We present the first results of a survey of the [CII]158um emission line in 241 luminous infrared galaxies (LIRGs) comprising the Great Observatories All-sky Survey (GOALS) sample, obtained with the PACS instrument on board Herschel. The [CII] luminosities of the LIRGs in GOALS range from ~10^7 to 2x10^9 Lsun. We find that LIRGs show a tight correlation of [CII]/FIR with far-IR flux density ratios, with a strong negative trend spanning from ~10^-2 to 10^-4, as the average temperature of dust increases. We find correlations between the [CII]/FIR ratio and the strength of the 9.7um silicate absorption feature as well as with the luminosity surface density of the mid-IR emitting region (Sigma_MIR), suggesting that warmer, more compact starbursts have substantially smaller [CII]/FIR ratios. Pure star-forming (SF) LIRGs have a mean [CII]/FIR ~ 4x10^-3, while galaxies with low 6.2um PAH equivalent widths (EWs), indicative of the presence of active galactic nuclei (AGN), span the full range in [CII]/FIR. However, we show that even when only pure SF galaxies are considered, the [CII]/FIR ratio drops by an order of magnitude, from 10^-2 to 10^-3, with Sigma_MIR and Sigma_IR, implying that the [CII] luminosity is not a good indicator of the star formation rate (SFR) for most LIRGs, for it does not scale linearly with the warm dust emission. Moreover, even in LIRGs in which we detect an AGN in the mid-IR, the majority (2/3) of galaxies show [CII]/FIR >= 10^-3 typical of high 6.2um PAH EW sources, suggesting that most AGNs do not contribute significantly to the far-IR emission. We provide an empirical relation between the [CII]/FIR and the specific SFR (SSFR) for SF LIRGs. Finally, we present predictions for the starburst size based on the observed [CII] and far-IR luminosities which should be useful for comparing with results from future surveys of high-redshift galaxies with ALMA and CCAT.
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