Does External Pressure Explain Recent Results for Molecular Clouds?
  The recent paper by Heyer et al (2009) indicates that observations of size,
linewidth and column density of interstellar clouds do not agree with simple
virial equilibrium (VE) as a balance between gravitational and kinetic energies
in the sense that the clouds either have too much kinetic energy or too little
mass to be bound. This may be explained by violation of VE as suggested by
Dobbs et al 2011, by observational underestimation of the masses as suggested
by Heyer et al 2009, or by an external pressure acting as an additional
confining force as suggested earlier by Heyer et al 2004. The data of Heyer et
al. 2009 cannot be explained with a single value for the external pressure, but
if different clouds in the sample have different external pressures in the
range of Pe/k = E4 to E7 cm-3 K, then most of the clouds could be in pressure
virial equilibrium (PVE). In this paper we discuss two consequences of the
external pressure. First, we show that the observational data are consistent
with the hypothesis (Chie\'ze 1987) that most clouds are at a critical mass for
dynamical stability determined solely by the pressure. Above this mass a cloud
is unstable to gravitational collapse or fragmentation. Second, we show that
the external pressure modifies the well-known size-linewidth relationship first
proposed by Larson (1981) so that the proportionality is no longer constant but
depends on the external pressure.
