Distant star-forming galaxies show a correlation between their star formation rates ( SFR ) and stellar masses , and this has deep implications for galaxy formation .
Here , we present a study on the evolution of the slope and scatter of the SFR–stellar mass relation for galaxies at 3.5 \leq z \leq 6.5 using multi-wavelength photometry in GOODS-S from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey ( CANDELS ) and Spitzer Extended Deep Survey .
We describe an updated , Bayesian spectral-energy distribution fitting method that incorporates effects of nebular line emission , star formation histories that are constant or rising with time , and different dust attenuation prescriptions ( starburst and Small Magellanic Cloud ) .
From z =6.5 to z =3.5 star-forming galaxies in CANDELS follow a nearly unevolving correlation between stellar mass and SFR that follows SFR \sim M _ { \star } ^ { a } with a = 0.54 \pm 0.16 at z \sim 6 and 0.70 \pm 0.21 at z \sim 4 .
This evolution requires a star formation history that increases with decreasing redshift ( on average , the SFRs of individual galaxies rise with time ) .
The observed scatter in the SFR–stellar mass relation is tight , \sigma ( \log \mathrm { SFR } / \mathrm { M } _ { \odot } yr ^ { -1 } ) < 0.3 - 0.4 dex , for galaxies with \log M _ { \star } / \mathrm { M } _ { \odot } > 9 dex .
Assuming that the SFR is tied to the net gas inflow rate ( SFR \sim \dot { M } _ { \mathrm { gas } } ) , then the scatter in the gas inflow rate is also smaller than 0.3 - 0.4 dex for star-forming galaxies in these stellar mass and redshift ranges , at least when averaged over the timescale of star formation .
We further show that the implied star formation history of objects selected on the basis of their co-moving number densities is consistent with the evolution in the SFR–stellar mass relation .