Measuring the filamentary structure of interstellar clouds through
  wavelets
  The ubiquitous presence of filamentary structures in the interstellar medium
asks for an unbiased characterization of their properties including a stability
analysis. We propose a novel technique to measure the spectrum of filaments in
any two-dimensional data set. Using anisotropic wavelets we can quantify and
distinguish local and global anisotropies and measure the size distribution of
filaments. The wavelet analysis does not need any assumptions on the alignment
or shape of filaments in the maps, but directly measures their typical spatial
dimensions. In a rigorous test program, we calibrate the scale-dependence of
the method and test the angular and spatial sensitivity. We apply the method to
molecular line maps from magneto-hydrodynamic (MHD) simulations and observed
column density maps from Herschel observations.
  When applying the anisotropic wavelet analysis to the MHD data, we find that
the observed filament sizes depend on the combination of magnetic-field
dominated density-velocity correlations with radiative transfer effects. This
can be exploited by observing tracers with different optical depth to measure
the transition from a globally ordered large-scale structure to small-scale
filaments with entangled field lines. The unbiased view to Herschel column
density maps does not confirm a universal characteristic filament width. The
map of the Polaris Flare shows an almost scale-free filamentary spectrum up to
the size of the dominating filament of about 0.4pc. For the Aquila molecular
cloud the range of filament widths is limited to 0.05-0.2pc. The filaments in
Polaris show no preferential direction in contrast to the global alignment that
we trace in Aquila. By comparing the power in isotropic and anisotropic
structures we can measure the relative importance of spherical and cylindrical
collapse modes and their spatial distribution.
