We report the detection of HCO+(J=4-3) 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(H2) ~= 10^5 cm^-3) within star-forming molecular clouds. We derive a lensing-corrected HCO+(J=4-3) line luminosity of L(HCO+(4-3)) = (1.6+/-0.3) x 10^9 (mu_L/11)^-1 K km/s pc^2, which corresponds to only 48% of the HCO+(J=1=0) luminosity, and <~4% of the CO(J=3-2) luminosity. The HCO+ excitation thus is clearly subthermal in the J=4-3 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 2x 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 ~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 APM08279+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.
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