  We have investigated dynamical heterogeneity in a highly supercooled liquid
using molecular-dynamics simulations in three dimensions. Dynamical
heterogeneity can be characterized by three quantities: correlation length
$\xi_4$, intensity $\chi_4$, and lifetime $\tau_{\text{hetero}}$. We evaluated
all three quantities consistently from a single order parameter. In a previous
study (H. Mizuno and R. Yamamoto, Phys. Rev. E {\bf 82}, 030501(R) (2010)), we
examined the lifetime $\tau_{\text{hetero}}(t)$ in two time intervals
$t=\tau_\alpha$ and $\tau_{\text{ngp}}$, where $\tau_\alpha$ is the
$\alpha$-relaxation time and $\tau_{\text{ngp}}$ is the time at which the
non-Gaussian parameter of the Van Hove self-correlation function is maximized.
In the present study, in addition to the lifetime $\tau_{\text{hetero}}(t)$, we
evaluated the correlation length $\xi_4(t)$ and the intensity $\chi_4(t)$ from
the same order parameter used for the lifetime $\tau_{\text{hetero}}(t)$. We
found that as the temperature decreases, the lifetime $\tau_{\text{hetero}}(t)$
grows dramatically, whereas the correlation length $\xi_4(t)$ and the intensity
$\chi_4(t)$ increase slowly compared to $\tau_{\text{hetero}}(t)$ or plateaus.
Furthermore, we investigated the lifetime $\tau_{\text{hetero}}(t)$ in more
detail. We examined the time-interval dependence of the lifetime
$\tau_{\text{hetero}}(t)$ and found that as the time interval $t$ increases,
$\tau_{\text{hetero}}(t)$ monotonically becomes longer and plateaus at the
relaxation time of the two-point density correlation function. At the large
time intervals for which $\tau_{\text{hetero}}(t)$ plateaus, the heterogeneous
dynamics migrate in space with a diffusion mechanism, such as the particle
density.
