Understanding star formation in molecular clouds III. Probability
  distribution functions of molecular lines in Cygnus X
  Column density (N) PDFs serve as a powerful tool to characterize the physical
processes that influence the structure of molecular clouds. Star-forming clouds
can best be characterized by lognormal PDFs for the lower N range and a
power-law tail for higher N, commonly attributed to turbulence and self-gravity
and/or pressure, respectively. We report here on PDFs obtained from
observations of 12CO, 13CO, C18O, CS, and N2H+ in the Cygnus X North region and
compare to a PDF derived from dust observations with the Herschel satellite.
The PDF of 12CO is lognormal for Av~1-30, but is cut for higher Av due to
optical depth effects. The PDFs of C18O and 13CO are mostly lognormal up for
Av~1-15, followed by excess up to Av~40. Above that value, all CO PDFs drop,
most likely due to depletion. The high density tracers CS and N2H+ exhibit only
a power law distribution between Av~15 and 400, respectively. The PDF from dust
is lognormal for Av~3-15 and has a power-law tail up to Av~500. Absolute values
for the molecular line column densities are, however, rather uncertain due to
abundance and excitation temperature variations. Taken the dust PDF face value,
we 'calibrate' the molecular line PDF of CS to the one of the dust and
determined an abundance [CS]/[H2] of 10^-9. The slopes of the power-law tails
of the CS, N2H+, and dust PDFs are consistent with free-fall collapse of
filaments and clumps. A quasi static configuration of filaments and clumps can
possibly also account for the observed N-PDFs, as long as they have a
sufficiently condensed density structure and external ram pressure by gas
accretion is provided. The somehow flatter slopes of N2H+ and CS can reflect an
abundance change and/or subthermal excitation at low column densities.
