Collapsing Index: A New Method to Identify Star-forming Cores Based on
  ALMA Images
  Stars form through the gravitational collapse of molecular cloud cores.
Before collapsing, the cores are supported by thermal pressure and turbulent
motions. A question of critical importance for the understanding of star
formation is how to observationally discern whether a core has already
initiated gravitational collapse or is still in hydrostatic balance. The
canonical method to identify gravitational collapse is based on the observed
density radial profile, which would change from a Bonnor-Ebert type toward
power laws as the core collapses. In practice, due to the projection effect,
the resolution limit, and other caveats, it has been difficult to directly
reveal the dynamical status of cores, particularly in massive star-forming
regions. We here propose a novel, straight-forward diagnostic, namely, the
collapsing index (CI), which can be modeled and calculated based on the radial
profile of the line width of dense gas. A meaningful measurement of CI requires
spatially and spectrally resolved images of optically thin and chemically
stable dense gas tracers. ALMA observations are making such data sets
increasingly available for massive star-forming regions. Applying our method to
one of the deepest dense-gas spectral images ever taken toward such a region,
namely, the Orion molecular cloud, we detect the dynamical status of selected
cores therein. We observationally distinguished a collapsing core in a massive
star-forming region from a hydrostatical one. Our approach would help
significantly improve our understanding of the interaction between gravity and
turbulence within molecular cloud cores in the process of star formation.
