The Carina Nebula complex (CNC) represents one of the most massive star-forming regions in our Galaxy and shows strong feedback from the high massive stars. We use our Herschel FIR observations to study the properties of the clouds over the entire area of the CNC. The good angular resolution of the Herschel maps corresponds to physical scales of 0.1 - 0.4 pc, and allows us to analyze the small-scale structures of the clouds. The full extent of the CNC was mapped with PACS and SPIRE from 70 to 500 micron. We determine temperatures and column densities at each point in this maps by modeling the observed FIR SEDs. We also derive a map showing the strength of the UV field. We investigate the relation between the cloud properties and the spatial distribution of the high-mass stars, and compute total cloud masses for different density thresholds. Our Herschel maps resolve, for the first time, the small-scale structure of the dense clouds. Several particularly interesting regions, including the prominent pillars south of eta Car, are analyzed in detail. We compare the cloud masses derived from the Herschel data to previous mass estimates based on sub-mm and molecular line data. Our maps also reveal a peculiar wave-like pattern in the northern part of the Carina Nebula. Finally, we characterize two prominent cloud complexes at the periphery of our Herschel maps, which are probably molecular clouds in the Galactic background. We find that the density and temperature structure of the clouds in most parts of the CNC is dominated by the strong feedback from the numerous massive stars, rather than random turbulence. Comparing the cloud mass and the star formation rate derived for the CNC to other Galactic star forming regions suggests that the CNC is forming stars in an particularly efficient way. We suggest this to be a consequence of triggered star formation by radiative cloud compression.
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