The Probability Distribution Function of Gas Surface Density in M33
  The probability distribution functions (PDFs) for atomic, molecular, and
total gas surface densities of M33 are determined at a resolution of about
50~pc over regions that share coherent morphological properties to unveil
fingerprints of self-gravity across the star-forming disk. Most of the total
gas PDFs from the central region to the edge of the star-forming disk are
well-fitted by log-normal functions whose width decreases radially outwards.
Because the HI velocity dispersion is approximately constant across the disk,
the decrease of the PDF width is consistent with a lower Mach number for the
turbulent ISM at large galactocentric radii where a higher fraction of HI is in
the warm phase. The atomic gas is found mostly at face-on column densities
below N$_{H}^{lim}$=2.5 10$^{21}$~cm$^{-2}$, with small radial variations of
N$_{H}^{lim}$. The molecular gas PDFs do not show strong deviations from
log-normal functions in the central region where molecular fractions are high.
Here the high pressure and rate of star formation shapes the PDF as a
log-normal function dispersing self-gravitating complexes with intense feedback
at all column densities that are spatially resolved. Power law PDFs for the
molecules are found near and above N$_H^{lim}$, in the well defined southern
spiral arm and in a continuous dense filament extending at larger
galactocentric radii; this is evident in cloud samples at different
evolutionary stages along the star formation cycle. In the filament nearly half
of the molecular gas departs from a log-normal PDF and power laws are also
observed in pre-star forming molecular complexes. The slope of the power law is
between -1 and -2. This slope, combined with maps showing where the different
parts of the power law PDFs come from, suggest a power-law stratification of
density within molecular cloud complexes, which is consistent with the
dominance of self-gravity.
