Dense gas is not enough: environmental variations in the star formation efficiency of dense molecular gas at 100 pc scales in M 51

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 M51 in 33GHz radio continuum, an extinction-free tracer of star formation, at 3" scales (~100pc). We combined this map with interferometric PdBI/NOEMA observations of CO(1-0) and HCN(1-0) at matched resolution for three regions in M51 (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 M51, e.g. the southern arm segment is more quiescent due to low star formation efficiency (SFE) of the dense gas, despite having a high dense gas fraction. Combining our results with measurements from the literature at 100pc 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.