Virial Ratio: Direct Evaluation from Molecular Cloud Data and the
  Challenges of Improving Accuracy
  The virial ratio between kinetic and gravitational terms provides key insight
into the balance of forces that confine a molecular cloud, but the clumpy and
filamentary structures of resolved clouds make it difficult to evaluate this
ratio in a consistent way. For clouds with resolved maps of column density as
well as a line tracer, we demonstrate that the gravitational energy can be
estimated directly from observations in a manner similar to the kinetic energy.
This offers improved diagnostic power and consistency. Disentangling a cloud
from foreground and background materials is a persistent challenge, for which
we introduce a strategy based on Abel's transform. We provide proofs of
principle using simulated clouds.
