  Observations of stars in the the solar vicinity show a clear tendency for old
stars to have larger velocity dispersions. This relation is called the
age-velocity dispersion relation (AVR) and it is believed to provide insight
into the heating history of the Milky Way galaxy. Here, in order to investigate
the origin of the AVR, we performed smoothed particle hydrodynamic simulations
of the self-gravitating multiphase gas disks in the static disk-halo
potentials. Star formation from cold and dense gas is taken into account, and
we analyze the evolution of these star particles. We find that exponents of
simulated AVR and the ratio of the radial to vertical velocity dispersion are
close to the observed values. We also find that the simulated AVR is not a
simple consequence of dynamical heating. The evolution tracks of stars with
different epochs evolve gradually in the age-velocity dispersion plane as a
result of: (1) the decrease in velocity dispersion in star forming regions, and
(2) the decrease in the number of cold/dense/gas as scattering sources. These
results suggest that the AVR involves not only the heating history of a stellar
disk, but also the historical evolution of the ISM in a galaxy.
