We report a sensitive search for the HCN ( J =2 \to 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 ( { H _ { 2 } } ) \geq 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 ^ { \prime } _ { HCN } < 3.3 \times 10 ^ { 9 } K km s ^ { -1 } pc ^ { 2 } , corresponding to a HCN/CO luminosity ratio of L ^ { \prime } _ { HCN } / L ^ { \prime } _ { 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 ^ { \prime } _ { HCN } / L ^ { \prime } _ { CO } =0.17 ^ { +0.05 } _ { -0.08 } ) and HCN-detected z > 2 galaxies ( 0.17 ^ { +0.09 } _ { -0.08 } ) .
The relationship between L ^ { \prime } _ { HCN } and L _ { FIR } 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 L _ { FIR } / L ^ { \prime } _ { HCN } > 6600 .
This is significantly higher than the average ratios for normal nearby spiral galaxies ( L _ { FIR } / L ^ { \prime } _ { 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 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 ^ { \prime } _ { 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 .