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

## TL;DR

This study uses Monte Carlo simulations to analyze the stellar populations in the Tycho-2 Catalogue with specific B-V color indices, focusing on their proper motions, distances, and distribution for various star types.

## Contribution

The paper introduces a detailed simulation approach to reproduce and analyze the stellar composition and kinematics of Tycho-2 stars within a specific B-V range, validating previous star selection methods.

## Key findings

- Sample of thin-disk giants within 500 pc can be produced with less than 10% contamination.
- Sample of dwarfs within 100 pc can be almost free of contamination.
- Distances derived from photometric and photoastrometric methods have specific correlations and systematic differences.

## Abstract

The stellar composition of the Tycho-2 Catalogue in the range $0.75<B-V<1.25$ 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.