Understanding star formation in molecular clouds III. Probability distribution functions of molecular lines in Cygnus X

The probability distribution function of column density (N-PDF) serves as a powerful tool to characterise the various physical processes that influence the structure of molecular clouds. Studies that use extinction maps or H-2 column-density maps (N) that are derived from dust show that star-forming clouds can best be characterised by lognormal PDFs for the lower N range and a power-law tail for higher N, which is commonly attributed to turbulence and self-gravity and/or pressure, respectively. While PDFs from dust cover a large dynamic range (typically N similar to 10(20-24) cm(-2) or A(v) similar to 0.1-1000), PDFs obtained from molecular lines -converted into H-2 column density - potentially trace more selectively different regimes of (column) densities and temperatures. They also enable us to distinguish different clouds along the line of sight through using the velocity information. We report here on PDFs that were obtained from observations of (CO)-C-12, (CO)-C-13, (CO)-O-18, CS, and N2H+ in the Cygnus X North region, and make a comparison to a PDF that was derived from dust observations with the Herschel satellite. The PDF of (CO)-C-12 is lognormal for A(v) similar to 1-30, but is cut for higher Av because of optical depth effects. The PDFs of (CO)-O-18 and (CO)-C-13 are mostly lognormal up to A(v) similar to 1-15, followed by excess up to A(v) similar to 40. Above that value, all CO PDFs drop, which is most likely due to depletion. The high density tracers CS and N2H+ exhibit only a power law distribution between A(v) similar to 15 and 400, respectively. The PDF from dust is lognormal for A(v) similar to 3-15 and has a power-law tail up to A(v) similar to 500. Absolute values for the molecular line column densities are, however, rather uncertain because of abundance and excitation temperature variations. If we take the dust PDF at face value, we "calibrate" the molecular line PDF of CS to that of the dust and determine an abundance [CS]/[H-2] of 10(-9). The slopes of the power-law tails of the CS, N2H+, and dust PDFs are -1.6, -1.4, and -2.3, respectively, and are thus consistent with free-fall collapse of filaments and clumps. A quasi static configuration of filaments and clumps can also possibly account for the observed N-PDFs, providing 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.