We present the deepest 100 to 500 \mu m far-infrared observations obtained with the Herschel Space Observatory as part of the GOODS– Herschel key program , and examine the infrared ( IR ) 3–500 \mu m spectral energy distributions ( SEDs ) of galaxies at 0 < z < 2.5 , supplemented by a local reference sample from IRAS , ISO , Spitzer and AKARI data .
We determine the projected star formation densities of local galaxies from their radio and mid-IR continuum sizes .

We find that the ratio of total IR luminosity to rest-frame 8 \mu m luminosity , IR 8 ( \equiv L _ { IR } ^ { tot } / L _ { 8 } ) , follows a Gaussian distribution centered on IR 8 =4 ( \sigma =1.6 ) and defines an IR main sequence for star-forming galaxies independent of redshift and luminosity .
Outliers from this main sequence produce a tail skewed toward higher values of IR 8 .
This minority population ( < 20 % ) is shown to consist of starbursts with compact projected star formation densities . IR 8 can be used to separate galaxies with normal and extended modes of star formation from compact starbursts with high– IR 8 , high projected IR surface brightness ( \Sigma _ { IR } > 3 \times 10 ^ { 10 } L _ { \odot } kpc ^ { -2 } ) and a high specific star formation rate ( i.e. , starbursts ) .
The rest-frame , UV-2700 Ã Â size of these distant starbursts is typically half that of main sequence galaxies , supporting the correlation between star formation density and starburst activity that is measured for the local sample .

Locally , luminous and ultraluminous IR galaxies , ( U ) LIRGs ( L _ { IR } ^ { tot } \geq 10 ^ { 11 } L _ { \odot } ) , are systematically in the starburst mode , whereas most distant ( U ) LIRGs form stars in the “ normal ” main sequence mode .
This confusion 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 .
Main sequence galaxies have strong polycyclic aromatic hydrocarbon ( PAH ) emission line features , a broad far-IR bump resulting from a combination of dust temperatures ( T _ { dust } \sim 15 – 50 K ) , and an effective T _ { dust } \sim 31 K , as derived from the peak wavelength of their infrared SED .
Galaxies in the starburst regime instead exhibit weak PAH equivalent widths and a sharper far-IR bump with an effective T _ { dust } \sim 40 K. Finally , we present evidence that the mid-to-far IR emission of X-ray active galactic nuclei ( AGN ) is predominantly produced by star formation and that candidate dusty AGNs with a power-law emission in the mid-IR systematically occur in compact , dusty starbursts .
After correcting for the effect of starbursts on IR 8 , we identify new candidates for extremely obscured AGNs .