Recent observational studies have shown that H _ { 2 } O emission at ( rest ) submillimeter wavelengths is ubiquitous in infrared galaxies , both in the local and in the early Universe , suggestive of far-infrared pumping of H _ { 2 } O by dust in warm regions .
In this work , models are presented that show that ( i ) the highest-lying H _ { 2 } O lines ( E _ { \mathrm { upper } } > 400 K ) are formed in very warm ( T _ { \mathrm { dust } } \gtrsim 90 K ) regions and require high H _ { 2 } O columns ( N _ { \mathrm { H _ { 2 } O } } \gtrsim 3 \times 10 ^ { 17 } cm ^ { -2 } ) , while lower lying lines can be efficiently excited with T _ { \mathrm { dust } } \sim 45 - 75 K and N _ { \mathrm { H _ { 2 } O } } \sim ( 0.5 - 2 ) \times 10 ^ { 17 } cm ^ { -2 } ; ( ii ) significant collisional excitation of the lowest lying ( E _ { \mathrm { upper } } < 200 K ) levels , which enhances the overall L _ { \mathrm { H _ { 2 } O } } - L _ { \mathrm { IR } } ratios , is identified in sources where the ground-state para-H _ { 2 } O 1 _ { 11 } -0 _ { 00 } line is detected in emission ; ( iii ) the H _ { 2 } O-to-infrared ( 8 - 1000 \mu m ) luminosity ratio is expected to decrease with increasing T _ { \mathrm { dust } } for all lines with E _ { \mathrm { upper } } \lesssim 300 K , as has recently been reported in a sample of LIRGs , but increases with T _ { \mathrm { dust } } for the highest lying H _ { 2 } O lines ( E _ { \mathrm { upper } } > 400 K ) ; ( iv ) we find theoretical upper limits for L _ { \mathrm { H _ { 2 } O } } / L _ { \mathrm { IR } } in warm environments , owing to H _ { 2 } O line saturation ; ( v ) individual models are presented for two very different prototypical galaxies , the Seyfert 2 galaxy NGC 1068 and the nearest ultraluminous infrared galaxy Arp 220 , showing that the excited submillimeter H _ { 2 } O emission is dominated by far-infrared pumping in both cases ; ( vi ) the L _ { \mathrm { H _ { 2 } O } } - L _ { \mathrm { IR } } correlation previously reported in observational studies indicates depletion or exhaustion time scales , t _ { \mathrm { dep } } = \Sigma _ { \mathrm { gas } } / \Sigma _ { \mathrm { SFR } } , of \lesssim 12 Myr for star-forming sources where lines up to E _ { \mathrm { upper } } = 300 K are detected , in agreement with the values previously found for ( U ) LIRGs from HCN millimeter emission .
We conclude that the submillimeter H _ { 2 } O line emission other than the para-H _ { 2 } O 1 _ { 11 } -0 _ { 00 } transition is pumped primarily by far-infrared radiation , though some collisional pumping may contribute to the low-lying para-H _ { 2 } O 2 _ { 02 } -1 _ { 11 } line , and that collisional pumping of the para- 1 _ { 11 } and ortho- 2 _ { 12 } levels enhances the radiative pumping of the higher lying levels .