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We provide a coherent, uniform measurement of the evolution of the logarithmic star formation rate (SFR)-stellar mass (M-*) relation, called the main sequence (MS) of star-forming galaxies, for star-forming and all galaxies out to z similar to 5. We measure the MS using mean stacks of 3 GHz radio-continuum images to derive average SFRs for similar to 200,000 mass-selected galaxies at z > 0.3 in the COSMOS field. We describe the MS relation by adopting a new model that incorporates a linear relation at low stellar mass (log(M-*/M-circle dot)

There is a severe tension between the observed star formation rate (SFR) - stellar mass (${\rm M}_{\star}$) relations reported by different authors at $z = 1-4$. In addition, the observations have not been successfully reproduced by state-of-the-art cosmological simulations which tend to predict a factor of 2-4 smaller SFRs at a fixed ${\rm M}_{\star}$. We examine the evolution of the SFR$-{\rm M}_{\star}$ relation of $z = 1-4 $ galaxies using the SKIRT simulated spectral energy distributions of galaxies sampled from the EAGLE simulations. We derive SFRs and stellar masses by mimicking different observational techniques. We find that the tension between observed and simulated SFR$-{\rm M}_{\star}$ relations is largely alleviated if similar methods are used to infer the galaxy properties. We find that relations relying on infrared wavelengths (e.g. 24 ${\rm \mu m}$, MIPS - 24, 70 and 160 ${\rm \mu m}$ or SPIRE - 250, 350, 500 ${\rm \mu m}$) have SFRs that exceed the intrinsic relation by 0.5 dex. Relations that rely on the spectral energy distribution fitting technique underpredict the SFRs at a fixed stellar mass by -0.5 dex at $z \sim 4$ but overpredict the measurements by 0.3 dex at $z \sim 1$. Relations relying on dust-corrected rest-frame UV luminosities, are flatter since they overpredict/underpredict SFRs for low/high star forming objects and yield deviations from the intrinsic relation from 0.10 dex to -0.13 dex at $z \sim 4$. We suggest that the severe tension between different observational studies can be broadly explained by the fact that different groups employ different techniques to infer their SFRs., Comment: 15 pages, 6 Figures, 4 tables, accepted for publication in MNRAS, Figures 1, 2, 3, 4 summarize results

The scatter (${\rm\sigma_{\text{sSFR}}}$) of the specific star formation rates (sSFRs) of galaxies is a measure of the diversity in their star formation histories (SFHs) at a given mass. In this paper we employ the EAGLE simulations to study the dependence of the ${\rm \sigma_{\text{sSFR}}}$ of galaxies on stellar mass (${\rm M_{\star}}$) through the ${\rm \sigma_{\text{sSFR}}}$-${\rm M_{\star}}$ relation in $ {\rm z \sim 0-4}$. We find that the relation evolves with time, with the dispersion depending on both stellar mass and redshift. The models point to an evolving U-shape form for the ${\rm \sigma_{\text{sSFR}}}$-${\rm M_{\star}}$ relation with the scatter being minimal at a characteristic mass $M^{\star}$ of ${\rm 10^{9.5}}$ ${\rm M_{\odot}}$ and increasing both at lower and higher masses. This implication is that the diversity of SFHs increases towards both at the low- and high-mass ends. We find that active galactic nuclei feedback is important for increasing the ${\rm \sigma_{\text{sSFR}}}$ for high mass objects. On the other hand, we suggest that SNe feedback increases the ${\rm \sigma_{\text{sSFR}}}$ of galaxies at the low-mass end. We also find that excluding galaxies that have experienced recent mergers does not significantly affect the ${\rm \sigma_{\text{sSFR}}}$-${\rm M_{\star}}$ relation. Furthermore, we employ the combination of the EAGLE simulations with the radiative transfer code SKIRT to evaluate the effect of SFR/stellar mass diagnostics in the ${\rm \sigma_{\text{sSFR}}}$-${\rm M_{\star}}$ relation and find that the ${\rm SFR/M_{\star}}$ methodologies (e.g. SED fitting, UV+IR, UV+IRX-$\beta$) widely used in the literature to obtain intrinsic properties of galaxies have a large effect on the derived shape and normalization of the ${\rm \sigma_{\text{sSFR}}}$-${\rm M_{\star}}$ relation.