We present new observations made with the IRAM 30m telescope of the J=1-0 and 3-2 lines of HCN and HCO^+ used to probe the dense molecular gas content in a sample of 17 local luminous and ultraluminous infrared galaxies (LIRGs and ULIRGs). These observations have allowed us to derive an updated version of the power law describing the correlation between the FIR luminosity (L_FIR) and the HCN(1-0) luminosity (L_HCN(1-0)) of local and high-redshift galaxies. We present the first clear observational evidence that the star formation efficiency of the dense gas (SFE_dense), measured as the L_FIR/L_HCN(1-0) ratio, is significantly higher in LIRGs and ULIRGs than in normal galaxies, a result that has also been found recently in high-redshift galaxies. This may imply a statistically significant turn upward in the Kennicutt-Schmidt law derived for the dense gas at L_FIR >= 10^11 L_sun. We have used a one-phase Large Velocity Gradient (LVG) radiative transfer code to fit the three independent line ratios derived from our observations. The results of this analysis indicate that the [HCN]/[HCO^+] abundance ratios could be up to one order of magnitude higher than normal in a significant number of LIRGs and ULIRGs of our sample. An overabundance of HCN at high L_FIR implies that the reported trend in the L_FIR/L_HCN ratio as a function of L_FIR would be underestimating a potentially more dramatic change of the SFE_dense. Results obtained with two-phase LVG models corroborate that the L_HCN(1-0)-to-M_dense conversion factor must be lowered at high L_FIR. We discuss the implications of these findings for the use of HCN as a tracer of the dense molecular gas in local and high-redshift luminous infrared galaxies.
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