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 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 scale heights ranging from \approx 50 \mathrm { pc } for A stars to \approx 150 \mathrm { pc } for G and K dwarfs and giants .
We determine the luminosity function along the main sequence for M _ { V } < 7 ( M \gtrsim 0.72 \mathrm { M } _ { \odot } ) and along the giant branch for M _ { J } \gtrsim - 2.5 in detail .
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 \mathrm { d } n / \mathrm { d } M = 0.016 ( M / M _ { \odot } ) ^ { -4.7 } \mathrm { stars \mathrm { % pc } } ^ { -3 } M _ { \odot } ^ { -1 } .
Extrapolating below M = 0.72 \mathrm { M } _ { \odot } , we find a total mid-plane stellar density of 0.040 \pm 0.002 \mathrm { M } _ { \odot } \mathrm { pc } ^ { -3 } .
Giants contribute 0.00039 \pm 0.00001 stars \mathrm { pc } ^ { -3 } or about 0.00046 \pm 0.00005 \mathrm { M } _ { \odot } \mathrm { pc } ^ { -3 } .
The star-formation rate surface density is \Sigma ( t ) = 7 \pm 1 \exp ( - t / 7 \pm 1 \mathrm { Gyr } ) M _ { \odot } \mathrm { pc } ^ { -2 } % \mathrm { Gyr } ^ { -1 } .
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 .