We present Herschel/PACS observations of extended [CII]157.7{mu}m line emission detected on ~ 1 - 10 kpc scales in 60 local luminous infrared galaxies (LIRGs) from the Great Observatories All-sky LIRG Survey (GOALS). We find that most of the extra-nuclear emission show [CII]/FIR ratios >~ 4 x 10^-3, larger than the mean ratio seen in the nuclei, and similar to those found in the extended disks of normal star-forming galaxies and the diffuse inter-stellar medium (ISM) of our Galaxy. The [CII] deficits found in the most luminous local LIRGs are therefore restricted to their nuclei. There is a trend for LIRGs with warmer nuclei to show larger differences between their nuclear and extra-nuclear [CII]/FIR ratios. We find an anti-correlation between [CII]/FIR and the luminosity surface density, {Sigma}_IR, for the extended emission in the spatially-resolved galaxies. However, there is an offset between this trend and that found for the LIRG nuclei. We use this offset to derive a beam filling-factor for the star-forming regions within the LIRG disks of ~ 6 % relative to their nuclei. We confront the observed trend to photo-dissociation region (PDR) models and find that the slope of the correlation is much shallower than the model predictions. Finally, we compare the correlation found between [CII]/FIR and {Sigma}_IR with measurements of high-redshift starbursting IR-luminous galaxies.
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