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We present the deepest far-IR observations obtained with Herschel and examinethe 3-500um SEDs of galaxies at 0<z<2.5, supplemented by a local referencesample from IRAS, ISO, Spitzer and AKARI data. We find that the ratio of totalIR luminosity to rest-frame 8um luminosity, IR8 (=Lir/L8), follows a Gaussiandistribution centered on IR8=4 and defines an IR main sequence (MS). A minoritypopulation (<20 %) of outliers producing a tail skewed toward higher values ofIR8 consist of starbursts (SB) with compact projected star formation densities.IR8 can be used to separate galaxies with normal and extended modes of starformation from compact SBs with high-IR8, high projected IR surface brightness(>3x10^10 Lsun kpc^-2) and a high specific SFR (i.e., SBs). The rest-frame,UV-2700A size of these distant SBs is typically half that of MS galaxies,supporting the correlation between star formation density and SB activity thatis measured for the local sample. Locally, (U)LIRGs are systematically in theSB mode, whereas most distant (U)LIRGs form stars in the "normal" MS mode. Thisconfusion between two modes of star formation is the cause of the so-called"mid-IR excess" population of galaxies found at z>1.5 by previous studies. MSgalaxies have strong PAH emission line features, a broad far-IR bump resultingfrom a combination of dust temperatures (Tdust~15-50 K), and an effectiveTdust~31 K, as derived from the peak wavelength of their IR SED. Galaxies inthe SB regime instead exhibit weak PAH EW and a sharper far-IR bump with aneffective Tdust~40 K. Finally, we present evidence that the mid-to-far IRemission of X-ray AGNs is predominantly produced by star formation and thatcandidate dusty AGNs with a power-law emission in the mid-IR systematicallyoccur in compact, dusty SBs. After correcting for the effect of SBs on IR8, weidentify new candidates for extremely obscured AGNs.

GOODS-Herschel: an infrared main sequence for star-forming galaxies