{\rm kpc}$. At equally high significance, we detect a previously
unknown wave-like pattern of $\overline{W}$ over guiding centre $R_g$ with
amplitude $\sim1{\rm kms}^{-1}$ and wavelength $\sim2.5{\rm kpc}$. This pattern
is present in both the centre and anti-centre directions, consistent with a
winding (corrugated) warp or bending wave, likely related to known features in
the outer disc (TriAnd and Monoceros over-densities), and may be caused by the
interaction with the Sgr dwarf galaxy $\sim1{\rm Gyr}$ ago. The only
significant deviation from this simple fit is a stream-like feature near
$R_g\sim9{\rm kpc}$ ($|L_z|\sim2150{\rm kpckms}^{-1}$).
