  Evidence for a large scale flow of low density gas onto the Cepheus A young
stellar cluster is presented. Observations of K-band near-infrared and
multi-transition CS and N2H+ millimeter line emission are shown in relation to
a sub-millimeter map of the cool dust around the most embedded stars. The
near-infrared emission is offset from the dust peak suggesting a shift in the
location of star formation over the history of the core. The CS emission is
concentrated toward the core center but N2H+ peaks in two main cores offset
from the center, opposite to the chemistry observed in low mass cores. A
starless core with strong CS but weak N2H+ emission is found toward the western
edge of the region. The average CS(2-1) spectrum over the cluster forming core
is asymmetrically self-absorbed suggesting infall. We analyze the large scale
dynamics by applying a one-dimensional radiative transfer code to a model
spherical core with constant temperature and linewidth, and a density profile
measured from an archival 850 micron map of the region. The best fit model that
matches the three CS profiles requires a low CS abundance in the core and an
outer, infalling envelope with a low density and undepleted CS abundance. The
integrated intensities of the two N2H+ lines is well matched with a constant
N2H+ abundance. The envelope infall velocity is tightly constrained by the
CS(2-1) asymmetry and is sub-sonic but the size of the infalling region is
poorly determined. The picture of a high density center with depleted CS slowly
accreting a low density outer envelope with normal CS abundance suggests that
core growth occurs at least partially by the dissipation of turbulent support
on large scales.
