We explore star-formation histories ( SFHs ) of galaxies based on the evolution of the star-formation rate stellar mass relation ( SFR - M _ { * } ) .
Using data from the FourStar Galaxy Evolution Survey ( ZFOURGE ) in combination with far-IR imaging from the Spitzer and Herschel observatories we measure the SFR - M _ { * } relation at 0.5 < z < 4 .
Similar to recent works we find that the average infrared SEDs of galaxies are roughly consistent with a single infrared template across a broad range of redshifts and stellar masses , with evidence for only weak deviations .
We find that the SFR - M _ { * } relation is not consistent with a single power-law of the form \mathrm { SFR } \propto M _ { * } ^ { \alpha } at any redshift ; it has a power-law slope of \alpha \sim 1 at low masses , and becomes shallower above a turnover mass ( M _ { 0 } ) that ranges from 10 ^ { 9.5 } - 10 ^ { 10.8 } M _ { \odot } , with evidence that M _ { 0 } increases with redshift .
We compare our measurements to results from state-of-the-art cosmological simulations , and find general agreement in the slope of the SFR - M _ { * } relation albeit with systematic offsets .
We use the evolving SFR - M _ { * } sequence to generate SFHs , finding that typical SFRs of individual galaxies rise at early times and decline after reaching a peak .
This peak occurs earlier for more massive galaxies .
We integrate these SFHs to generate mass-growth histories and compare to the implied mass-growth from the evolution of the stellar mass function .
We find that these two estimates are in broad qualitative agreement , but that there is room for improvement at a more detailed level .
At early times the SFHs suggest mass-growth rates that are as much as 10 \times higher than inferred from the stellar mass function .
However , at later times the SFHs under-predict the inferred evolution , as is expected in the case of additional growth due to mergers .