  In this paper, we study the large time asymptotic behavior toward rarefaction
waves for solutions to the 1-dimensional compressible Navier-Stokes equations
with density-dependent viscosities for general initial data whose far fields
are connected by a rarefaction wave to the corresponding Euler equations with
one end state being vacuum.
  First, a global-in-time weak solution around the rarefaction wave is
constructed by approximating the system and regularizing the initial data with
general perturbations, and some a priori uniform-in-time estimates for the
energy and entropy are obtained. Then it is shown that the density of any weak
solution satisfying the natural energy and entropy estimates will converge to
the rarefaction wave connected to vacuum with arbitrary strength in super-norm
time-asymptotically. Our results imply, in particular, that the initial vacuum
at far fields will remain for all the time which are in contrast to the case of
non-vacuum rarefaction waves studied in \cite{JWX} where all the possible
vacuum states will vanish in finite time. Finally, it is proved that the weak
solution becomes regular away from the vacuum region of the rarefaction wave.
