Looking for phase-space structures in star-forming regions: An MST-based
  methodology
  We present a method for analysing the phase space of star-forming regions. In
particular we are searching for clumpy structures in the 3D subspace formed by
two position coordinates and radial velocity. The aim of the method is the
detection of kinematic segregated radial velocity groups, that is, radial
velocity intervals whose associated stars are spatially concentrated. To this
end we define a kinematic segregation index, $\tilde{\Lambda}$(RV), based on
the Minimum Spanning Tree (MST) graph algorithm, which is estimated for a set
of radial velocity intervals in the region. When $\tilde{\Lambda}$(RV) is
significantly greater than 1 we consider that this bin represents a grouping in
the phase space. We split a star-forming region into radial velocity bins and
calculate the kinematic segregation index for each bin, and then we obtain the
spectrum of kinematic groupings, which enables a quick visualization of the
kinematic behaviour of the region under study. We carried out numerical models
of different configurations in the subspace of the phase space formed by the
coordinates and the radial velocity that various case studies illustrate. The
analysis of the test cases demonstrates the potential of the new methodology
for detecting different kind of groupings in phase space.
