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We present an analysis of [OI]63, [OIII]88, [NII]122 and [CII]158far-infrared (FIR) fine-structure line observations obtained withHerschel/PACS, for ~240 local luminous infrared galaxies (LIRGs) in the GreatObservatories All-sky LIRG Survey (GOALS). We find pronounced declines-deficits- of line-to-FIR-continuum emission for [NII]122, [OI]63 and [CII]158as a function of FIR color and infrared luminosity surface density,$\Sigma_{\rm IR}$. The median electron density of the ionized gas in LIRGs,based on the [NII]122/[NII]205 ratio, is $n_{\rm e}$ = 41 cm$^{-3}$. We findthat the dispersion in the [CII]158 deficit of LIRGs is attributed to a varyingfractional contribution of photo-dissociation-regions (PDRs) to the observed[CII]158 emission, f([CII]PDR) = [CII]PDR/[CII], which increases from ~60% to~95% in the warmest LIRGs. The [OI]63/[CII]158PDR ratio is tightly correlatedwith the PDR gas kinetic temperature in sources where [OI]63 is notoptically-thick or self-absorbed. For each galaxy, we derive the average PDRhydrogen density, $n_{\rm H}$, and intensity of the interstellar radiationfield, in units of G$_0$, and find G$_0$/$n_{\rm H}$ ratios ~0.1-50 cm$^3$,with ULIRGs populating the upper end of the distribution. There is a relationbetween G$_0$/$n_{\rm H}$ and $\Sigma_{\rm IR}$, showing a critical break at$\Sigma_{\rm IR}^{\star}$ ~ 5 x 10$^{10}$ Lsun/kpc$^2$. Below $\Sigma_{\rmIR}^{\star}$, G$_0$/$n_{\rm H}$ remains constant, ~0.32 cm$^3$, and variationsin $\Sigma_{\rm IR}$ are driven by the number density of star-forming regionswithin a galaxy, with no change in their PDR properties. Above $\Sigma_{\rmIR}^{\star}$, G$_0$/$n_{\rm H}$ increases rapidly with $\Sigma_{\rm IR}$,signaling a departure from the typical PDR conditions found in normalstar-forming galaxies towards more intense/harder radiation fields and compactgeometries typical of starbursting sources.

A Herschel/PACS Far Infrared Line Emission Survey of Local Luminous Infrared Galaxies