A Search for Dense Molecular Gas in High Redshift Infrared-Luminous Galaxies

We present a search for HCN emission from four high redshift far infrared (IR) luminous galaxies. Current data and models suggest that these high $z$ IR luminous galaxies represent a major starburst phase in the formation of spheroidal galaxies, although many of the sources also host luminous active galactic nuclei (AGN), such that a contribution to the dust heating by the AGN cannot be precluded. HCN emission is a star formation indicator, tracing dense molecular hydrogen gas within star-forming molecular clouds (n(H${}_2$) $\sim 10^5$cm$^{-3}$). HCN luminosity is linearly correlated with IR luminosity for low redshift galaxies, unlike CO emission which can also trace gas at much lower density. We report a marginal detection of HCN (1-0) emission from the $z=2.5832$ QSO J1409+5628, with a velocity integrated line luminosity of $L_{\mathrm{H}\mathrm{C}\mathrm{N}}^{\mathrm{\prime }}=6.7\pm 2.2\times {10}^9$ K km s${}^{-1}$ pc${}^2$, while we obtain 3$\sigma$ upper limits to the HCN luminosity of the $z=3.200$ QSO J0751+2716 of $L_{\mathrm{H}\mathrm{C}\mathrm{N}}^{\mathrm{\prime }}=1.0\times {10}^9$ K km s${}^{-1}$ pc${}^2$, $L_{\rm HCN}'=1.6\times10^{9}$Kkms$^{-1}$pc$^2$forthe$z= 2.565$ starburst galaxy J1401+0252, and $L_{\mathrm{H}\mathrm{C}\mathrm{N}}^{\mathrm{\prime }}=1.0\times {10}^{10}$ K km s${}^{-1}$ pc${}^2$ for the $z = 6.42$ QSO J1148+5251. We compare the HCN data on these sources, plus three other high-$z$ IR luminous galaxies, to observations of lower redshift star-forming galaxies. The values of the HCN/far-IR luminosity ratios (or limits) for all the high $z$ sources are within the scatter of the relationship between HCN and far-IR emission for low $z$ star-forming galaxies (truncated).