NUMERICAL SIMULATIONS FOR THE STUDY OF THE METHODS FOR STELLAR KINEMATICS AND LUMINOSITY CALIBRATION

We created numerical simulations of a sample of K0 III stars with an e llipsoidal velocity distribution, an exponentially increasing density distribution and a prefixed solar motion. On the basis of the numerica l samples we study the solar motion, using the known classical methods . We can assess in this way the external errors of the methods. We fin d that the dispersion of the results is rather large, except for large samples. Typical values of the uncertainty in the apex position for s amples of one thousand stars are +/-0.7 km s(-1) in V-0 and +/-2 degre es in both l(0) and b(0). We study the possible influence upon the sol ar motion of different factors which one encounters in practice like i ncomplete sky coverage, different ellipsoidal distributions and differ ent values of the absolute magnitude dispersion. For the first factor, the uncertainty increases with decreasing sky coverage. For the two o thers we found that no important bias is produced, if these are not to o far away from the normal values. In the second part we use the artif icial samples to compare the accuracy of different methods fo statisti cal parallax determinations. We conclude that the maximum likelihood m ethod is definitely better than the classical methods, providing typic ally results with erros of +/-0.2, whereas in the classical methods th e errors are of the order of +/-0.5.