Using the reduced proper motions of Tycho-2 stars with B-V from 0.75 to 1.25: Monte Carlo simulations

Abstract

The stellar composition of the Tycho-2 Catalogue in the range B-V = 0{_·/ ^m }75-1{_·/ ^m }25 has been reproduced through Monte Carlo simulations. For young and old stars of the red giant clump (RGC), the red giant branch, subgiants, red dwarfs, and thick-disk giants, we have specified the distributions in coordinates, velocities, B-V, and M _V as a function of B-V and calculated their reduced proper motions, photometric distances from the ( B-V)- M _V calibration, and photoastrometric distances from the reduced proper motion- M _V calibration. Our simulations have shown the following: (1) a sample of thin-disk giants within 500 pc with an admixture of less than 10% of other stars can be produced; (2) a sample of dwarfs within 100 pc almost without any admixture of other stars can be produced; (3) the Local Spiral Arm affects the RGC composition of any magnitude-limited catalog in favor of giants younger than 2 Gyr; (4) the samples produced using reduced proper motions can be used for kinematic studies, provided that the biases of the quantities being determined are simulated and taken into account; (5) the photometric distances correlate with the photoastrometric ones because of the correlation between the proper motion and magnitude; (6) the photometric distances are closer to the true ones for the red giant branch and red dwarfs as the categories of stars with a clear ( B-V)- M _V relation, while the photoastrometric distances are closer to the true ones for the RGC, subgiants, and thick-disk giants; (7) the calculated distances differ systematically from the true ones, but they can be used to analyze the three-dimensional distribution of stars. Our simulations confirm the validity of our previous selection of RGC stars from Tycho-2.