Constraining resolved extragalactic $R_{21}$ variation with well calibrated ALMA observations

CO(1-0) and CO(2-1) are commonly used as bulk molecular gas tracers. The CO line ratios (especially CO(2-1)/CO(1-0) - $R_{21}$) vary within and among galaxies, yet previous studies on $R_{21}$ and alike often rely on measurements constructed by combining data from facilities with substantial relative calibration uncertainties that have the same order as physical line ratio variations. Hence robustly determining systematic $R_{21}$ variations is challenging. Here, we compare CO(1-0) and CO(2-1) mapping data from ALMA for 14 nearby galaxies, at a common physical resolution of 1.7 kpc. Our dataset includes new ALMA (7m+TP) CO(1-0) maps of 12 galaxies. We investigate $R_{21}$ variation to understand its dependence on global galaxy properties, kpc-scale environmental factors, and its correlation with star formation rate (SFR) surface density and metallicity. We find that the galaxy-to-galaxy scatter is 0.05 dex. This is lower than previous studies which reported over 0.1 dex variation, likely reflecting significant flux calibration uncertainties in single-dish surveys. Within individual galaxies, $R_{21}$ has a typical mean value of ~0.64 and 0.1 dex variation, with an increase to ~0.75 towards galactic centers. We find strong correlations between $R_{21}$ and various galactic parameters, particularly SFR surface density, which shows a power-law slope of 0.10-0.11 depending on the adopted binning/fitting methods. Our findings suggest that, for studies covering main sequence galaxy samples, assuming a fixed $R_{21}$=0.64 does not significantly bias kpc-scale molecular gas mass estimates from CO(2-1). Instead, systematic uncertainties from flux calibration and the CO-to-H$_2$ conversion factor account for more systematic scatter of CO-derived molecular gas properties.