A search for dense molecular gas in high-redshift infrared-luminous galaxies

We present a search for HCN emission from four high-redshift far-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 (AGNs), 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(H2) similar to 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 = 25832 QSO J1409+5628, with a velocity-integrated line luminosity of L-HCN' (6.7 +/- 2.2) x 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-HCN' = 1.0 x 10(9) K km s(-1) pc(2), L-HCN' = 1.6 x 10(9) K km s(-1) pc(2) for the z = 2.565 starburst galaxy J1401+0252, and L-HCN' = 1.0 x 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. These observations are consistent with dust heating by a massive starburst in these systems, with two important caveats. First, about half the measurements are strictly upper limits to the HCN luminosities. Second, the IR spectral energy distributions for most of the high-z sources are well constrained only on the Rayleigh-Jeans side of the thermal dust peak. We also present a spatially resolved 42 GHz continuum image of the gravitational lens J0751+2716.