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The absolute number and the density profiles of different types of stars inthe solar neighborhood are a fundamental anchor for studies of the initial massfunction, stellar evolution, and galactic structure. Using data from the GaiaDR1 Tycho-Gaia Astrometric Solution, we reconstruct Gaia's selection functionand we determine Gaia's volume completeness, the local number density, and thevertical profiles of different spectral types along the main sequence fromearly A stars to late K stars as well as along the giant branch. We clearlydetect the expected flattening of the stellar density profile near themid-plane for all stellar types: All vertical profiles are well represented bysech^2 profiles, with scale heights ranging from ~50 pc for A stars to ~150 pcfor G and K dwarfs and giants. We determine the luminosity function along themain sequence for M_V < 7 (M >~ $0.72 M_\odot$) and along the giant branch forM_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 about0.00046+/-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 thatGaia DR1's selection biases are manageable and allow a detailed new inventoryof the solar neighborhood to be made that agrees with and extends previousstudies. This bodes well for mapping the Milky Way with the full Gaia data set.

Stellar Inventory of the Solar Neighborhood using Gaia DR1