| Summary: | Understanding the physical processes that drive star formation is a key challenge for galaxy formation models. In this paper, we study the tight correlation between the star formation rate (SFR) and stellar mass of galaxies at a given redshift, how halo growth influences star formation, and star formation histories of individual galaxies. We study these topics using Illustris, a state-of-the-art cosmological hydrodynamical simulation of galaxy formation. Illustris reproduces the observed relation (the star formation main sequence, SFMS) between SFR and stellar mass at redshifts z = 0 and 4, but at intermediate redshifts of z ≃ 1-2, the simulated SFMS has a significantly lower normalization than reported by observations. The scatter in the relation is consistent with the observed scatter. However, the fraction of outliers above the SFR-stellar mass relation in Illustris is less than that observed. Galaxies with halo masses of ~10[superscript 12]M[subscript ⊙] dominate the SFR density of the Universe, in agreement with the results of abundance matching. Furthermore, more-massive galaxies tend to form the bulk of their stars at high redshift, which indicates that 'downsizing' occurs in Illustris. We also studied the star formation histories of individual galaxies, including the use of a principal component analysis decomposition. We find that for fixed stellar mass, galaxies that form earlier have more-massive black holes at z = 0, indicating that star formation and black hole growth are tightly linked processes in Illustris. While many of the properties of normal star-forming galaxies are well reproduced in the Illustris simulation, forming a realistic population of starbursts will likely require higher resolution and probably a more sophisticated treatment of star formation and feedback from stars and black holes.
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