We present new Institut de Radioastronomie Millimétrique (IRAM) 30 m spectroscopic observations of the ~88 GHz band, including emission from the CCH (N = 1 → 0) multiplet, HCN (J = 1 → 0), HCO^+ (J = 1 → 0), and HNC(J = 1 → 0), for a sample of 58 local luminous and ultraluminous infrared galaxies from the Great Observatories All-sky LIRG Survey (GOALS). By combining our new IRAM data with literature data and Spitzer/IRS spectroscopy, we study the correspondence between these putative tracers of dense gas and the relative contribution of active galactic nuclei (AGNs) and star formation to the mid-infrared luminosity of each system. We find the HCN (1–0) emission to be enhanced in AGN-dominated systems (〈L'_(HCN(1-0))/L'_(HCN(1-0)^+(1-0)〉 =1.84), compared to composite and starburst-dominated systems 〈L'_(HCN(1-0))/L'_(HCN(1-0)^+(1-0)〉 = 1.14, and 0.88, respectively). However, some composite and starburst systems have 〈L'_(HCN(1-0))/L'_(HCN(1-0)^+(1-0)〉 ratios comparable to those of AGNs, indicating that enhanced HCN emission is not uniquely associated with energetically dominant AGNs. After removing AGN-dominated systems from the sample, we find a linear relationship (within the uncertainties) between log10 〈L'_(HCN(1-0))/L'_(HCN(1-0)^+(1-0)〉 and log10(L_(IR)), consistent with most previous findings. L'_(HCN(1-0))/L_(IR), typically interpreted as the dense-gas depletion time, appears to have no systematic trend with LIR for our sample of luminous and ultraluminous infrared galaxies, and has significant scatter. The galaxy-integrated L'_(HCN(1-0)) and L'_(HCN^+(1-0)) emission do not appear to have a simple interpretation in terms of the AGN dominance or the star formation rate, and are likely determined by multiple processes, including density and radiative effects.
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