The molecular gas mass of M 33

Do some environments favor efficient conversion of molecular gas into stars? To answer this, we need to be able to estimate the H-2 mass. Traditionally, this is done using CO observations and a few assumptions but the Herschel observations which cover the far-IR dust spectrum make it possible to estimate the molecular gas mass independently of CO and thus to investigate whether and how the CO traces H-2. Previous attempts to derive gas masses from dust emission suffered from biases. Generally, dust surface densities, HI column densities, and CO intensities are used to derive a gas-to-dust ratio (GDR) and the local CO intensity to H-2 column density ratio (X-CO), sometimes allowing for an additional CO-dark gas component (K-dark). We tested earlier methods, revealing degeneracies among the parameters, and then used a sophisticated Bayesian formalism to derive the most likely values for each of the parameters mentioned above as a function of position in the nearby prototypical low metallicity (12 + log(O/H) similar to 8.4) spiral galaxy M 33. The data are from the IRAM Large Program mapping in the CO(2-1) line along with high-resolution HI and Herschel dust continuum observations. Solving for GDR, X-CO, and K-dark in macropixels 500 pc in size, each containing many individual measurements of the CO, HI, and dust emission, we find that (i) allowing for CO dark gas (K-dark) significantly improves fits; (ii) Kdark decreases with galactocentric distance; (iii) GDR is slightly higher than initially expected and increases with galactocentric distance; (iv) the total amount of dark gas closely follows the radially decreasing CO emission, as might be expected if the dark gas is H-2 where CO is photodissociated. The total amount of H-2, including dark gas, yields an average XCO of twice the galactic value of 2 x 10(20) cm(-2)/Kkm s(-1), with about 55% of this traced directly through CO. The rather constant fraction of dark gas suggests that there is no large population of diffuse H-2 clouds (unrelated to GMCs) without CO emission. Unlike in large spirals, we detect no systematic radial trend in XCO, possibly linked to the absence of a radial decrease in CO line ratios