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Both the CO(2-1) and CO(1-0) lines are used to trace the mass of moleculargas in galaxies. Translating the molecular gas mass estimates between studiesusing different lines requires a good understanding of the behaviour of theCO(2-1)-to-CO(1-0) ratio, $R_{21}$. We compare new, high quality CO(1-0) datafrom the IRAM 30-m EMPIRE survey to the latest available CO(2-1) maps fromHERACLES, PHANGS-ALMA, and a new IRAM 30-m M51 Large Program. This allows us tomeasure $R_{21}$ across the full star-forming disc of nine nearby, massive,star-forming spiral galaxies at 27" (${\sim} 1{-}2$ kpc) resolution. We find anaverage $R_{21} = 0.64\pm0.09$ when we take the luminosity-weighted mean of allindividual galaxies. This result is consistent with the mean ratio for discgalaxies that we derive from single-pointing measurements in the literature,$R_{\rm 21, lit}~=~0.59^{+0.18}_{-0.09}$. The ratio shows weak radialvariations compared to the point-to-point scatter in the data. In six out ofnine targets the central enhancement in $R_{21}$ with respect to thegalaxy-wide mean is of order $\sim 10{-}20\%$. We estimate an azimuthal scatterof $\sim$20% in $R_{21}$ at fixed galactocentric radius but this measurement islimited by our comparatively coarse resolution of 1.5 kpc. We find mildcorrelations between $R_{21}$ and CO brightness temperature, IR intensity,70-to-160$ \mu$m ratio, and IR-to-CO ratio. All correlations indicate that$R_{21}$ increases with gas surface density, star formation rate surfacedensity, and the interstellar radiation field.

New Constraints on the $^{12}$CO(2-1)/(1-0) Line Ratio Across Nearby Disc Galaxies