Local disc model in view of Gaia DR1 and RAVE data
  We test the performance of the semi-analytic self-consistent Just-Jahrei{\ss}
disc model (JJ model) with the astrometric data from the Tycho-Gaia Astrometric
Solution (TGAS) sub-catalogue of the first Gaia data release (Gaia DR1), as
well as the radial velocities from the fifth data release of the Radial
Velocity Experiment survey (RAVE DR5). We use a sample of 19,746 thin disc
stars from the TGAS$\times$RAVE cross-match selected in the local solar
cylinder of 300 pc radius and 1 kpc height below the Galactic plane and
simulate this sample via the forward modelling technique. First, we convert the
predicted vertical density laws of the thin disc populations into a mock
sample. Then the obtained mock populations are reddened with a 3D dust map and
are subjected to the selection criteria corresponding to the RAVE and TGAS
observational limitations as well as to additional cuts applied to the data
sample. We calculate the quantities of interest separately at different heights
above the Galactic plane taking into account the distance error effects
separately in horizontal and vertical directions. We investigate the simulated
sample in terms of the vertical number density profiles, Hess diagrams and
velocity distribution functions. Basing on a good agreement of our simulations
with the data, we conclude that our fiducial disc model confidently reproduces
the vertical trends in the thin disc stellar population properties. Thus, it
can serve as a starting point for the future extension of the JJ model to other
Galactocentric distances.
