A Statistical Relation between Mass, Age, and Velocity Dispersion in the Solar Neighborhood

The stellar kinematics of the Galactic disk are the main factors constraining disk formation and evolution processes in the Milky Way. In this paper, we investigate a statistical relation between stellar mass, age, and velocity dispersion for stars in the solar neighborhood. Age–velocity dispersion relations, with their applications, have been studied in detail before, but their correlation with mass was mostly neglected. To investigate this relation, we use proper motion data of more than 113,035 stars in the Galactic disk (with solar distances less than 150 pc) provided by the third data release of the Gaia mission, and for stellar mass and age, Gaia's Final Luminosity Age Mass Estimator is implemented. We analyze this data and the correlations between the parameters with random forest regression, which is an ensemble statistical-learning technique. Finally, we show that, by considering stellar mass alongside age, we can determine velocity dispersions with an average relative error and a mean absolute error of about 9% and 2.68 km s ^−1 , respectively. We also find that the correlation of stellar age with velocity dispersion is 3–8 times more than mass, which varies due to the different stellar types and masses.