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We investigate the star-formation rate (SFR) and stellar mass ($M_*$)relation of a star-forming (SF) galaxy sample in the XMM-LSS field to $z\sim3.0$ using the near-infrared data from the VISTA Deep ExtragalacticObservations (VIDEO) survey. Combining VIDEO with broad-band photometry, we usethe SED fitting algorithm CIGALE to derive SFRs and $M_*$ and have adapted itto account for the full photometric redshift PDF uncertainty. Applying a SFselection using the D4000 index, we find evidence for strong evolution in thenormalisation of the SFR-$M_*$ relation out to $z\sim 3$ and a roughly constantslope of (SFR $\propto M_*^{\alpha}$) $\alpha=0.69\pm0.02$ to $z\sim 1.7$. Wefind this increases close to unity toward $z\sim2.65$. Alternatively, if weapply a colour selection, we find a distinct turnover in the SFR-$M_*$ relationbetween $0.7\lesssim z\lesssim2.0$ at the high mass end, and suggest that thisis due to an increased contamination from passive galaxies. We find evolutionof the specific SFR $\propto(1+z)^{2.60}$ at $\log(M_*)\sim$10.5, out to$z\lesssim2.4$ with an observed flattening beyond $z\sim$ 2 with increasedstellar mass. Comparing to a range of simulations we find the analyticalscaling relation approaches, that invoke an equilibrium model, a good fit toour data, suggesting that a continual smooth accretion regulated by continualoutflows may be a key driver in the overall growth of SFGs.

The evolving relation between star-formation rate and stellar mass in the VIDEO Survey since $z=3$