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# The relation between star formation rate and stellar mass of galaxies at z $$\sim$$ 1-4

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### Abstract

The relation between the Star Formation Rate (SFR) and stellar mass ($${\rm M}_{\star}$$) of galaxies represents a fundamental constraint on galaxy formation. 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 or that observations contain biases. In this paper, we examine the evolution of the SFR$$-{\rm M}_{\star}$$ relation of $$z\sim 1-4$$ galaxies and display the inconsistency between observed relations that are obtained using different techniques. We employ cosmological hydrodynamic simulations from various groups and compare these with a range of observations. The comparison suggests that using Spectral Energy Distributions (SEDs) to estimate star formation rates, dust corrections and stellar masses produces the most reliable SFR$$-{\rm M}_{\star}$$ relations. On the contrary, the combination of IR and UV luminosities (UV+IR) overpredicts the SFR and dust corrections at a fixed stellar mass almost by a factor of 5 for $$z \sim 1.5-4$$. For $$z < 1.5$$, the SED fitting technique and IR+UV conversion agree well. 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 ISM models and are tuned to reproduce statistical properties of galaxies, produce similar results for the SFR$$-{\rm M}_{\star}$$ relation by construction, regardless of resolution, box size and, to some extent, the adopted feedback prescriptions.

### Author and article information

###### Journal
1508.01615

Galaxy astrophysics