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 \pm 0.3 km s ^ { -1 } ) comparable to that in a virial state ( \sim 0.8 km s ^ { -1 } ) .
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 .