The star-forming main sequence and the contribution of dust-obscured star formation since $z\sim 4$ from the FUV+IR luminosity functions

An analytical approach is proposed to study the evolution of the star-forming galaxy (SFG) main sequence (MS) and the fraction of dust-obscured SF up to $z\sim 4$. Far-ultraviolet (FUV) and infrared (IR) star formation rates, SFRs, are described as conditional probability functions of $M_{\ast }$. We convolve them with the galaxy stellar mass function (GSMF) of SFGs to derive the FUV and IR LFs. The 2 SF modes formalism is used to describe starburst galaxies. By fitting observed FUV and IR LFs, the parametrization of SFR${\rm FUV}-M{\ast}$andSFR${\rm IR}-M{\ast}$ are constrained. Our derived SFR${}_{\mathrm{F}\mathrm{U}\mathrm{V}+\mathrm{I}\mathrm{R}}-M_{\ast }$ reproduces the evolution of the MS as compared to other observational inferences. At any redshift, we find that the sSFR${\rm FUV+IR}-M{\ast}$ relation for MS SFGs approaches to a power law at the high-mass end. At lower masses, it bends and eventually the slope sign changes from negative to positive at very low masses. At $z\sim 0$, this change of sign is at $M_{\ast }\sim 5\times {10}^8{\mathrm{M}}_{\odot }$ close to dust-obscured SF regime, $M_{\ast }\sim 6\times {10}^8{\mathrm{M}}_{\odot }$. The slope sign change is related to the knee of the FUV LF. Our derived dust-obscured fractions agree with previous determinations at $0\le z\le 2.5$. Dust-obscured fractions depend strongly on mass with almost no dependence with redshift at $z\gtrsim 1.2$. At $z\lesssim 0.75$ high-mass galaxies become more “transparent” compared to their high redshift counterparts. On the opposite, low- and intermediate-mass galaxies have become more obscured by dust. The joint evolution of the GSMF and the FUV and IR LFs is a promising approach to study mass growth and dust formation/destruction mechanisms.