We present a 190-307 GHz broadband spectrum obtained with Z-Spec of NGC 1068 with new measurements of molecular rotational transitions. After combining our measurements with those previously published and considering the specific geometry of this Seyfert 2 galaxy, we conduct a multi-species Bayesian likelihood analysis of the density, temperature, and relative molecular abundances of HCN, HNC, CS, and HCO+. We find that these molecules trace warm (T > 100 K) gas of H2 number densities 10^4.2 - 10^4.9 cm^-3. Our models also place strong constraints on the column densities and relative abundances of these molecules, as well as on the total mass in the circumnuclear disk. Using the uniform calibration afforded by the broad Z-Spec bandpass, we compare our line ratios to X-ray dominated region (XDR) and photon-dominated region models. The majority of our line ratios are consistent with the XDR models at the densities indicated by the likelihood analysis, lending substantial support to the emerging interpretation that the energetics in the circumnuclear disk of NGC 1068 are dominated by accretion onto an active galactic nucleus.
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