The local stellar luminosity function and mass-to-light ratio in the near-infrared

A new sample of stars, representative of the solar neighbourhood luminosity function (LF), is constructed from the Hipparcos catalogue and the Fifth Catalogue of Nearby Stars. We have cross-matched to sources in the Two Micron All Sky Survey catalogue so that for all stars individually determined near-infrared (NIR) photometry 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 LF of the stars has been derived by direct star counts. We find a local volume luminosity of 0.121 ± 0.004 L_K⊙ pc^-3, corresponding to a volumetric mass-to-light ratio (M/L) of M/L_K = 0.31 ± 0.02 {M}_{⊙}/L_{K⊙}, 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⊙ pc^-2 with an uncertainty of approximately 10 per cent. This corresponds to an M/L for the solar cylinder of M/L_K = 0.34 {M}_{⊙}/L_{K⊙}. The M/L for the solar cylinder is only 10 per cent 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 scaleheights 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 relations from the literature.