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Dust correction factors over $0 < z < 3$ in massive star-forming galaxies from stacking in \emph{Herschel}

In this work we use stacking analysis in \emph{Herschel} PACS to study the accuracy of several dust-correction factors typically employed to estimate total star-formation rate (SFR) of high-redshift star-forming (SF) galaxies. We also analyze what stacking suggests about the relation between SFR and stellar mass and the redshift evolution of the specific SFR (${\rm sSFR} = {\rm SFR} / {\rm M_*}$). We find that the dust properties of massive SF galaxies evolve with redshift, being galaxies at $z \sim 2-3$ more attenuated than at $z \sim 1$ for a given UV continuum slope and stellar mass. As a consequence, a single IRX-$β$ relation can not be used to recover the total SFR of massive SF galaxies at $0 \lesssim z \lesssim 3$. This might have implications for higher redshift studies, where a single IRX-$β$ relation derived for local starburst is usually assumed to be valid. However, we find that the local relation between dust attenuation and stellar mass is valid at least up to $z \sim 1$, although deviations are found for higher redshift galaxies where only $\log{\left( M_* / M_\odot \right)} > 10.25-10.50$ galaxies are detected through stacking. This, therefore, does not rule out the possibility that the local dust-mass relation can be valid for less massive SF galaxies at $z \sim 2-3$. The SED fitting procedure with stellar population templates gives over-estimated values (about 0.3--0.5 dex in $\log{\rm SFR}$) of the dust-corrected SFR at all redshifts studied here. We find that the slope of the main-sequence of star formation is less steep than previously found in massive galaxies with $\log{\left( M_* / M_\odot \right)} \geq 10$, and the redshift evolution of the sSFR reported in previous works in massive is well recovered.