%0 Journal Article %T Excitation Mechanisms for HCN (1-0) and HCO+ (1-0) in Galaxies from the Great Observatories All-sky LIRG Survey %A G. C. Privon %A R. Herrero-Illana %A A. S. Evans %A K. Iwasawa %A M. A. Perez-Torres %A L. Armus %A T. Diaz-Santos %A E. J. Murphy %A S. Stierwalt %A S. Aalto %A J. M. Mazzarella %A L. Barcos-Munoz %A H. J. Borish %A H. Inami %A D. -C. Kim %A E. Treister %A J. A. Surace %A S. Lord %A J. Conway %A D. T. Frayer %A A. Alberdi %J Physics %D 2015 %I arXiv %X We present new IRAM 30m spectroscopic observations of the $\sim88$ GHz band, including emission from the CCH (n=1-0) multiplet, HCN (1-0), HCO+ (1-0), and HNC (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 (AGN) 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 ($\langle$L'$_{HCN (1-0)}$/L'$_{HCO^+ (1-0)}\rangle=1.84$), compared to composite and starburst-dominated systems ($\langle$L'$_{HCN (1-0)}$/L'$_{HCO^+ (1-0)}\rangle=1.14$, and 0.88, respectively). However, some composite and starburst systems have L'$_{HCN (1-0)}$/L'$_{HCO^+ (1-0)}$ ratios comparable to those of AGN, indicating that enhanced HCN emission is not uniquely associated with energetically dominant AGN. After removing AGN-dominated systems from the sample, we find a linear relationship (within the uncertainties) between $\log_{10}$(L'$_{HCN (1-0)}$) and $\log_{10}$(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 L$_{IR}$ for our sample of luminous and ultraluminous infrared galaxies, and has significant scatter. The galaxy-integrated HCN (1-0) and HCO+ (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. %U http://arxiv.org/abs/1509.07512v1