Dense gas star formation efficiency and the L_HCN (4-3) /L_HCO + (4-3) ratio: insights from a statistical study of infrared bright star-forming galaxies

We present a statistical study on dense molecular gas tracers of HCN (4-3), HCO+ (4-3) lines and molecular tracers of [C I], and CO observations for a sample of 26 infrared bright star-forming (SF) galaxies. We investigate the dependence of dense gas star formation efficiency traced by HCN (4-3), HCO+ (4-3) (that is L-IR/L-HCN(') (4-3), and LIR/L-HCO+(')(4-3)), and luminosity ratio of L-HCN(')(4-3)/L-HCO+(')(4-3) on [C I]-CO ratios of L-[C (')(I] (1-0))/LCO (1-0), L[C I](2-1)'/L-CO (1-0()') and L-[C I](2-1)(')/L-[C I] (1-0)(') (hereafter R-[CI]) which are sensitive to interstellar medium conditions. Our findings show that both LIR/L ' HCN (4-3) and LIR/L ' HCO+ (4-3) have moderate correlations with L '[C I](2-1)/L ' CO (1-0) and R[CI], while L ' HCN(4-3)/L ' HCO+ (4-3) does not show any significant correlations with any of the [C I]-CO ratios. We compare the L ' HCN (4-3)/L ' HCO+ (4-3) ratios of AGN and SF galaxies, and find that although the higher L ' HCN (4-3)/L ' HCO+ (4-3) ratios are mainly found in AGN, the majority of the L ' HCN (4-3)/L ' HCO+ (4-3) values in SF galaxies are comparable to those in AGN. Based on our findings, it appears that the L ' HCN (4-3)/L ' HCO+ (4-3) ratio may not be a reliable indicator of the presence of an AGN, although further investigation is needed to confirm this conclusion.