Stellar inventory of the solar neighbourhood using Gaia DR1

The absolute number and the density profiles of different types of stars in the solar neighbourhood are a fundamental anchor for studies of the initial mass function, stellar evolution, and Galactic structure. Using data from Gaia DR1, we reconstruct Gaia's selection function and 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: All vertical profiles are well represented by sech(2) profiles, with scaleheights ranging from approximate to 50 pc for A stars to approximate to 150 pc for G and K dwarfs and giants. We determine the luminosity function along the main sequence for MV < 7 (M = 0.72M(circle dot)) and along the giant branch for M-J greater than or similar to -2.5 in detail. Converting this to a mass function, we find that the high-mass (M > 1M(circle dot)) present-day mass function along the main sequence is dn/ dM = 0.016 (M/M-circle dot)(-4.7) stars pc(-3)M(-1). Extrapolating below M = 0.72M(circle dot), we find a totalmid-plane stellar density of 0.040 +/- 0.002M(circle dot) pc(-3). Giants contribute 0.00039 +/- 0.00001 stars pc(-3) or about 0.00046 +/- 0.00005M(circle dot)pc(-3). The star formation rate surface density is Sigma(t) = 7 +/- 1 exp (-t/7 +/- 1Gyr) M-circle dot pc(-2) Gyr(-1). Overall, we find that Gaia DR1' s selection biases are manageable and allow a detailed new inventory of the solar neighbourhood to be made that agrees with and extends previous studies. This bodes well for mapping the Milky Way with the full Gaia data set.