  We consider here the collective accretion of gas by globular clusters and
dwarf galaxies moving through the interstellar medium. In the limit of high
velocity and/or sound speed of the ISM, the collective potential of the cluster
is insufficient to accrete significant amounts of gas, and stars within the
systems accrete gas individually. We show, however, that when the sound speed
or the relative velocity of the ambient medium is less than the central
velocity dispersion of the cluster, it is accreted into the collective
potential of the cluster prior to being accreted onto the individual stars
within the cluster. The collective rate is strongly enhanced relative to the
individual rates. This effect may potentially modify the white dwarf cooling
sequence in globular clusters with low-inclination and low-eccentricity
Galactic orbits, and lead to the rejuvenation of some marginally surviving
cores of globular clusters and nucleated dwarf galaxies near the Galactic
center. Such effects will only occur rarely, but may explain the existence of
clusters of young, massive stars near the Galactic center.
