CO isotopologue-derived molecular gas conditions and CO-to-H₂ conversion factors in M51

Over the past decade, several millimeter interferometer programs have mapped the nearby star-forming galaxy M51 at a spatial resolution of ≤170 pc. This study combines observations from three major programs: the PdBI Arcsecond Whirlpool Survey (PAWS), the SMA M51 large program (SMA-PAWS), and the Surveying the Whirlpool at Arcseconds with NOEMA (SWAN). The dataset includes the (1-0) and (2-1) rotational transitions of ¹²CO, ¹³CO, and C¹⁸O isotopologues. The observations cover the r<3kpc region including center and part of the disk, thereby ensuring strong detections of the weaker ¹³CO and C¹⁸O lines. All observations are convolved in this analysis to an angular resolution of 4′′, corresponding to a physical scale of ∼170 pc. We investigate empirical line ratio relations and quantitatively evaluate molecular gas conditions such as temperature, density, and the CO-to-H2 conversion factor (αCO). We employ two approaches to study the molecular gas conditions: (i) assuming local thermal equilibrium (LTE) to analytically determine the CO column density and αCO, and (ii) using non-LTE modeling with RADEX to fit physical conditions to observed CO isotopologue intensities. We find that the αCO values {in the center and along the inner spiral arm} are ∼0.5 dex (LTE) and ∼0.1 dex (non-LTE) below the Milky Way inner disk value. The average non-LTE αCO is 2.4±0.5 M⊙ pc−2 (K km s⁻¹)⁻¹. While both methods show dispersion due to underlying assumptions, the scatter is larger for LTE-derived values. This study underscores the necessity for robust CO line modeling to accurately constrain the molecular ISM's physical and chemical conditions in nearby galaxies.