A complete 12CO 2-1 map of M 51 with HERA II. Total gas surface densities and gravitational stability

Context. To date the onset of large-scale star formation in galaxies and its link to gravitational stability of the galactic disk have not been fully understood. The nearby face-on spiral galaxy M 51 is an ideal target for studying this subject. Aims. This paper combines CO, dust, HI, and stellar maps of M 51 and its companion galaxy to study the H-2/HI transition, the gas-to-dust ratios, and the stability of the disk against gravitational collapse. Methods. We combine maps of the molecular gas using (CO)-C-12 2-1 map HERA/IRAM-30 m data and HI VLA data to study the total gas surface density and the phase transition of atomic to molecular gas. The total gas surface density is compared to the dust surface density from 850 mu m SCUBA data. Taking into account the velocity dispersions of the molecular and atomic gas, and the stellar surface densities derived from the 2MASS K-band survey, we derive the total Toomre Q parameter of the disk. Results. The gas surface density Sigma(gas) in the spiral arms is similar to 2-3 higher compared to that of the interarm regions. The ratio of molecular to atomic surface density shows a nearly power-law dependence on the hydrostatic pressure P-hydro. The Sigma(gas) distribution in M 51 shows an underlying exponential distribution with a scale length of h(gas) = 7.6 kpc representing 55% of the total gas mass, comparable to the properties of the exponential dust disk. In contrast to the velocity widths observed in Hi, the CO velocity dispersion shows enhanced line widths in the spiral arms compared to the interarm regions. The contribution of the stellar component in the Toomre Q-parameter analysis is significant and lowers the combined Q-parameter Q(tot) by up to 70% towards the threshold for gravitational instability. The value of Q(tot) varies from 1.5-3 in radial averages. A map of Q(tot) shows values around 1 on the spiral arms indicating self-regulation at play.