  We discuss the spatiotemporal behavior of local density and its relation to
dynamical heterogeneity in a highly supercooled liquid by using molecular
dynamics simulations of a binary mixture with different particle sizes in two
dimensions. To trace voids heterogeneously existing with lower local densities,
which move along with the structural relaxation, we employ the minimum local
density for each particle in a time window whose width is set along with the
structural relaxation time. Particles subject to free volumes correspond well
to the configuration rearranging region of dynamical heterogeneity. While the
correlation length for dynamical heterogeneity grows with temperature decrease,
no growth in the correlation length of heterogeneity in the minimum local
density distribution takes place. A comparison of these results with those of
normal mode analysis reveals that superpositions of lower-frequency soft modes
extending over the free volumes exhibit spatial correlation with the broken
bonds. This observation suggests a possibility that long-ranged vibration modes
facilitate the interactions between fragile regions represented by free
volumes, to induce dynamical correlations at a large scale.
