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We present 1 and 3 mm observations of the 13C- and 15N-bearing isotopologues of dense gas tracers towards eight nearby infrared-bright galaxies. With the Institut de Radioastronomie Millimétrique 30-m telescope, we observed the J  = 1–0 transitions of H13CN, HC15N, H13CO+, HN13C, and H15NC towards M 82, NGC 3079, IC 694, Mrk 231, and NGC 6240. The J  = 3–2 transition of H13CN was obtained in M 82, NGC 3079, NGC 3504, NGC 4418, NGC 6240, and NGC 6946, using the 10-m Submillimeter Telescope (SMT). We report the first detections of HN13C J  = 1–0 and H13CN J  = 3–2 in M 82, and H13CN J  = 3–2 in NGC 6240 and NGC 3079. We find different line profiles between the J  = 1–0 and 3–2 transitions of H13CN in both M 82 and NGC 3079. The optical depths of HCN show significant variations among the sample, indicating that dense gas masses estimated from the line luminosities of HCN J  = 1–0 and 3–2 should be treated with caution for individual galaxies. Optical depth of HCN J  = 3–2 is found to be higher than that of HCN J  = 1–0 in M 82, NGC 3079, NGC 4418, and NGC 6240, which indicates that ground state transitions of dense gas tracers might better trace the star-forming gas than the high-J transitions. Based on the H13CN/HC15N line ratios, with the double-isotopic method, low 14N/15N abundance ratios of 120 and 140 are found in NGC 3079 and Mrk 231, respectively.

Isotopologues of dense gas tracers in nearby infrared bright galaxies