  We numerically examine dynamical heterogeneity in a highly supercooled
three-dimensional liquid via molecular-dynamics simulations. To define the
local dynamics, we consider two time intervals, $\tau_\alpha$ and
$\tau_{\text{ngp}}$. $\tau_\alpha$ is the $\alpha$ relaxation time, and
$\tau_{\text{ngp}}$ is the time at which non-Gaussian parameter of the van Hove
self-correlation function is maximized. We determine the lifetimes of the
heterogeneous dynamics in these two different time intervals,
$\tau_{\text{hetero}}(\tau_\alpha)$ and
$\tau_{\text{hetero}}(\tau_{\text{ngp}})$, by calculating the time correlation
function of the particle dynamics, i.e., the four-point correlation function.
We find that the difference between $\tau_{\text{hetero}}(\tau_\alpha)$ and
$\tau_{\text{hetero}}(\tau_{\text{ngp}})$ increases with decreasing
temperature. At low temperatures, $\tau_{\text{hetero}}(\tau_\alpha)$ is
considerably larger than $\tau_{\alpha}$, while
$\tau_{\text{hetero}}(\tau_{\text{ngp}})$ remains comparable to
$\tau_{\alpha}$. Thus, the lifetime of the heterogeneous dynamics depends
strongly on the time interval.
