Characterizing the dynamical state of star clusters from snapshots of
  their spatial distributions
  We determine the distribution of stellar surface densities, \Sigma, from
models of static and dynamically evolving star clusters with different
morphologies, including both radially smooth and substructured clusters. We
find that the \Sigma distribution is degenerate, in the sense that many
different cluster morphologies (smooth or substructured) produce similar
cumulative distributions. However, when used in tandem with a measure of
structure, such as the Q-parameter, the current spatial and dynamical state of
a star cluster can be inferred. The effect of cluster dynamics on the \Sigma
distribution and the Q-parameter is investigated using N-body simulations and
we find that, depending on the assumed initial conditions, the \Sigma
distribution can rapidly evolve from high to low densities in less than 5Myr.
This suggests that the \Sigma distribution can only be used to assess the
current density of a star forming region, and provides little information on
its initial density. However, if the \Sigma distribution is used together with
the Q-parameter, then information on the amount of substructure can be used as
a proxy to infer the amount of dynamical evolution that has taken place.
Substructure is erased quickly through dynamics, which can disrupt binary star
systems and planets, as well as facilitate dynamical mass segregation.
Therefore, dynamical processing in young star forming regions could still be
significant, even without currently observed high densities.
