The Star-forming Main Sequence and the Contribution of Dust-obscured Star Formation since z ∼ 4 from the Far-UV+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 star formation (SF) up to z ∼ 4. Far-ultraviolet (FUV) and infrared (IR) star formation rates (SFRs) are described as conditional probability functions of M_*. We convolve them with the galaxy stellar mass function (GSMF) of SFGs to derive the FUV and IR luminosity functions (LFs). The two SF modes formalism is used to describe starburst galaxies. By fitting observed FUV and IR LFs, the parameterization of SFR_FUV-M_* and SFR_IR- M_* is constrained. Our derived SFR_FUV+IR-M_* reproduces the evolution of the MS as compared to other observational inferences. At any redshift, we find that the sSFR_FUV+IR-M_* relation for MS SFGs approaches 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 ∼ 0, this change of sign is at M_* ∼ 5 × 10⁸ M_⊙, close to the dust-obscured SF regime, M_* ∼ 6 × 10⁸ M_⊙. The slope sign change is related to the knee of the FUV LF. Our derived dust-obscured fractions agree with previous determinations at 0 ≤ z ≤ 2.5. Dust-obscured fractions depend strongly on mass with almost no dependence on redshift at z ≳ 1.2. At z ≲ 0.75, high-mass galaxies become more "transparent" compared to their high-redshift counterparts. On the other hand, 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.