The [NII] 205 micron Emission in Local Luminous Infrared Galaxies
  In this paper, we present the measurements of the [NII] 205micron line
([NII]205) for a flux-limited sample of 122 (ultra-)luminous infrared galaxies
[(U)LIRGs] and 20 additional normal galaxies, obtained with the Herschel Space
Observatory. We explore the far-infrared (FIR) color dependence of the [NII]205
(L[NII]205) to the total infrared (LIR) luminosity ratio, and find that
L[NII]205/LIR only depends modestly on the 70-to-160 micron flux density ratio
(f70/f160) when f70/f160 <~ 0.6, whereas such dependence becomes much steeper
for f70/f160> 0.6. We also investigate the relation between L[NII]205 and star
formation rate (SFR), and show that L[NII]205 has a nearly linear correlation
with SFR, albeit the intercept of such relation varies somewhat with f60/f100,
consistent with our previous conclusion that \NIIab\ emission can serve as a
SFR indicator with an accuracy of ~0.4 dex, or ~0.2 dex if f60/f100 is known
independently. Furthermore, together with the ISO measurements of [NII] 122
micron emission we use a total of ~200 galaxies to derive the local [NII]205
luminosity function (LF) by tying it to the known IR LF with a bivariate
method. As a practical application, we also compute the local SFR volume
density ($\dot{\rho}_{\rm SFR}$) using the newly derived SFR calibrator and LF.
The resulting $\log\,\dot{\rho}_{\rm SFR} = -1.96\pm0.11$
$M_\odot$\,yr$^{-1}$\,Mpc$^{-3}$ agrees well with previous studies. Finally, we
determine the electron densities ($n_e$) of the ionized medium for a subsample
of 12 (U)LIRGs with both [NII]205 and [NII]122 data, and find that $n_e$ is in
the range of ~1-100 cm$^{-3}$, with a median value of 22 cm$^{-3}$
