Shape Analysis of HII Regions - I. Statistical Clustering
  We present here our shape analysis method for a sample of 76 Galactic HII
regions from MAGPIS 1.4 GHz data. The main goal is to determine whether
physical properties and initial conditions of massive star cluster formation is
linked to the shape of the regions. We outline a systematic procedure for
extracting region shapes and perform hierarchical clustering on the shape data.
We identified six groups that categorise HII regions by common morphologies. We
confirmed the validity of these groupings by bootstrap re-sampling and the
ordinance technique multidimensional scaling. We then investigated associations
between physical parameters and the assigned groups. Location is mostly
independent of group, with a small preference for regions of similar longitudes
to share common morphologies. The shapes are homogeneously distributed across
Galactocentric distance and latitude. One group contains regions that are all
younger than 0.5 Myr and ionised by low- to intermediate-mass sources. Those in
another group are all driven by intermediate- to high-mass sources. One group
was distinctly separated from the other five and contained regions at the
surface brightness detection limit for the survey. We find that our
hierarchical procedure is most sensitive to the spatial sampling resolution
used, which is determined for each region from its distance. We discuss how
these errors can be further quantified and reduced in future work by utilising
synthetic observations from numerical simulations of HII regions. We also
outline how this shape analysis has further applications to other diffuse
astronomical objects.
