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(H2)>=104 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'HCN<3.3×109 K km s-1 pc2, 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 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 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+1300-475). 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 Kilometer Array (SKA) will offer the sensitivity required to further investigate this question