color criterion have a sSFR$>10^{-11}$yr$^{-1}$ according to the SED fitting of the optical/near-IR data [@Ilbert2013 their Fig.3]. However, the sSFRs obtained by SED fitting are highly uncertain, because of the degeneracies with the dust attenuation. These peculiar objects are at least 10 times less numerous than the color-selected star-forming sample in all redshift bins. Including them or not in the sample has a negligible impact ($\sim0.25$$\sigma$) on the mean SEDs measured by stacking (see Sect.\[stackfit\]). We thus based our study only on the color-selected population for simplicity.\

*Spitzer*/MIPS data
-------------------

The COSMOS field (2 deg$^2$) was observed by *Spitzer* at 24$\mu$m with the multiband imaging photometer (MIPS). A map and a catalog combined with the optical and near-IR data was produced from these observations [@Le_Floch2009]. The 1$\sigma$ point source sensitivity is $\sim$15$\mu$Jy and the full width at half maximum (FWHM) of the point spread function (PSF) is $\sim$6".\

*Herschel*/PACS data
--------------------

The PACS (photodetecting array camera and spectrometer, @Poglitsch2010) evolutionary probe survey (PEP, @Lutz2011) mapped the COSMOS field with the *Herschel*[^1] space observatory [@Pilbratt2010] at 100 and 160$\mu$m with a point-source sensitivity of 1.5 mJy and 3.3 mJy and a PSF FWHM of 7.7“ and 12”, respectively. Sources and fluxes 