A new sample of stars, representative of the solar neighbourhood luminosity function, is constructed from the Hipparcos catalogue and the Fifth Catalogue of Nearby Stars. We have cross-matched to sources in the 2MASS catalogue so that for all stars i
ndividually determined Near Infrared photometry (NIR) is available on a homogeneous system (typically K_s). The spatial completeness of the sample has been carefully determined by statistical methods, and the NIR luminosity function of the stars has been derived by direct star counts. We find a local volume luminosity of 0.121 +/- 0.004 L_K_sun/(pc**3), corresponding to a volumetric mass-to-light ratio of M/L_K = 0.31 +/- 0.02 M_sun/L_K_sun, where giants contribute 80 per cent to the light but less than 2 per cent to the stellar mass. We derive the surface brightness of the solar cylinder with the help of a vertical disc model. We find a surface brightness of 99 L_K_sun/(pc**2) with an uncertainty of approximately 10 %. This corresponds to a mass-to-light ratio for the solar cylinder of M/L_K = 0.34 M_sun/L_K_sun. The mass-to-light ratio for the solar cylinder is only 10% larger than the local value despite the fact that the local population has a much larger contribution of young stars. It turns out that the effective scale heights of the lower main sequence carrying most of the mass is similar to that of the giants, which are dominating the NIR light. The corresponding colour for the solar cylinder is V-K=2.89 mag compared to the local value of V-K = 2.46 mag. An extrapolation of the local surface brightness to the whole Milky Way yields a total luminosity of M_K = -24.2 mag. The Milky Way falls in the range of K band Tully-Fisher (TF) relations from the literature.
We use a new method to trace backwards the star formation history of the Milky Way disk, using a sample of M dwarfs in the solar neighbourhood which is representative for the entire solar circle. M stars are used because they show H_alpha emission un
til a particular age which is a well calibrated function of their absolute magnitudes. This allows us to reconstruct the rate at which disk stars have been born over about half the disks lifetime. Our star formation rate agrees well with those obtained by using other, independent, methods and seems to rule out a constant star formation rate. The principal result of this study is to show that a relation of the Schmidt-Kennicut type (which relates the star formation rate to the interstellar gas content of galaxy disks) has pertained in the Milky Way disk during the last 5 Gyr. The star formation rate we derive from the M dwarfs and the interstellar gas content of the disk can be inferred as a function of time from a model of the chemical enrichment of the disk, which is well constrained by the observations indicating that the metallicity of the Galactic disk has remained nearly constant over the timescales involved. We demonstrate that the star formation rate and gas surface densities over the last 5 Gyrs can be accurately described by a Schmidt-Kennicutt law with an index of Gamma = 1.45 (+0.22,-0.09). This is, within statistical uncertainties, the same value found for other galaxies.
