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The Water Vapor Spectrum of APM 08279+5255: X-Ray Heating and Infrared Pumping over Hundreds of Parsecs

We present the rest-frame 200--320 \mm\ spectrum of the z=3.91 quasar \apm, obtained with Z-Spec at the Caltech Submillimeter Observatory. In addition to the \jeight\ to \jthirteen\ CO rotational transitions which dominate the CO cooling, we find six transitions of water originating at energy levels ranging up to 643 K. Most are first detections at high redshift, and we have confirmed one transition with CARMA. The CO cooling is well-described by our XDR model, assuming L$_{\rm 1-100\,keV}\sim1\times10^{46}\rm\,erg\,s^{-1}$, and that the gas is distributed over a 550-pc sizescale, per the now-favored $μ$=4 lensing model. The total observed cooling in water corresponds to 6.5$\times10^{9}$ \ls, comparable to that of CO. We compare the water spectrum with that of Mrk 231, finding that the intensity ratios among the high-lying lines are similar, but with a total luminosity scaled up by a factor of $\sim$50. Using this scaling, we estimate an average water abundance relative to \hh\ of 1.4$\times10^{-7}$, a good match to the prediction of the chemical network in the XDR model. As with Mrk 231, the high-lying water transitions are excited radiatively via absorption in the rest-frame far-infrared, and we show that the powerful dust continuum in \apm\ is more than sufficient to pump this massive reservoir of warm water vapor.