The relation between the star-formation Rate and stellar mass (M⋆) of galaxies represents a fundamental constraint on galaxy formation, and has been studied extensively both in observations and cosmological hydrodynamic simulations. However, the observed amplitude of the star-formation rate—stellar mass relation has not been successfully reproduced in simulations, indicating either that the halo accretion history and baryonic physics are poorly understood/modelled or that observations contain biases. In this paper, we examine the evolution of the SFR − M⋆ relation of z ~ 1–4 galaxies and display the inconsistency between observed relations that are obtained using different techniques. We employ cosmological hydrodynamic simulations from various groups which are tuned to reproduce a range of observables and compare these with a range of observed SFR − M⋆ relations. We find that numerical results are consistent with observations that use Spectral Energy Distribution techniques to estimate star-formation rates, dust corrections, and stellar masses. On the contrary, simulations are not able to reproduce results that were obtained by combining only UV and IR luminosities (UV+IR). These imply star-formation rates at a fixed stellar mass that are larger almost by a factor of 5 than those of Spectral Energy Distribution measurements for z ~ 1.5–4. For z < 1.5, the results from simulations, Spectral Energy Distribution fitting techniques and IR+UV conversion agree well. We find that surveys that preferably select star-forming galaxies (e.g. by adopting Lyman-break or blue selection) typically predict a larger median/average star-formation rate at a fixed stellar mass especially for high mass objects, with respect to mass selected samples and hydrodynamic simulations. Furthermore, we find remarkable agreement between the numerical results from various authors who have employed different cosmological codes and run simulations with different resolutions. This is interesting for two reasons. (A) simulations can produce realistic populations of galaxies within representative cosmological volumes even at relatively modest resolutions. (B) It is likely that current numerical codes that rely on similar subgrid multiphase interstellar medium models and are tuned to reproduce statistical properties of galaxies, produce similar results for the SFR − M⋆ relation by construction, regardless of resolution, box size and, to some extent, the adopted feedback prescriptions.
