The molecular gas mass of M33
  [Abridged] Do some environments favor efficient conversion of molecular gas
into stars? To answer this, we need to be able to estimate the H2 mass.
Traditionally, this is done using CO and a few assumptions but the Herschel
observations in the FIR make it possible to estimate the molecular gas mass
independently of CO. 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 H2 column density ratio (XCO), sometimes allowing for an
additional CO-dark gas component (Kdark). We tested earlier methods, revealing
degeneracies among the parameters, and then used a Bayesian formalism to derive
the most likely values for each of the parameters mentioned above as a function
of position in the nearby low metallicity spiral galaxy M33. The data are from
the IRAM 30m CO(2-1) line, high-resolution HI and Herschel dust continuum
observations. Solving for GDR, XCO, and Kdark in macro pixels 500 pc in size,
we find that (i) allowing for CO-dark gas 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 H2 where CO is photodissociated. The total
amount of H2, including dark gas, yields an average XCO of twice the galactic
value of 2e20 cm^-2/(K km/s), 55% of this traced directly through CO. The
rather constant fraction of dark gas suggests that there is no large population
of diffuse H2 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.
