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

We report a sensitive search for the HCN( J = 2 → 1) emission line toward 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 (H 2 ) ≥ 10 4 cm -3 ] 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 < 3.3 × 10 9 K km s -1 pc 2 , corresponding to a HCN/CO luminosity ratio of L / L < 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 / L = 0.17 ) and HCN-detected z > 2 galaxies (0.17 ). The relationship between L and L FIR is considered to be a measure of 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 L FIR / L > 6600. This is significantly higher than the average ratios for normal nearby spiral galaxies ( L FIR / L = 580 ) and ULIRGs (740 ), but consistent with a rising trend as indicated by other z > 2 galaxies (predominantly quasars; 1525 ). It is unlikely that this rising trend can be accounted for by a contribution of active galactic nucleus (AGN) heating to L FIR 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 L FIR / L 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 Kilometer Array (SKA) will offer the sensitivity required to further investigate this question.