  In the present study, we analyze the radial velocity distribution as a
function of different stellar parameters such as stellar age, mass, rotational
velocity and distance to the Sun for a sample of 6781 single low--mass field
dwarf stars, located in the solar neighborhood. We show that the radial
velocity distributions are best fitted by $q$--Gaussians that arise within the
Tsallis nonextensive statistics. The obtained distributions cannot be described
by the standard Gaussian that emerges within Boltzmann-Gibbs (B--G) statistical
mechanics. The results point to the existence of a hierarchical structure in
phase space, in contrast to the uniformly occupied phase space of B--G
statistical mechanics, driven by the $q$--Central Limit Theorem, consistent
with nonextensive statistical mechanics.
