EXPLAINING THE [C II]157.7 μm DEFICIT IN LUMINOUS INFRARED GALAXIES—FIRST RESULTS FROM A<i>HERSCHEL</i>/PACS STUDY OF THE GOALS SAMPLE

&lt;p&gt;\n\tWe present the first results of a survey of the [C II]157.7 {$μ$}m emission line in 241 luminous infrared galaxies (LIRGs) comprising the Great Observatories All-sky LIRG Survey (GOALS) sample, obtained with the PACS instrument on board the Herschel Space Observatory. The [C II] luminosities, L $_{[C II]}$, of the LIRGs in GOALS range from ~{}10$^{7}$ to 2 {\times} 10$^{9}$ L $_{⊙}$. We find that LIRGs show a tight correlation of [C II]/FIR with far-IR (FIR) 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 [C II]/FIR ratio and the strength of the 9.7 {$μ$}m 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 [C II]/FIR ratios. Pure star-forming LIRGs have a mean [C II]/FIR ~{} 4 {\times} 10$^{-3}$, while galaxies with low polycyclic aromatic hydrocarbon (PAH) equivalent widths (EWs), indicative of the presence of active galactic nuclei (AGNs), span the full range in [C II]/FIR. However, we show that even when only pure star-forming galaxies are considered, the [C II]/FIR ratio still drops by an order of magnitude, from 10$^{-2}$ to 10$^{-3}$, with {$Sigma$}$_{MIR}$ and {$Sigma$}$_{IR}$, implying that the [C II]157.7 {$μ$}m luminosity is not a good indicator of the star formation rate (SFR) for most local LIRGs, for it does not scale linearly with the warm dust emission most likely associated to the youngest stars. Moreover, even in LIRGs in which we detect an AGN in the mid-IR, the majority (2/3) of galaxies show [C II]/FIR {gt}= 10$^{-3}$ typical of high 6.2 {$μ$}m PAH EW sources, suggesting that most AGNs do not contribute significantly to the FIR emission. We provide an empirical relation between the [C II]/FIR and the specific SFR for star-forming LIRGs. Finally, we present predictions for the starburst size based on the observed [C II] and FIR luminosities which should be useful for comparing with results from future surveys of high-redshift galaxies with ALMA and CCAT.&lt;/p&gt;