On the internal dynamics of starless cores: stability of starless cores
  with internal motions and collapse dynamics
  In order to understand the collapse dynamics of observed low-mass starless
cores, we revise the conventional stability condition of hydrostatic
Bonnor-Ebert spheres to take internal motions into account. Because observed
starless cores resemble Bonnor-Ebert density structures, the stability and
dynamics of the starless cores are frequently analyzed by comparing to the
conventional stability condition of a hydrostatic Bonnor-Ebert sphere. However,
starless cores are not hydrostatic but have observed internal motions. In this
study, we take gaseous spheres with a homologous internal velocity field and
derive stability conditions of the spheres utilizing a virial analysis. We
propose two limiting models of spontaneous gravitational collapse: the collapse
of critical Bonnor-Ebert spheres and uniform density spheres. The collapse of
these two limiting models are intended to provide the lower and the upper
limits, respectively, of the infall speeds for a given density structure. The
results of our study suggest that the stability condition sensitively depends
on internal motions. A homologous inward motion with a transonic speed can
reduce the critical size compared to the static Bonnor-Ebert sphere by more
than a factor of two. As an application of the two limiting models of
spontaneous gravitational collapse, we compare the density structures and
infall speeds of the observed starless cores L63, L1544, L1689B, and L694-2 to
the two limiting models. L1689B and L694-2 seem to have been perturbed to
result in faster infall motions than for spontaneous gravitational collapse.
