Dense Molecular Gas Excitation at High Redshift: Detection of
  HCO+(J=4-3) Emission in the Cloverleaf Quasar
  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.
