Towards a fully consistent Milky Way disc model – I. The local model based on kinematic and photometric data

We present a fully consistent evolutionary disc model of the solar cylinder. The model is based on a sequence of stellar subpopulations described by the star formation history (SFR) and the dynamical heating law [given by the age-velocity dispersion relation (AVR)]. The stellar subpopulations are in dynamical equilibrium and the gravitational potential is calculated self-consistently including the influence of the dark matter halo and the gas component. The combination of kinematic data from Hipparcos and the finite lifetimes of main-sequence (MS) stars enables us to determine the detailed vertical disc structure independent of individual stellar ages and only weakly dependent on the initial mass function (IMF). The disc parameters are determined by applying a sophisticated best-fitting algorithm to the MS star velocity distribution functions in magnitude bins. We find that the AVR is well constrained by the local kinematics, whereas for the SFR the allowed range is larger. The model is consistent with the local kinematics of MS stars and fulfils the known constraints on scaleheights, surface densities and mass ratios. A simple chemical enrichment model is included in order to fit the local metallicity distribution of G dwarfs. In our favoured Model A, the power-law index of the AVR is 0.375 with a minimum and maximum velocity dispersion of 5.1 and 25.0 km s -1 , respectively. The SFR shows a maximum 10 Gyr ago and declines by a factor of four to the present-day value of 1.5 M ⊙ pc -2 Gyr -1 . A best fit of the IMF leads to power-law indices of -1.46 below and -4.16 above 1.72M ⊙ avoiding a kink at 1 M ⊙ . An isothermal thick-disc component with local density of ~6 per cent of the stellar density is included. A thick disc containing more than 10 per cent of local stellar mass is inconsistent with the local kinematics of K and M dwarfs. Neglecting the thick-disc component results in slight variations of the thin-disc properties, but has a negligible influence on the AVR and the normalized SFR. The model allows detailed predictions of the density, age, metallicity and velocity distribution functions of MS stars as a function of height above the mid-plane. The complexity of the model does not allow to rule out other star formation scenarios using the local data alone. The incorporation of multiband star count and kinematic data of larger samples in the near future will improve the determination of the disc structure and evolution significantly.