  We report the detection of surprisingly strong HCN, HNC, and HCO+(J=6-5)
emission in the host galaxy of the z=3.91 quasar APM08279+5255 through
observations with CARMA. HCN, HNC, and HCO+ are typically used as star
formation indicators, tracing dense molecular hydrogen gas [n(H2) > 10^5,cm^-3]
within star-forming molecular clouds. However, the strength of their respective
line emission in the J=6-5 transitions in APM08279+5255 is extremely high,
suggesting that they are excited by another mechanism besides collisions in the
dense molecular gas phase alone. We derive J=6-5 line luminosities of
L'(HCN)=(4.9+/-0.6), L'(HNC)=(2.4+/-0.7), and L'(HCO+)=(3.0+/-0.6)x10^10
(mu_L)^-1 K km/s pc^2 (where mu_L is the lensing magnification factor),
corresponding to L' ratios of ~0.23-0.46 relative to CO(J=1-0). Such high line
ratios would be unusual even in the respective ground-state (J=1-0)
transitions, and indicate exceptional, collisionally and radiatively driven
excitation conditions in the dense, star-forming molecular gas in
APM08279+5255. Through an expansion of our previous modeling of the HCN line
excitation in this source, we show that the high rotational line fluxes are
caused by substantial infrared pumping at moderate opacities in a ~220K warm
gas and dust component. This implies that standard M_dense/L' conversion
factors would substantially overpredict the dense molecular gas mass M_dense.
We also find a HCN J=6-5/5-4 L' ratio greater than 1 (1.36+/-0.31) - however,
our models show that the excitation is likely not `super-thermal', but that the
high line ratio is due to a rising optical depth between both transitions.
These findings are consistent with the picture that the bulk of the gas and
dust in this source is situated in a compact, nuclear starburst, where both the
highly active galactic nucleus and star formation contribute to the heating.
