The origin of a distributed stellar population in the star-forming
  region W4
  Stellar kinematics provides the key to understanding the formation process
and dynamical evolution of stellar systems. Here, we present a kinematic study
of the massive star-forming region W4 in the Cassiopeia OB6 association using
the Gaia Data Release 2 and high-resolution optical spectra. This star-forming
region is composed of a core cluster (IC 1805) and a stellar population
distributed over 20 pc, which is a typical structural feature found in many OB
associations. According to a classical model, this structural feature can be
understood in the context of the dynamical evolution of a star cluster. The
core-extended structure exhibits internally different kinematic properties.
Stars in the core have an almost isotropic motion, and they appear to reach
virial equilibrium given their velocity dispersion (0.9 +/- 0.3 km/s)
comparable to that in a virial state (~0.8 km/s). On the other hand, the
distributed population shows a clear pattern of radial expansion. From the
N-body simulation for the dynamical evolution of a model cluster in subvirial
state, we reproduce the observed structure and kinematics of stars. This model
cluster experiences collapse for the first 2 Myr. Some members begin to
radially escape from the cluster after the initial collapse, eventually forming
a distributed population. The internal structure and kinematics of the model
cluster appear similar to those of W4. Our results support the idea that the
stellar population distributed over 20 pc in W4 originate from the dynamical
evolution of IC 1805.
