Stellar Inventory of the Solar Neighborhood using Gaia DR1
  The absolute number and the density profiles of different types of stars in
the solar neighborhood are a fundamental anchor for studies of the initial mass
function, stellar evolution, and galactic structure. Using data from the Gaia
DR1 Tycho-Gaia Astrometric Solution, we reconstruct Gaia's selection function
and we determine Gaia's volume completeness, the local number density, and the
vertical profiles of different spectral types along the main sequence from
early A stars to late K stars as well as along the giant branch. We clearly
detect the expected flattening of the stellar density profile near the
mid-plane for all stellar types: All vertical profiles are well represented by
sech^2 profiles, with scale heights ranging from ~50 pc for A stars to ~150 pc
for G and K dwarfs and giants. We determine the luminosity function along the
main sequence for M_V < 7 (M >~ $0.72 M_\odot$) and along the giant branch for
M_J >~ -2.5. Converting this to a mass function, we find that the high-mass (M
> $1\,M_\odot$) present-day mass function along the main sequence is d n / d M
= 0.016 $(M/M_\odot)^{-4.7}$ stars/pc^3/$M_\odot$. Extrapolating below M =
$0.72\,M_\odot$, we find a total mid-plane stellar density of 0.040+/-0.002
$M_\odot$/pc^3. Giants contribute 0.00039+/-0.00001 stars/pc^3 or about
0.00046+/-0.00005 $M_\odot$/pc^3. The star-formation rate surface density is
\Sigma(t) = 7+/-1 exp(-t/[7+/-1 Gyr]) $M_\odot$/pc^2/Gyr. Overall, we find that
Gaia DR1's selection biases are manageable and allow a detailed new inventory
of the solar neighborhood to be made that agrees with and extends previous
studies. This bodes well for mapping the Milky Way with the full Gaia data set.
