We present the detection of four rotational emission lines of water vapor , from energy levels E _ { u } / k = 101 - 454 \hbox { K } , in the gravitationally lensed z = 3.9 QSO host galaxy APM 08279+5255 .
While the lowest \hbox { H } _ { 2 } \hbox { O } lines are collisionally excited in clumps of warm , dense gas ( density of hydrogen nuclei n _ { \hbox { \scriptsize H } } = ( 3.1 \pm 1.2 ) \times 10 ^ { 6 } \hbox { cm } ^ { -3 } , gas temperature T _ { g } \sim 105 \pm 21 \hbox { K } ) , we find that the excitation of the higher lines is dominated by the intense local infrared radiation field .
Since only collisionally excited emission contributes to gas cooling , we conclude that \hbox { H } _ { 2 } \hbox { O } is not a significant coolant of the warm molecular gas .
Our excitation model requires the radiatively excited gas to be located in an extended region of high 100 \mu \hbox { m } opacity ( \tau _ { 100 } = 0.9 \pm 0.2 ) .
Locally , such extended infrared-opaque regions are found only in the nuclei of ultraluminous infrared galaxies .
We propose a model where the infrared-opaque circumnuclear cloud , which is penetrated by the X-ray radiation field of the QSO nucleus , contains clumps of massive star formation where the \hbox { H } _ { 2 } \hbox { O } emission originates .
The radiation pressure from the intense local infrared radiation field exceeds the thermal gas pressure by about an order of magnitude , suggesting close to Eddington-limited star formation in these clumps .