The structure and characteristic scales of molecular clouds
  The structure of molecular clouds (MCs) holds important clues on the physical
processes that lead to their formation and subsequent evolution. While it is
well established that turbulence imprints a self-similar structure to the
clouds, other processes, such as gravity and stellar feedback, can break their
scale-free nature. The break of self-similarity can manifest itself in the
existence of characteristic scales that stand out from the underlying structure
generated by turbulent motions. We investigate the structure of the Cygnus-X
North and the Polaris MCs which represent two extremes in terms of their star
formation activity. We characterize the structure of the clouds using the
delta-variance ($\Delta$-variance) spectrum. In Polaris, the structure of the
cloud is self-similar over more than one order of magnitude in spatial scales.
In contrast, the $\Delta$-variance spectrum of Cygnus-X exhibits an excess and
a plateau on physical scales of ~0.5-1.2 pc. In order to explain the
observations for Cygnus-X, we use synthetic maps in which we overlay
populations of discrete structures on top of a fractal Brownian motion (fBm)
image. The properties of these structures such as their major axis sizes,
aspect ratios, and column density contrasts are randomly drawn from
parameterized distribution functions. We show that it is possible to reproduce
a $\Delta$-variance spectrum that resembles the one of the Cygnus-X cloud. We
also use a "reverse engineering" approach in which we extract the compact
structures in the Cygnus-X cloud and re-inject them on an fBm map. The
calculated $\Delta$-variance using this approach deviates from the observations
and is an indication that the range of characteristic scales observed in
Cygnus-X is not only due to the existence of compact sources, but is a
signature of the whole population of structures, including more extended and
elongated structures
