Uncertainty of estimating the radial velocity dispersion in the solar region

The few high velocity stars in the solar region cause a significant uncertainty of the radial velocity dispersion which can change by a factor of 2 if these stars are taken into account. Assigning small finite weights to stars with large residual velocities results in velocity dispersions of 25.5 km/s, indicating that the Toomre's stability condition (1964) may not be fulfilled. Therefore, the velocity dispersion is a fluctuating random variable, with a characteristic transition period to deterministic distribution of 100,000 years. It is emphasized that the phase density should be considered a random function in investigating high-frequency nonstationary phenomena in star systems.