Numerical simulations for the study of the methods for stellar kinematics and luminousity calibration

Computer Science – Numerical Analysis

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Kinematics, Mathematical Models, Maximum Likelihood Estimates, Solar Oscillations, Solar Rotation, Stellar Luminosity, Computerized Simulation, Density Distribution, Numerical Analysis, Stellar Parallax, Velocity Distribution

Scientific paper

We created numerical simulations of a sample of KO 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 + or - 0.7 km/s in V0 and + or - 2 in both l0 and b0. 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 of statistical parallax determinations. We conclude that the maximum likelihood method is definitely better than the classical methods, providing typically results with errors of + or - 0.2, whereas in the classical methods the errors are of the order + or - 0.5.

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