Spatially resolved star-formation relations of dense molecular gas in NGC 1068

We analyse the influence of the dynamical environment on the star formation (SF) relations of the dense molecular gas in the starburst (SB) ring of the Seyfert 2 galaxy NGC 1068. We used ALMA to image the emission of the 1-0 transitions of HCN and HCO+ with a resolution of 56 pc. We also used ancillary data of CO(1-0) at a resolution of ~100 pc, and CO(3-2) and its underlying continuum emission at ~40 pc. These observations allow us to probe a range of molecular gas densities (n(H2)~10$^{3-5}cm^{-3}$). The SF rate (SFR) is derived from Pa$\alpha$ line emission imaged by HST/NICMOS. We analysed how SF relations change depending on the choice of aperture sizes and molecular gas tracer. The scatter in the Kennicutt-Schmidt relation is about a factor of two to three lower for the HCN and HCO+ lines compared to CO(1-0) for a common aperture. Correlations lose statistical significance below a critical spatial scale $\approx$300-400 pc. The SF efficiency of the dense molecular gas (SFEdense) shows a scattered distribution as a function of the HCN luminosity (L'(HCN)) around a mean value of $\simeq0.01$Myr$^{-1}$. An alternative prescription for SF relations, linking the SFEdense and the boundedness of the gas measured by the parameter b$\equiv\Sigma$dense/$\sigma^2$, where $\Sigma$dense is the dense molecular gas surface density and $\sigma$ the velocity dispersion, resolves the degeneracy associated with the SFEdense-L'(HCN) plot. We identify two branches in the SFEdense-b plot that correspond to two dynamical environments in the SB ring, which are defined by their proximity to the bar-ring interface region. This region corresponds to the crossing of two density wave resonances, where an increased rate of cloud-cloud collisions would favour an enhanced compression of molecular gas. Our results suggest that galactic dynamics plays a major role in the efficiency of the gas conversion into stars.