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ABSTRACT Both the CO(2–1) and CO(1–0) lines are used to trace the mass of molecular gas in galaxies. Translating the molecular gas mass estimates between studies using different lines requires a good understanding of the behaviour of the CO(2–1)-to-CO(1–0) ratio, R21. We compare new, high-quality CO(1–0) data from the IRAM 30-m EMIR MultiLine Probe of the ISM Regulating Galaxy Evolution survey to the latest available CO(2–1) maps from HERA CO-Line Extragalactic Survey, Physics at High Angular resolution in Nearby Galaxies-ALMA, and a new IRAM 30-m M51 Large Program. This allows us to measure R21 across the full star-forming disc of nine nearby, massive, star-forming spiral galaxies at 27 arcsec (∼1–2 kpc) resolution. We find an average R21 = 0.64 ± 0.09 when we take the luminosity-weighted mean of all individual galaxies. This result is consistent with the mean ratio for disc galaxies that we derive from single-pointing measurements in the literature, $$R_{\rm 21, lit}~=~0.59^{+0.18}_{-0.09}$$. The ratio shows weak radial variations compared to the point-to-point scatter in the data. In six out of nine targets, the central enhancement in R21 with respect to the galaxy-wide mean is of order of $${\sim}10{-}20{{\ \rm per\ cent}}$$. We estimate an azimuthal scatter of ∼20 per cent in R21 at fixed galactocentric radius but this measurement is limited by our comparatively coarse resolution of 1.5 kpc. We find mild correlations between R21 and carbon monoxide (CO) brightness temperature, infrared (IR) intensity, 70–160 µm ratio, and IR-to-CO ratio. All correlations indicate that R21 increases with gas surface density, star formation rate surface density, and the interstellar radiation field. 

It remains unclear what sets the efficiency with which molecular gas transforms into stars. Here we present a new VLA map of the spiral galaxy M 51 in 33 GHz radio continuum, an extinction-free tracer of star formation, at 3″ scales (∼100 pc). We combined this map with interferometric PdBI/NOEMA observations of CO(1–0) and HCN(1–0) at matched resolution for three regions in M 51 (central molecular ring, northern and southern spiral arm segments). While our measurements roughly fall on the well-known correlation between total infrared and HCN luminosity, bridging the gap between Galactic and extragalactic observations, we find systematic offsets from that relation for different dynamical environments probed in M 51; for example, the southern arm segment is more quiescent due to low star formation efficiency (SFE) of the dense gas, despite its high dense gas fraction. Combining our results with measurements from the literature at 100 pc scales, we find that the SFE of the dense gas and the dense gas fraction anti-correlate and correlate, respectively, with the local stellar mass surface density. This is consistent with previous kpc-scale studies. In addition, we find a significant anti-correlation between the SFE and velocity dispersion of the dense gas. Finally, we confirm that a correlation also holds between star formation rate surface density and the dense gas fraction, but it is not stronger than the correlation with dense gas surface density. Our results are hard to reconcile with models relying on a universal gas density threshold for star formation and suggest that turbulence and galactic dynamics play a major role in setting how efficiently dense gas converts into stars.