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Water vapor in nearby infrared galaxies as probed by Herschel

We report the first systematic study of the submillimeter water vapor rotational emission lines in infrared (IR) galaxies based on the Fourier Transform Spectrometer (FTS) data of {\it Herschel} SPIRE. Among the 176 galaxies with publicly available FTS data, 45 have at least one H$_2$O emission line detected. The H$_2$O line luminosities range from $\sim 1 \times 10^5$ $L_{\odot}$ to $\sim 5 \times 10^7 L_{\odot}$ while the total IR luminosities ($L_\mathrm{IR}$) have a similar spread ($\sim 1-300 \times 10^{10} L_{\odot}$). In addition, emission lines of H$_2$O$^+$ and H$_2^{18}$O are also detected. H$_2$O is found, for most galaxies, to be the strongest molecular emitter after CO in FTS spectra. The luminosity of the five most important H$_2$O lines is near-linearly correlated with $L_\mathrm{IR}$, no matter whether strong active galactic nucleus signature is present or not. However, the luminosity of H$_2$O($2_{11}-2_{02}$) and H$_2$O($2_{20}-2_{11}$) appears to increase slightly faster than linear with $L_\mathrm{IR}$. Although the slope turns out to be slightly steeper when $z\sim 2-4$ ULIRGs are included, the correlation is still closely linear. We find that $L_\mathrm{H_2O}/L_\mathrm{IR}$ decreases with increasing $f_{25}/f_{60}$, but see no dependence on $f_{60}/f_{100}$, possibly indicating that very warm dust contributes little to the excitation of the submillimeter H$_2$O lines. The average spectral line energy distribution (SLED) of the entire sample is consistent with individual SLEDs and the IR pumping plus collisional excitation model, showing that the strongest lines are H$_2$O($2_{02}-1_{11}$) and H$_2$O($3_{21}-3_{12}$).