2023A&A...671A..59I

New measurements of 46 nearby galaxy centers in up to three transitions of HCN, HNC, and HCO⁺ combined with literature surveys establish a database of 130 galaxies measured in both HCN and HCO⁺, and 94 galaxies in HNC as well, allowing a systematic exploration of the relations between normalized luminosities and line ratios. The almost linear relations between luminosities are predominantly caused by distance effects and do not reflect galaxy physical properties. Individual galaxies show significant dispersion in both their luminosity and line ratio, which will be analyzed in more detail in a later paper. Very few line ratios correlate either with luminosities or with other line ratios. Only the normalized transition ladders of HCN and HCO⁺ and the J = 1 - 0 ¹²CO/¹³CO isotopologue ratio are positively correlated with CO and far infrared (FIR) luminosity. On average, HCN and HCO⁺ have very similar intensities and trace the same gas. In galaxies dominated by an active nucleus, HCO⁺ intensities appear to be depressed relative to HCN intensities. Only a small fraction of CO emission is associated with gas emitting in HCN and HCO⁺, yet a significant fraction of even that gas appears to be translucent molecular gas. In the observed galaxy centers, the HCN/CO line intensity ratio is not a proxy for the dense gas fraction, and the FIR/HCN and FIR/CO ratios are not proxies for the star formation efficiency. A proper understandig of star formation requires a more appropriate determination of gas mass than provided by the intensities of individual HCN or CO transitions. The observed molecular line emission is fully consistent with UV-photon heating boosted by significant mechanical heating. The molecular gas sampled by HCN and HCO⁺ has low kinetic temperatures T_kin = 10 - 50 K, low densities n_H = 10⁴ - 10⁵ cm^–3, and low optical depths in the ground-state lines. Most of the gas sampled by CO has densities lower by one to two orders of magnitude. For a mechanical heating fraction of 0.5, a modest energy input of only G = 300 G₀ is required.