  We use new HCN(1-0) data from the ALMOND (ACA Large-sample Mapping Of Nearby
galaxies in Dense gas) survey to trace the kpc-scale molecular gas density
structure and CO(2-1) data from PHANGS-ALMA to trace the bulk molecular gas
across 25 nearby, star-forming galaxies. At 2.1 kpc scale, we measure the
density-sensitive HCN/CO line ratio and the SFR/HCN ratio to trace the star
formation efficiency in the denser molecular medium. At 150 pc scale, we
measure structural and dynamical properties of the molecular gas via CO(2-1)
line emission, which is linked to the lower resolution data using an
intensity-weighted averaging method. We find positive correlations (negative)
of HCN/CO (SFR/HCN) with the surface density, the velocity dispersion and the
internal turbulent pressure of the molecular gas. These observed correlations
agree with expected trends from turbulent models of star formation, which
consider a single free-fall time gravitational collapse. Our results show that
the kpc-scale HCN/CO line ratio is a powerful tool to trace the 150 pc scale
average density distribution of the molecular clouds. Lastly, we find
systematic variations of the SFR/HCN ratio with cloud-scale molecular gas
properties, which are incompatible with a universal star formation efficiency.
Overall, these findings show that mean molecular gas density, molecular cloud
properties and star formation are closely linked in a coherent way, and
observations of density-sensitive molecular gas tracers are a useful tool to
analyse these variations, linking molecular gas physics to stellar output
across galaxy discs.
