Observations of Dense Molecular Gas in a Quasar Host Galaxy at Z=6.42: Further Evidence for a Non-linear Dense Gas – Star Formation Relation at Early Cosmic Times

We report a sensitive search for the HCN(J=2→1) emission line towards SDSS J114816.64+525150.3 (hereafter: J1148+5251) at z=6.42 with the Very Large Array (VLA). HCN emission is a star formation indicator, tracing dense molecular hydrogen gas (n(H2) ≥ 10 4 cm) within star-forming molecular clouds. No emission was detected in the deep interferometer maps of J1148+5251. We derive a limit for the HCN line luminosity of L′HCN < 3.3 × 10 K kmspc, corresponding to a HCN/CO luminosity ratio of L′HCN/L ′ CO<0.13. This limit is consistent with a fraction of dense molecular gas in J1148+5251 within the range of nearby ultraluminous infrared galaxies (ULIRGs; median value: L′HCN/L ′ CO=0.17 +0.05 −0.08) and HCN-detected z>2 galaxies (0.17 +0.09 −0.08). The relationship between L ′ HCN and LFIR is considered to be a measure for the efficiency at which stars form out of dense gas. In the nearby universe, these quantities show a linear correlation, and thus, a practically constant average ratio. In J1148+5251, we find LFIR/L ′ HCN>6600. This is significantly higher than the average ratios for normal nearby spiral galaxies (LFIR/L ′ HCN=580 +510 −270) and ULIRGs (740 +505 −50 ), but consistent with a rising trend as indicated by other z>2 galaxies (predominantly quasars; 1525 −475 ). It is unlikely that this rising trend can be accounted for by a contribution of active galactic nucleus (AGN) heating to LFIR alone, and may hint at a higher median gas density and/or elevated star-formation efficiency toward the more luminous high-redshift systems. There is marginal evidence that the LFIR/L ′ HCN ratio in J1148+5251 may even exceed the rising trend set by other z>2 galaxies; however, only future facilities with very large collecting areas such as the Square Kilometre Array (SKA) will offer the sensitivity required to further investigate this question. Subject headings: galaxies: active, starburst, formation, high redshift — cosmology: observations — radio lines: galaxies