  Herschel/PACS observations of 29 local (Ultra-)Luminous Infrared Galaxies,
including both starburst and AGN-dominated sources as diagnosed in the
mid-infrared/optical, show that the equivalent width of the absorbing OH 65 um
Pi_{3/2} J=9/2-7/2 line (W_{eq}(OH65)) with lower level energy E_{low}~300 K,
is anticorrelated with the [C ii]158 um line to far-infrared luminosity ratio,
and correlated with the far-infrared luminosity per unit gas mass and with the
60-to-100 um far-infrared color. While all sources are in the active
L_{IR}/M_{H2}>50 Lsun/Msun mode as derived from previous CO line studies, the
OH65 absorption shows a bimodal distribution with a discontinuity at
L_{FIR}/M_{H2}~100 Lsun/Msun. In the most buried sources, OH65 probes material
partially responsible for the silicate 9.7 um absorption. Combined with
observations of the OH 71 um Pi_{1/2} J=7/2-5/2 doublet (E_{low}~415 K),
radiative transfer models characterized by the equivalent dust temperature,
Tdust, and the continuum optical depth at 100 um, tau_{100}, indicate that
strong [C ii]158 um deficits are associated with far-IR thick (tau_{100}>~0.7,
N_{H}>~10^{24} cm^{-2}), warm (Tdust>~60 K) structures where the OH 65 um
absorption is produced, most likely in circumnuclear disks/tori/cocoons. With
their high L_{FIR}/M_{H2} ratios and columns, the presence of these structures
is expected to give rise to strong [C ii] deficits. W_{eq}(OH65) probes the
fraction of infrared luminosity arising from these compact/warm environments,
which is >~30-50% in sources with high W_{eq}({OH65}). Sources with high
W_{eq}({OH65}) have surface densities of both L_{IR} and M_{H2} higher than
inferred from the half-light (CO or UV/optical) radius, tracing coherent
structures that represent the most buried/active stage of (circum)nuclear
starburst-AGN co-evolution.
