  In a previous paper we demonstrated that non-radial hydrodynamic oscillations
of a thermally-supported (Bonnor-Ebert) sphere embedded in a low-density,
high-temperature medium persist for many periods. The predicted column density
variations and molecular spectral line profiles are similar to those observed
in the Bok globule B68 suggesting that the motions in some starless cores may
be oscillating perturbations on a thermally supported equilibrium structure.
Such oscillations can produce molecular line maps which mimic rotation,
collapse or expansion, and thus could make determining the dynamical state from
such observations alone difficult.
  However, while B68 is embedded in a very hot, low-density medium, many
starless cores are not, having interior/exterior density contrasts closer to
unity. In this paper we investigate the oscillation damping rate as a function
of the exterior density. For concreteness we use the same interior model
employed in Broderick et al. (2007), with varying models for the exterior gas.
We also develop a simple analytical formalism, based upon the linear
perturbation analysis of the oscillations, which predicts the contribution to
the damping rates due to the excitation of sound waves in the external medium.
We find that the damping rate of oscillations on globules in dense molecular
environments is always many periods, corresponding to hundreds of thousands of
years, and persisting over the inferred lifetimes of the globules.
