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

aastex format, 4 figures. to appear in the Astrophysical Journal; Revised lens magnification estimate for 1401+0252We 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 $L_{\\rm HCN}\'=6.7\\pm2.2 \\times10^{9}$ 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 $L_{\\rm HCN}\'=1.0\\times10^{9}$ K km s$^{-1}$ pc$^2$, $L_{\\rm HCN}\'=1.6\\times10^{9}$ K km s$^{-1}$ pc$^2$ for the $z= 2.565$ starburst galaxy J1401+0252, and $L_{\\rm HCN}\'=1.0\\times10^{10}$ 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)