Numerical simulations for the study of the methods for stellar

Abstract

We created numerical simulations of a sample of K0 III stars with an ellipsoidal velocity distribution, an exponentially increasing density distribution and a prefixed solar motion. On the basis of the numerical samples we study the solar motion, using the known classical methods. We can assess in this way the external errors of the methods. We find that the dispersion of the results is rather large, except for large samples. Typical values of the uncertainty in the apex position for samples of one thousand stars are +/-0.7km/sin(V_0_) and +/-2deg in both l_0_ and b_0_. We study the possible influence upon the solar motion of different factors which one encounters in practice like incomplete sky coverage, different ellipsoidal distributions and different values of the absolute magnitude dispersion. For the first factor, the uncertainty increases with decreasing sky coverage. For the two others we found that no important bias is produced, if these are not too far away from the normal values. In the second part we use the artificial samples to compare the accuracy of different methods fo statistical parallax determinations. We conclude that the maximum likelihood method is definitely better than the classical methods, providing typically results with erros of +/-0.2, whereas in the classical methods the errors are of the order of +/-0.5.