Our Galaxy's youngest disc
  We investigate the structure of our Galaxy's young stellar disc by fitting
the distribution functions (DFs) of a new family to five-dimensional Gaia data
for a sample of $47\,000$ OB stars. Tests of the fitting procedure show that
the young disc's DF would be strongly constrained by Gaia data if the
distribution of Galactic dust were accurately known. The DF that best fits the
real data accurately predicts the kinematics of stars at their observed
locations, but it predicts the spatial distribution of stars poorly, almost
certainly on account of errors in the best-available dust map. We argue that
dust models could be greatly improved by modifying the dust model until the
spatial distribution of stars predicted by a DF agreed with the data. The
surface density of OB stars is predicted to peak at $R\simeq5.5\mbox{kpc}$,
slightly outside the reported peak in the surface density of molecular gas; we
suggest that the latter radius may have been under-estimated through the use of
poor kinematic distances. The velocity distributions predicted by the best-fit
DF for stars with measured line-of-sight velocities $v_\parallel$ reveal that
the outer disc is disturbed at the level of 10 $\mbox{km}~\mbox{s}^{-1}$ in
agreement with earlier studies, and that the measured values of $v_\parallel$
have significant contributions from the orbital velocities of binaries. Hence
the outer disc is colder than it is sometimes reported to be.
