Gao–Solomon relation. SFR (top) and SFR/L_HCN (a proxy of SFE_dense; bottom) as a function of HCN luminosity across a literature compilation and the ALMOND (blue circles) and EMPIRE (red circles) surveys. Note that we re-calculated the SFR across EMPIRE galaxies using a combination of IR and FUV data (see Sect. 2). Our literature compilation contains HCN observations that include Galactic clumps and clouds (squares), resolved nearby galaxies (circles), and unresolved entire galaxies (diamonds). For more details on the compilation, see Appendix B. The plotted data points show all (3-sigma) detected sightlines. The solid black line shows the median SFR/HCN computed from these data points across all datasets (without duplicates across targets), and the dashed lines mark the 1-sigma scatter (Table 1). The bottom panel shows the ratio SFR/HCN as a function of L_HCN, grouping the data into the same subsamples, for which the 10-percentile density contours of the respective subsamples are shown. We plot ALMOND and EMPIRE data separately, and the blue and red contours present the 10-percentile levels of these surveys.