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($3_{21}-3_{12}$).
