CO Isotopologue-Derived Molecular Gas Conditions and CO-to-H_2 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, the SMA M51 large program, and the Surveying the Whirlpool at Arcseconds with NOEMA. The data set includes the (1-0) and (2-1) rotational transitions of (CO)-C-12, (CO)-C-13, and (CO)-O-18 isotopologues. The observations cover the r < 3 kpc region, including the center and part of the disk, thereby ensuring strong detections of the weaker (CO)-C-13 and (CO)-O-18 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-H-2 conversion factor (alpha(CO)). We employ two approaches to study the molecular gas conditions: (i) assuming local thermodynamic equilibrium (LTE) to analytically determine the CO column density and alpha(CO), and (ii) using non-LTE modeling with RADEX to fit physical conditions to observed CO isotopologue intensities. We find that the alpha(CO) values in the center and along the inner spiral arm are similar to 0.5 dex (LTE) and 0.1 dex (non-LTE) below the Milky Way inner disk value. The average non-LTE alpha(CO) is 2.4 +/- 0.5 M-circle dot 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 interstellar medium's physical and chemical conditions in nearby galaxies.