We report the detection of HCO ^ { + } ( J =4 \to 3 ) emission in the Cloverleaf Quasar at z =2.56 , using the IRAM Plateau de Bure Interferometer .
HCO ^ { + } emission is a star formation indicator similar to HCN , tracing dense molecular hydrogen gas ( n ( { H _ { 2 } } ) \simeq 10 ^ { 5 } cm ^ { -3 } ) within star-forming molecular clouds .
We derive a lensing-corrected HCO ^ { + } ( J =4 \to 3 ) line luminosity of L ^ { \prime } _ { HCO ^ { + } ( 4 - 3 ) } = ( 1.6 \pm 0.3 ) \times 10 ^ { 9 } ( \mu _ { L } / 11 ) ^ { -1 } K km s ^ { -1 } pc ^ { 2 } , which corresponds to only 48 % of the HCO ^ { + } ( J =1 \to 0 ) luminosity , and \lesssim 4 % of the CO ( J =3 \to 2 ) luminosity .
The HCO ^ { + } excitation thus is clearly subthermal in the J =4 \to 3 transition .
Modeling of the HCO ^ { + } line radiative transfer suggests that the HCO ^ { + } emission emerges from a region with physical properties comparable to that exhibiting the CO line emission , but 2 \times higher gas density .
This suggests that both HCO ^ { + } and CO lines trace the warm , dense molecular gas where star formation actively takes place .
The HCO ^ { + } lines have only \sim 2/3 the width of the CO lines , which may suggest that the densest gas is more spatially concentrated .
In contrast to the z =3.91 quasar APM 08279+5255 , the dense gas excitation in the Cloverleaf is consistent with being purely collisional , rather than being enhanced by radiative processes .
Thus , the physical properties of the dense gas component in the Cloverleaf are consistent with those in the nuclei of nearby starburst galaxies .
This suggests that the conditions in the dense , star-forming gas in active galactic nucleus-starburst systems at early cosmic times like the Cloverleaf are primarily affected by the starburst itself , rather than the central active black hole .