NGC1068 I-HCN(1-0) and I-HCO+(1-0) maps

We analysed how different formulations of SF relations change depending on the adopted aperture sizes and on the choice of molecular gas tracer. The scatter in the Kennicutt-Schmidt relation, linking the SFR density (SFR) with the (dense) molecular gas surface density ({SIGMA}_dense_), is about a factor of two to three lower for the HCN and HCO^+^ lines compared to that derived from CO(1-0) for a common aperture. Correlations lose statistical significance below a critical spatial scale 300-400pc for all gas tracers.

The efficiency of SF of the dense molecular gas, defined as SFE_dense_={SIGMA}SFR_/{SIGMA}_dense_, shows a scattered distribution as a function of the HCN luminosity (L0(HCN)) around a mean value of ~=0.01Myr^-1^. An alternative prescription for SF relations, which includes the dependence of SFE_dense_ on the combination of {SIGMA}_dense_ and the velocity dispersion ({sigma}), resolves the degeneracy associated with the SFE_dense_-L'(HCN) plot.

The SFE_dense_ values show a positive trend with the boundedness of the gas, measured by the parameter b={SIGMA}_dense_/{sigma}^2^.We identify two branches in the SFE_dense_-b plot that correspond to two dynamical environments within the SB ring, which are defined by their proximity to the region where the spiral structure is connected to the stellar bar. This region corresponds to the crossing of two overlapping density wave resonances, where an increased rate of cloud-cloud collisions would favour an enhanced compression of molecular gas.

These results suggest that galactic dynamics plays a major role in the efficiency of the gas conversion into stars. Our work adds supporting evidence that density-threshold star formation models, which argue that the SFE_dense_ should be roughly constant, fail to account for spatially resolved SF relations of dense gas in the SB ring of NGC 1068.