With the incorporation of high-J molecular lines, we aim to constrain the physical conditions of the dense gas in the central region of the Seyfert 2 galaxy NGC 1068 and to determine signatures of the AGN or the starburst contribution. We used the James Clerk Maxwell Telescope to observe the J=4-3 transition of HCN, HNC, and HCO+, as well as the CN N_J=2_{5/2}-1_{3/2} and N_J=3_{5/2}-2_{5/2}, in NGC 1068. We estimate the excitation conditions of HCN, HNC, and CN, based on the line intensity ratios and radiative transfer models. We find that the bulk emission of HCN, HNC, CN, and the high-J HCO+ emerge from dense gas n(H_2)>=10^5 cm^-3). However, the low-J HCO+ lines (dominating the HCO+ column density) trace less dense (n(H_2)<10^5 cm^-3) and colder (T_K<=20 K) gas, whereas the high-J HCO+ emerges from warmer (>30 K) gas than the other molecules. The HCO+ J=4-3 line intensity, compared with the lower transition lines and with the HCN J=4-3 line, support the influence of a local XDR environment. The estimated N(CN)/N(HCN)~1-4 column density ratios are indicative of an XDR/AGN environment with a possible contribution of grain-surface chemistry induced by X-rays or shocks.
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