Kinematics and stellar content of the Milky Way populations toward the North Galactic Pole

Aims. The formation and evolution of galaxies is one of the forefront problems of Astrophysics. Detailed studies of our own Galaxy are the first step to understand these complex processes. In this paper we discuss the stellar populations and kinematics toward the North Galactic Pole (NGP) using data taken from the Guide Star Catalog II. Methods. The Padova Galaxy model has been upgraded including the possibility of simulating in a consistent way color magnitude diagrams, luminosity functions and proper motions. Particular care is paid to simulate the kinematics of the thin disk, using a velocity dispersion tensor with off-diagonal term accounting for the vertical tilt. Results. To reproduce the observational color distribution of the studied fields, one of the most critical parameters is the IMF slope. The canonical Kroupa IMF gives a poor fit of the data. The most convincing solutions are obtained assuming that about 40% of the stars are in binaries and that the initial mass function changes slope at 0.8 M-circle dot instead than at the canonical value of 0.5 M-circle dot. We derive a Thin Disk IMF slope of alpha = 0.9 +/- 0.2 in the mass range 0.2-0.8 M-circle dot. We derive the velocity ellipsoids of the Thin disk populations. The Thick disk and the Thin disk are well separated concerning their kinematic properties. The Thick disk is found to have a mean rotational velocity of (v(c)) over bar = 178 +/- 8 km s(-1) implying a moderate rotational lag with respect to the solar motion. The data are not consistent with a significant vertical velocity gradient. This points in favor of a formation of the Thick disk by a quick heating of the precursor disk. Finally, no significant rotation velocity is found in the Halo.