G-virial: Gravity-based structure analysis of molecular clouds
  We present the G-virial method (available at http://gxli.github.io/G-virial/)
which aims to quantify (1) the importance of gravity in molecular clouds in the
position-position-velocity (PPV) space, and (2) properties of the gas
condensations in molecular clouds. Different from previous approaches that
calculate the virial parameter for different regions, our new method takes
gravitational interactions between all the voxels in 3D PPV data cubes into
account, and generates maps of the importance of gravity. This map can be
combined with the original data cube to derive relations such as the
mass-radius relation. Our method is important for several reasons. First, it
offers the the ability to quantify the centrally condensed structures in the 3D
PPV data cubes, and enables us to compare them in an uniform framework. Second,
it allows us to understand the importance of gravity at different locations in
the data cube, and provides a global picture of gravity in clouds. Third, it
offers a robust approach to decomposing the data into different regions which
are gravitationally coherent. To demonstrate the application of our method we
identified regions from the Perseus and Ophiuchus molecular clouds, and
analyzed their properties. We found an increase in the importance of gravity
towards the centers of the individual molecular condensations. We also
quantified the properties of the regions in terms of mass-radius and
mass-velocity relations. Through evaluating the virial parameters based on the
G-virial, we found that all our regions are almost gravitationally bound.
Cluster-forming regions appear are more centrally condensed.
