SIMBAD references

We present a comprehensive study of the star-forming main sequence (SFMS) and its scatter at redshifts $3 \le z \le 9$, using Near Infrared Camera (NIRCam) photometry from the JADES (JWST Advanced Deep Extragalactic Survey) survey in the Great Observatories Origins Deep Survey (GOODS) South (GOODS-S) and North (GOODS-N) fields. Our analysis is based on a sample of galaxies that is stellar mass complete down to $\log \left(M_{\star }/{\rm M}_{\odot }\right) \approx 8.1$. The redshift evolution of the SFMS at an averaging time-scale of 10 Myr follows a relation, quantified by the specific star formation rates (sSFR$_{10}$), of $\mathrm{sSFR}\propto (1+z)^{\mu }$ with $\mu = 2.30^{+0.03}_{-0.01}$, in good agreement with theoretical predictions and the specific mass accretion rate of dark matter haloes. We find that the SFMS normalization varies in a complex way with the SFR averaging time-scale, reflecting the combined effects of bursty star formation and rising star formation histories (SFHs). We quantify the scatter of the SFMS, revealing that it decreases with longer SFR averaging time-scales, from $\sigma _{\rm {int}} \approx 0.4-0.5~\mathrm{dex}$ at 10 Myr to $\sigma _{\rm {int}} \approx 0.2~\mathrm{dex}$ at 100 Myr, indicating that shorter term fluctuations dominate the scatter, although long-term variations in star formation activity are also present. Our findings suggest that bursty SFHs are more pronounced at lower stellar masses. Furthermore, we explore the implications of our results for the observed overabundance of UV-bright galaxies at $z > 10$, concluding that additional mechanisms, such as top-heavy initial mass functions, increased star formation efficiencies, or increased burstiness in star formation are needed to explain these observations. Finally, we emphasize the importance of accurate stellar mass completeness limits when fitting the SFMS, especially for galaxies with bursty SFHs.